# Using Machine Translation to Augment Multilingual Classification

Adam King
GumGum
<EMAIL_ADDRESS>
(May 6, 2024)

###### Abstract

An all-too-present bottleneck for text classification model development is the
need to annotate training data and this need is multiplied for multilingual
classifiers. Fortunately, contemporary machine translation models are both
easily accessible and have dependable translation quality, making it possible
to translate labeled training data from one language into another. Here, we
explore the effects of using machine translation to fine-tune a multilingual
model for a classification task across multiple languages. We also investigate
the benefits of using a novel technique, originally proposed in the field of
image captioning, to account for potential negative effects of tuning models
on translated data. We show that translated data are of sufficient quality to
tune multilingual classifiers and that this novel loss technique is able to
offer some improvement over models tuned without it.

##  1 Introduction

One of the most common uses of machine learning for natural language
processing (NLP) is the classification of text into one of multiple mutually-
inclusive or mutually-exclusive labels. Recently, generative LLMs, such as
PaLM [Chung et al., 2022] and ChatGPT [Ouyang et al., 2022] have shown
exciting and impressive capabilities to do zero- or few-shot prompting,
classify text given only a few examples for the task across a variety of
languages. Nevertheless, it is still the case that the highest performing and
most efficient means to classify text is the use of a bespoke classifier
trained with hundreds or thousands labeled examples [Pires et al., 2019],
particularly when the task requires a level of human-like subjectivity or
general reasoning ability [Kocoń et al., 2023, see discussion]. To this end,
finding or creating a corpus of labeled examples is a necessary step in the
creation of any classifier.

For high-resource languages like English, which have many existing labeled
corpora available and large populations of annotators on crowd-sourced workers
such as Amazon Mechanical Turk, the challenge of creating or finding training
and evaluation data can be costly, but not prohibitively so. Yet, for lower-
resourced languages which lack existing annotated corpora and have smaller or
even non-existent populations on these large annotation platforms, acquiring
the required training data can prove to be much more difficult. Moreover, if
the model is intended to be able to perform the same classification across
multiple languages, the time and effort required to annotate training data
becomes multiplicative. Fortunately, classification is not alone in the
applications of machine learning in NLP. Machine translation (MT) has seen
major improvements in recent years [Stahlberg, 2020], accelerated by the
adoption of the transformer architecture [Vaswani et al., 2017].

To date, several options for high quality machine translation currently exist,
between API services and open-source models. MT API services, such as Google
translate, have become nearly ubiquitous, provide high quality translations,
while still being relatively inexpensive. In fact, in one experiment,
translating data using Google translate into English and using existing
English-trained classifier models outperformed certain models trained on the
original language directly [Araujo et al., 2016]. In addition to MT API
services, several open-source translation models are easily available, such as
the multilingual M2M100 model [Fan et al., 2020], NLLB200 model [Team et al.,
2022] or the over 1400 models trained by the University of Helsinki [Tiedemann
and Thottingal, 2020], with many of these models have performance that
approaches or exceeds that of MT APIs [Stahlberg, 2020].

With this in mind, it may be the case that translating an existing, labeled
dataset with one of the aforementioned MT options is a feasible alternative to
creating a novel dataset directly in that language. This has several benefits.
Firstly, it avoids the problem of existing corpora or annotation options not
existing for the language in question. Secondly, it minimizes the data needed
for multilingual models and allows annotations for one language to serve
another. Here, we ask if it is possible to use MT to train a multilingual
model, given only original, annotated data for a single language.

Of course, the potential benefits of using MT to train a multilingual model
are still affected by the old machine learning adage: garbage in, garbage out.
Even the best translations, either human or machine, will lose some of the
information of the original language, which will inevitably lead to dropped
performance for a model trained on the translated examples. Fortunately, the
problem of training models using semantically similar but imperfect pairs of
data is not unique to the task at hand and there is a growing body of research
which may provide some benefit. In particular, image captioning is a task to
generate the ideal natural language text caption for an image and these
captioning models must learn to represent semantically related data from very
different modalities similarly, i.e., text and images [Li et al., 2021]. In
this way, image captioning is somewhat analogous to the task of training on
translated data, where we want to have semantically identical text from
different languages predicted to have the same labels. As a result, we ask in
addition whether some of the model training techniques used in image
captioning models can lead to improved performance for multilingual models
trained using MT data.

##  2 Related Work

This work is by no means the first to suggest the usage of machine translation
to create or augment datasets for lower resourced languages. Wei and Pal [Wei
and Pal, 2010] and Pan et al. [Pan et al., 2011] augmented Chinese language
corpora with annotated data translated from English to improve the performance
of a Chinese-language sentiment analysis model. On the other hand, Barriere
and Balahur [Barriere and Balahur, 2020] and Ghafoor et al. [Ghafoor et al.,
2021] used existing API translation services to translate annotated data from
English into lower-resourced languages and trained classifiers solely on these
translated data, finding that classifiers trained on translated data were
fairly accurate but did see drops in performance, likely due to the effects of
imperfect translations of the training data.

It should be noted that training a model from scratch is not the only means to
create an accurate classifier, particularly for lower-resourced languages.
Large multilingual transformer models such as m-BERT [Devlin et al., 2018],
xlm-RoBERTa [Conneau et al., 2019] or gpt-3 [Brown et al., 2020] have been
shown to have the ability to generalize from one language to the other, i.e.,
train in one language and improve test performance in another language, [Pires
et al., 2019], but benefits of this vary on the languages in question, with
languages that share closer genealogical origin or structural similarities
benefiting more from inter-language transfer. Regardless, training a model
with examples of a particular language dependably yields the best classifier
for new data in that language.

Nevertheless, to date there has been no investigation of how fine-tuning large
multilingual transformer models on translated data affects final performance
compared to simple interlanguage transfer. Moreover, previous work to train
models using translated data employed a naive approach, treating translated
data as if it were no different than original, untranslated data which
annotated itself. In this work, we investigate both how multilingual
transformer models trained on translated data perform compared to
interlanguage transfer and explore a means to mitigate imperfect translation
quality when creating these training datasets.

##  3 Image captioning and Image-Text Contrastive Loss

Image-text Contrastive (ITC) loss is a technique used when training multimodal
models to caption images with natural language descriptions [Li et al., 2021].
For example, BLIP [Li et al., 2022] is a image-captioning model that was
trained with a mix of human- and artificially-annotated images where ITC loss
was integral to the models ability to learn from noisy, artificially-annotated
data. ITC loss, then, has been shown to mitigate negative effects of both
noise and different modalities for multimodal models.

At an intuitional level, these captioning models decompose text and images
into a shared embedding space and ITC loss seeks to penalize cases where
related image-text pairs are dissimilar in this shared embedding space. In
other words, ITC looks seeks to bring semantically related items from
disparate modalities closer in a shared embedded space and has empirically
improved image-captioning models, with little impact on training time or
resources.

Training multilingual classification models with translated data bears a
similarity to captioning, though rather than have semantically related
examples from different modalities, there are semantically parallel data in
different languages. That being the case, we will be a slightly modified form
of ITC loss, namely original-translated contrastive (OTC) loss, to enforce
similarity within a batch between data from the original language and its
translated counterpart. Like ITC loss, OTC loss penalizes a transformer model
for dissimilar embedding representations for translated pairs. One way to
think of it is that this loss encourages the model to embed sentences with the
same meaning identically, regardless of language.

In detail, we implement OTC loss as follows. We begin by deriving a
probability of each original/translated pairing in a training minibatch,
$p^{o2t}$ and $p^{t2o}$, that is, which original examples pairs with which
translated example and vice versa.

$p^{o2t}_{m}=\frac{exp(s(O,T_{m})/\tau)}{\Sigma_{m}^{M}exp(s(O,T_{m})/\tau)}$
(1)
$p^{t2o}_{m}=\frac{exp(s(T,O_{m})/\tau)}{\Sigma_{m}^{M}exp(s(T,O_{m})/\tau)}$
(2)

Here, $s(T,O)$ is a similarity function between the original, untranslated
data and the translated examples in a minibatch. We compute $s(T,O)$ by first
extracting and normalizing the embedding for the initial [cls] token after the
final attention head of the encoder stack in m-BERT, computing a pairwise dot
product for all possible pairs of original and translated data and dividing by
$\tau$, which is a learnable parameter. We then apply the softmax function as
a way to represent the likelihood of each original/translated match. Ideally,
each correct original/translated pair will have the most similar embeddings,
resulting in a value close to 1 after softmax. As a final step, we compute the
cross-entropy between the result of the previous step and a target vector
which encodes the correct original/translated pairs, weighting this by a
hyperparameter, $\alpha_{otc}$. Following BLIP [Li et al., 2022], we set
$\alpha_{otc}=.4$ for all runs.

$\ell_{otc}=\alpha_{otc}*\frac{1}{2}\mathbb{E}_{(O,T)}[H(\textbf{y}^{o2t}(O),\textbf{p}^{o2t}(O)+\\\
H(\textbf{y}^{t2o}(T),\textbf{p}^{t2o}(T)]$ (3)

##  4 Experiments

###  4.1 Data

For these experiments, we use a multilingual dataset of Amazon product reviews
across 6 languages: English, Spanish, French, German, Chinese and Japanese
[Keung et al., 2020]. This dataset is comprised of over 1 million total
examples, split into a train and test partition. The reviews are equally
distributed across the six languages, as well as the total stars given to the
reviewed product (1-5) for both the train and test partition, i.e., each
number of stars comprises 20% of the examples for that language. This dataset
is particularly useful due to its size, number of available languages and
presence of an established training and test data split.

We began by translating each review from the training partition of the
original dataset into each of the other respective languages and assigned the
same star value to the review (see example 1), i.e., if a review was
originally in English and had star star, when translating it into French it
would also be labeled with one star. We did this translation once before
carrying out the rest of the experiment to ensure each classifier would be
trained on the same set of translations. To translate, we used a single
multilingual translation model, M2M100 [Fan et al., 2020]. We chose to use a
single multilingual translation model in order to mitigate any potential
differences from translation quality coming from different machine translation
architectures.

id | translated | language | text | stars
---|---|---|---|---
1 | 0 | en | My daughter really likes the backpack and … | 5
1 | 1 | es | Mi hija realmente le gusta el bolsillo y … | 5
… | … | … | … | …
2 | 0 | en | This product is BS, I washed my face with hot water … | 1
2 | 1 | fr | Ce produit est BS, je me suis lavé le visage à l’eau chaude … | 1
… | … | … | … | …
Figure 1: Example original and translated data. Each unique review (id) in the
original dataset was translated to the other languages and assigned the same
star value. Texts truncated here for formatting.

###  4.2 Experiment design

To investigate any potential improvement in classifier accuracy with the use
OTC loss, we fine-tuned pretrained transformer models on datasets that
included original, untranslated data for a single language111We restricted the
experimental conditions to only including a single language’s original data,
rather than use the full set of $6!=720$ possible permutations of language
combinations for the sake of efficiency and resources. and only translated
data for all others in the six language set. As an example, in one training
run, the model would be tuned on the original English training data and only
translated data for all other languages, which were translated from the set of
the original English data. We did this for all six languages in the original
set to ensure any results were not restricted to one language in the dataset.
Though the exact training examples varied for each model, we tested each on
the original testing split of the dataset, which was solely comprised of
original data, i.e., non-translated, for the six languages.

In each case, we tuned a multilingual DistilBERT model [Sanh et al., 2019], a
distilled version of the original multilingual m-BERT [Devlin et al., 2018],
to predict the number of stars on a review as a categorical classification
problem, using categorical cross-entropy loss and varying between using OTC
loss as an additional loss parameter between runs. We chose to use a distilled
variant of BERT due to the distilled variants increased speed of training,
while still maintaining 97% of overall language understanding of the original.

Because of the mechanics of OTC loss, each translated datum must have an
original match in the minibatch and each original must have at least one
translated variant. As such, we constructed minibatches during training such
that half the samples were always original, untranslated data and the other
half were a randomly selected translated example for each original datum. For
each original example, we randomly selected a translated example from the
other languages, meaning that the model saw an equal number of original and
translated examples during tuning overall, though it saw far fewer individual
examples of each translated language, i.e., roughly $\frac{1}{5}$. For
simplicity, we restricted our tests to a 1:1 original:translated ratio and we
used the same batch sampling method for runs without OTC loss, to make results
more easily comparable.

For each tuning run, we used a batch size of 32 (16 original and 16 translated
examples per batch)222For baseline conditions where there was no translated
data, mini-batching happened as normal with 32 examples original, untranslated
data per batch. and used the AdamW [Loshchilov and Hutter, 2017] optimizer
with a linear warm-up of 500 updates with a learning rate of 2e-5. All
training was done on g5.2xlarge AWS instances which contain NVIDIA A10G GPUs.
We tuned 3 separate tuning runs for each set of hyperparameters and report
their mean values in the next section.

##  5 Results

In these experiments, we asked two simple questions: 1) how feasible is it to
tune a multilingual transformer model on translated data and 2) does the
inclusion of OTC loss improve model performance for languages where only
translated training data was used.

In answer to the first, for each of the six languages in the original dataset,
models fine-tuned with translated data showed higher F1-micro
scores333F1-micro is an example-weighted version of the F1-score, which is the
harmonic mean or precision and recall. For more details on F1-score, see
[Jurafsky and Martin, 2008]. on the held-out test set, compared to models
trained with only original data for a single language (see Table 1). As was
expected from Pires et al. [Pires et al., 2019], even if a model was never
exposed to data for a language, original or translated, the final model did
have F1-micro greater than chance for that language (which would be 20% for a
balanced, 5-label problem), indicating there was interlingual knowledge
transfer happening within the model during training. Moreover, it appears that
there was more transfer between related, similar languages, compared to more
dissimilar languages; models trained with data for a European language showed
higher performance on other European languages, compared to Japanese or
Chinese. Nevertheless, for all languages, the use of translated data did show
a noticeable improvement (.02-.11), though for each language, models trained
with only translated data did underperform models trained with the full set of
origina, untranslated training examples for that language (.07-.12).

That said, it is clear that the use of translated training data does improve
model performance, even if the trained model only sees translated examples for
that language. It should also be noted that due to the batching and sampling
strategy used here, models trained with translated data saw far fewer examples
of each language where they only saw translated data. That is, because each
original review was paired with a single translated example out of five
possible translated, these models were exposed to roughly one fifth of the
data for translated languages and still saw a sizable boost in performance.

Language | F1-micro
---|---
| No data | Translated | Original
en | 0.407 | 0.481 | 0.554
fr | 0.379 | 0.468 | 0.544
de | 0.359 | 0.465 | 0.581
es | 0.376 | 0.474 | 0.55
ja | 0.307 | 0.396 | 0.543
zh | 0.352 | 0.372 | 0.458
Table 1: F1-micro for models trained with no samples for the specified
language (No data), with only translated samples (Translated) and with the
original training data for that language (Original). All languages saw a
sizeable boost to performance over their respective baselines when using
translated data (.02-.11) but all languages did perform markedly better when
given actual data for each language.

Moving on to the effect of OTC loss, Table 3 shows the mean F1-micro per
language in the testing set, for models fine-tuned using original data for the
specified language and translations for all other languages. For all
languages, models trained using OTC loss saw an improvement over models
trained without for all languages except Chinese, which showed a mixed set of
negligible differences or lowered performance. However, these values include
runs where the specific language was included as original, untranslated data.
When averaging across all runs where a language in the testing set was only
represented by translated data, OTC loss shows an improvement over models
trained without it for all languages. Table 2 shows the mean F1-micro for all
models trained where the specified language was not the original language.

Language | F1-micro
---|---
| No OTC | OTC
en | 0.479 | 0.483
fr | 0.464 | 0.472
de | 0.463 | 0.467
es | 0.472 | 0.476
ja | 0.393 | 0.399
zh | 0.368 | 0.376
Table 2: Comparison on final performance per language for models that only
included translated examples for the specified language. Though the gain was
less than .1, each language consistently performed better when trained with
OTC loss.

To ensure that the results here were in fact statistically significant, we fit
a linear mixed-effect model to predict final model F1-micro for a language,
given the hyperparameters of a particular tuning run. Mixed-effect models are
able to accurately evaluate the contribution of different fixed-effect
independent variables, e.g., whether OTC was used when training a particular
model, on dependent variables, e.g., the final accuracy of the trained model,
all the while being robust to expected random variance between trials, e.g.,
because of random initialization and batching, some deep learning models score
higher than others with identical hyperparameters (see Baayen et al. [Baayen
et al., 2008], Jaeger [Jaeger, 2008] for more).

This statistical model was fit to predict per-language test f1-micro, given a
random effect of each model run and three fixed effects: i) the tested
language, ii) the identity of the single original language and iii) whether
OTC loss was added. OTC was found to have a significant, positive effect
(coef=0.036, Std.Error=0.017, for all model details see 2), indicating that
even after taking into consideration differences between languages and random
variance for each multilingual model, the inclusion of OTC loss did yield an
improved final model F1-micro.

Orig. Training Language | OTC | en | fr | de | es | ja | zh
---|---|---|---|---|---|---|---
en | No OTC | 0.548 | 0.488 | 0.493 | 0.489 | 0.425 | 0.423
| OTC | 0.553 | 0.507 | 0.522 | 0.512 | 0.434 | 0.422
fr | No OTC | 0.504 | 0.539 | 0.504 | 0.493 | 0.424 | 0.426
| OTC | 0.512 | 0.539 | 0.517 | 0.511 | 0.428 | 0.412
de | No OTC | 0.514 | 0.495 | 0.577 | 0.495 | 0.436 | 0.427
| OTC | 0.524 | 0.506 | 0.581 | 0.506 | 0.449 | 0.425
es | No OTC | 0.506 | 0.497 | 0.500 | 0.544 | 0.433 | 0.419
| OTC | 0.523 | 0.510 | 0.518 | 0.548 | 0.441 | 0.413
ja | No OTC | 0.470 | 0.460 | 0.477 | 0.468 | 0.526 | 0.436
| OTC | 0.493 | 0.474 | 0.499 | 0.487 | 0.522 | 0.424
zh | No OTC | 0.486 | 0.439 | 0.441 | 0.444 | 0.398 | 0.482
| OTC | 0.488 | 0.467 | 0.473 | 0.472 | 0.421 | 0.503
Table 3: F1-micro results on untranslated test data. Each row shows the per-
language performance for models trained with original data for the specified
language and translated data for all other languages, using OTC loss and
without. Each cell shows the mean of 3 runs per condition. Bolded values show
a difference of .03 or greater.

##  6 Discussion and future directions

We investigated the feasibility of using translated text to fine-tune a
multilingual transformer model, as well as any potential gains by utilizing a
novel application of deep learning technique to improve performance. We found
that models trained using only translated data for a language do show a
noticeable improvement over baselines, though as expected, there was still a
performance drop from using original, untranslated data for that language. We
also found that slight further gains can be achieved by the use of OTC loss,
suggesting that training the model in such a way where it is sensitive to
potential data issues improves its ability to generalize.

Granted, this is a very open problem and results of using translated data to
tune a multilingual classifier will vary highly depending on the quality of MT
model used, architecture of the classifier being tuned and the type of
classification being modeled. Nevertheless, the results here are exciting for
multiple reasons. Firstly, as suggested by previous works [Shalunts et al.,
2016, as an example], MT is useful tool for language-specific dataset creation
when creating a dataset for that language directly may prove difficult. In
this case, we showed that m-BERT models tuned on translated examples showed
large gains over simple multilingual transfer during training. This is
particularly interesting given that for each translated language, the model
was only given a fraction of samples compared to the original language due to
the 1:1 ratio of original and translated data. A future direction for this
work may be to adjust this ratio or the number of languages in the dataset to
investigate how this affects model training. Secondly, the use of OTC loss was
shown to lead to a small, but robust boost to performance. This suggests that
methods of mitigating the natural effects of translation have a potential to
bridge the gap, so to speak, between models trained on translated data and on
datasets in the target language directly. Particularly relevant, Chinese,
which is linguistically dissimilar from the majority of languages in the set
used here, showed a mixed ability to benefit from training with other
languages, but a clearer improvement using OTC loss. This may suggest that OTC
loss is able to mitigate structural differences between languages and a future
direction for this may be to explore exactly how OTC loss affects individual
examples and how other noise-reduction techniques may lead to further gains in
model performance.

Putting this together, this is an indication that MT-augmented datasets stand
as a good first step for developing multilingual classification models. Given
that MT can quickly and efficiently expand an annotated dataset from one
language into another and that translated dataset is of sufficient quality to
improve over basic interlingual transfer, this technique has great potential
to expanding classification tasks to new languages quickly. In addition, OTC
loss may be able to slightly but significantly increase the quality of these
models with no additional data. All in all, we are confident that the use of
MT augmentation is an exciting and interesting topic for future exploration.

##  7 Acknowledgements

This work was carried out as a part of the R&D for GumGum’s Verity product.
Special thanks go to the members of the AI team (names, names, names) for
their suggestions and audience during brainstorming, development and analysis
of this project.

## References

  * [Araujo et al., 2016]  Araujo, Matheus, Julio Reis, Adriano Pereira, and Fabricio Benevenuto.  2016\.  An evaluation of machine translation for multilingual sentence-level sentiment analysis.  In Proceedings of the 31st annual ACM symposium on applied computing, pages 1140–1145.
  * [Baayen et al., 2008]  Baayen, R Harald, Douglas J Davidson, and Douglas M Bates.  2008\.  Mixed-effects modeling with crossed random effects for subjects and items.  Journal of memory and language, 59(4):390–412.
  * [Barriere and Balahur, 2020]  Barriere, Valentin and Alexandra Balahur.  2020\.  Improving sentiment analysis over non-english tweets using multilingual transformers and automatic translation for data-augmentation.  arXiv preprint arXiv:2010.03486.
  * [Brown et al., 2020]  Brown, Tom B., Benjamin Mann, Nick Ryder, Melanie Subbiah, Jared Kaplan, Prafulla Dhariwal, Arvind Neelakantan, Pranav Shyam, Girish Sastry, Amanda Askell, Sandhini Agarwal, Ariel Herbert-Voss, Gretchen Krueger, Tom Henighan, Rewon Child, Aditya Ramesh, Daniel M. Ziegler, Jeffrey Wu, Clemens Winter, Christopher Hesse, Mark Chen, Eric Sigler, Mateusz Litwin, Scott Gray, Benjamin Chess, Jack Clark, Christopher Berner, Sam McCandlish, Alec Radford, Ilya Sutskever, and Dario Amodei.  2020\.  Language models are few-shot learners.  CoRR, abs/2005.14165.
  * [Chung et al., 2022]  Chung, Hyung Won, Le Hou, Shayne Longpre, Barret Zoph, Yi Tay, William Fedus, Yunxuan Li, Xuezhi Wang, Mostafa Dehghani, Siddhartha Brahma, et al.  2022\.  Scaling instruction-finetuned language models.  arXiv preprint arXiv:2210.11416.
  * [Conneau et al., 2019]  Conneau, Alexis, Kartikay Khandelwal, Naman Goyal, Vishrav Chaudhary, Guillaume Wenzek, Francisco Guzmán, Edouard Grave, Myle Ott, Luke Zettlemoyer, and Veselin Stoyanov.  2019\.  Unsupervised cross-lingual representation learning at scale.  CoRR, abs/1911.02116.
  * [Devlin et al., 2018]  Devlin, Jacob, Ming-Wei Chang, Kenton Lee, and Kristina Toutanova.  2018\.  BERT: pre-training of deep bidirectional transformers for language understanding.  CoRR, abs/1810.04805.
  * [Fan et al., 2020]  Fan, Angela, Shruti Bhosale, Holger Schwenk, Zhiyi Ma, Ahmed El-Kishky, Siddharth Goyal, Mandeep Baines, Onur Celebi, Guillaume Wenzek, Vishrav Chaudhary, Naman Goyal, Tom Birch, Vitaliy Liptchinsky, Sergey Edunov, Edouard Grave, Michael Auli, and Armand Joulin.  2020\.  Beyond english-centric multilingual machine translation.  CoRR, abs/2010.11125.
  * [Ghafoor et al., 2021]  Ghafoor, Abdul, Ali Shariq Imran, Sher Muhammad Daudpota, Zenun Kastrati, Rakhi Batra, Mudasir Ahmad Wani, et al.  2021\.  The impact of translating resource-rich datasets to low-resource languages through multi-lingual text processing.  IEEE Access, 9:124478–124490.
  * [Jaeger, 2008]  Jaeger, T Florian.  2008\.  Categorical data analysis: Away from anovas (transformation or not) and towards logit mixed models.  Journal of memory and language, 59(4):434–446.
  * [Jurafsky and Martin, 2008]  Jurafsky, Daniel and James H Martin.  2008\.  Speech and language processing: An introduction to speech recognition, computational linguistics and natural language processing.  Upper Saddle River, NJ: Prentice Hall.
  * [Keung et al., 2020]  Keung, Phillip, Yichao Lu, György Szarvas, and Noah A. Smith.  2020\.  The multilingual amazon reviews corpus.  In Proceedings of the 2020 Conference on Empirical Methods in Natural Language Processing.
  * [Kocoń et al., 2023]  Kocoń, Jan, Igor Cichecki, Oliwier Kaszyca, Mateusz Kochanek, Dominika Szydło, Joanna Baran, Julita Bielaniewicz, Marcin Gruza, Arkadiusz Janz, Kamil Kanclerz, et al.  2023\.  Chatgpt: Jack of all trades, master of none.  Information Fusion, page 101861.
  * [Li et al., 2021]  Li, Junnan, Ramprasaath R. Selvaraju, Akhilesh Deepak Gotmare, Shafiq R. Joty, Caiming Xiong, and Steven C. H. Hoi.  2021\.  Align before fuse: Vision and language representation learning with momentum distillation.  CoRR, abs/2107.07651.
  * [Li et al., 2022]  Li, Junnan, Dongxu Li, Caiming Xiong, and Steven Hoi.  2022\.  Blip: Bootstrapping language-image pre-training for unified vision-language understanding and generation.
  * [Loshchilov and Hutter, 2017]  Loshchilov, Ilya and Frank Hutter.  2017\.  Fixing weight decay regularization in adam.  CoRR, abs/1711.05101.
  * [Ouyang et al., 2022]  Ouyang, Long, Jeffrey Wu, Xu Jiang, Diogo Almeida, Carroll Wainwright, Pamela Mishkin, Chong Zhang, Sandhini Agarwal, Katarina Slama, Alex Ray, et al.  2022\.  Training language models to follow instructions with human feedback.  Advances in Neural Information Processing Systems, 35:27730–27744.
  * [Pan et al., 2011]  Pan, Junfeng, Gui-Rong Xue, Yong Yu, and Yang Wang.  2011\.  Cross-lingual sentiment classification via bi-view non-negative matrix tri-factorization.  In Advances in Knowledge Discovery and Data Mining: 15th Pacific-Asia Conference, PAKDD 2011, Shenzhen, China, May 24-27, 2011, Proceedings, Part I 15, pages 289–300. Springer.
  * [Pires et al., 2019]  Pires, Telmo, Eva Schlinger, and Dan Garrette.  2019\.  How multilingual is multilingual bert?  CoRR, abs/1906.01502.
  * [Sanh et al., 2019]  Sanh, Victor, Lysandre Debut, Julien Chaumond, and Thomas Wolf.  2019\.  Distilbert, a distilled version of bert: smaller, faster, cheaper and lighter.  ArXiv, abs/1910.01108.
  * [Shalunts et al., 2016]  Shalunts, Gayane, Gerhard Backfried, and Nicolas Commeignes.  2016\.  The impact of machine translation on sentiment analysis.  Data Analytics, 63:51–56.
  * [Stahlberg, 2020]  Stahlberg, Felix.  2020\.  Neural machine translation: A review.  Journal of Artificial Intelligence Research, 69:343–418.
  * [Team et al., 2022]  Team, NLLB, Marta R. Costa-jussà, James Cross, Onur Çelebi, Maha Elbayad, Kenneth Heafield, Kevin Heffernan, Elahe Kalbassi, Janice Lam, Daniel Licht, Jean Maillard, Anna Sun, Skyler Wang, Guillaume Wenzek, Al Youngblood, Bapi Akula, Loic Barrault, Gabriel Mejia Gonzalez, Prangthip Hansanti, John Hoffman, Semarley Jarrett, Kaushik Ram Sadagopan, Dirk Rowe, Shannon Spruit, Chau Tran, Pierre Andrews, Necip Fazil Ayan, Shruti Bhosale, Sergey Edunov, Angela Fan, Cynthia Gao, Vedanuj Goswami, Francisco Guzmán, Philipp Koehn, Alexandre Mourachko, Christophe Ropers, Safiyyah Saleem, Holger Schwenk, and Jeff Wang.  2022\.  No language left behind: Scaling human-centered machine translation.
  * [Tiedemann and Thottingal, 2020]  Tiedemann, Jörg and Santhosh Thottingal.  2020\.  OPUS-MT – building open translation services for the world.  In Martins, André, Helena Moniz, Sara Fumega, Bruno Martins, Fernando Batista, Luisa Coheur, Carla Parra, Isabel Trancoso, Marco Turchi, Arianna Bisazza, Joss Moorkens, Ana Guerberof, Mary Nurminen, Lena Marg, and Mikel L. Forcada, editors, Proceedings of the 22nd Annual Conference of the European Association for Machine Translation, pages 479–480, Lisboa, Portugal, November. European Association for Machine Translation.
  * [Vaswani et al., 2017]  Vaswani, Ashish, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, Łukasz Kaiser, and Illia Polosukhin.  2017\.  Attention is all you need.  Advances in neural information processing systems, 30.
  * [Wei and Pal, 2010]  Wei, Bin and Christopher Pal.  2010\.  Cross lingual adaptation: an experiment on sentiment classifications.  In Proceedings of the ACL 2010 conference short papers, pages 258–262.

                  Mixed Linear Model Regression Results
    ==========================================================
    Model:              MixedLM  Dependent Variable:  test_acc
    No. Observations:   108      Method:              REML
    No. Groups:         18       Scale:               0.0038
    Min. group size:    6        Log-Likelihood:      111.7634
    Max. group size:    6        Converged:           Yes
    Mean group size:    6.0
    ----------------------------------------------------------
                           Coef.  Std.Err.   z    P>|z| [0.025 0.975]
    ----------------------------------------------------------
    Intercept              0.465    0.024 19.128 0.000  0.418  0.513
    otc[T.True]            0.036    0.017  2.105 0.035  0.002  0.069
    original_lang[T.en]   -0.020    0.028 -0.714 0.475 -0.074  0.035
    original_lang[T.es]   -0.012    0.028 -0.432 0.666 -0.066  0.042
    original_lang[T.fr]   -0.015    0.028 -0.555 0.579 -0.070  0.039
    original_lang[T.ja]   -0.030    0.028 -1.093 0.274 -0.085  0.024
    original_lang[T.zh]   -0.050    0.028 -1.801 0.072 -0.104  0.004
    test_lang[T.en]        0.016    0.020  0.762 0.446 -0.025  0.056
    test_lang[T.es]        0.003    0.020  0.130 0.897 -0.037  0.043
    test_lang[T.fr]       -0.000    0.020 -0.005 0.996 -0.040  0.040
    test_lang[T.ja]       -0.061    0.020 -2.972 0.003 -0.101 -0.021
    test_lang[T.zh]       -0.068    0.020 -3.336 0.001 -0.108 -0.028
    Group Var              0.001    0.009
    ==========================================================

Figure 2: Full model details for MLE model trained to predict F1-micro per
laguage. otc has a positive contribution to an increase F1-micro score, even
when controlling for variance between languages and model runs.


* Zhai . (20092) zhai2009roughZhai, LY., Khoo, LP. Zhong, ZW.  20092\.  A rough set based QFD approach to the management of imprecise design information in product development A rough set based qfd approach to the management of imprecise design information in product development. Advanced Engineering Informatics232222–228.
  * Q. Zhang . (2018) zhang2018surveyZhang, Q., Yang, LT., Chen, Z. Li, P.  2018\.  A survey on deep learning for big data A survey on deep learning for big data. Information Fusion42146–157.
  * X. Zhang . (2016) zhang2016dataZhang, X., Brown, HF. Shankar, A.  2016\.  Data-driven personas: Constructing archetypal users with clickstreams and user telemetry Data-driven personas: Constructing archetypal users with clickstreams and user telemetry. Proceedings of the 2016 CHI conference on human factors in computing systems Proceedings of the 2016 chi conference on human factors in computing systems ( 5350–5359).
  * Zhou, Alsaid . (2020) zhou2020driverZhou, F., Alsaid, A., Blommer, M., Curry, R., Swaminathan, R., Kochhar, D.Lei, B.  2020\.  Driver fatigue transition prediction in highly automated driving using physiological features Driver fatigue transition prediction in highly automated driving using physiological features. Expert Systems with Applications147113204.
  * Zhou, Ayoub . (2020) zhou2020machineZhou, F., Ayoub, J., Xu, Q. Jessie Yang, X.  2020\.  A machine learning approach to customer needs analysis for product ecosystems A machine learning approach to customer needs analysis for product ecosystems. Journal of Mechanical Design1421.
  * Zhou . (2013) zhou2013affectiveZhou, F., Ji, Y. Jiao, JR.  2013\.  Affective and cognitive design for mass personalization: status and prospect Affective and cognitive design for mass personalization: status and prospect. Journal of Intelligent Manufacturing2451047–1069.
  * Zhou, Ji Jiao (20141) zhou2014augmentedZhou, F., Ji, Y. Jiao, JR.  20141\.  Augmented affective-cognition for usability study of in-vehicle system user interface Augmented affective-cognition for usability study of in-vehicle system user interface. Journal of computing and information science in engineering142.
  * Zhou, Ji Jiao (20142) zhou2014prospectZhou, F., Ji, Y. Jiao, JR.  20142\.  Prospect-theoretic modeling of customer affective-cognitive decisions under uncertainty for user experience design Prospect-theoretic modeling of customer affective-cognitive decisions under uncertainty for user experience design. IEEE Transactions on Human-Machine Systems444468–483.
  * Zhou, Jiao, Chen Zhang (2010) zhou2010caseZhou, F., Jiao, JR., Chen, S. Zhang, D.  2010\.  A case-driven ambient intelligence system for elderly in-home assistance applications A case-driven ambient intelligence system for elderly in-home assistance applications. IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews)412179–189.
  * Zhou . (2015) zhou2015latentZhou, F., Jiao, JR. Linsey, JS.  2015\.  Latent customer needs elicitation by use case analogical reasoning from sentiment analysis of online product reviews Latent customer needs elicitation by use case analogical reasoning from sentiment analysis of online product reviews. Journal of Mechanical Design1377.
  * Zhou, Jiao, Schaefer Chen (2010) zhou2010hybridZhou, F., Jiao, JR., Schaefer, D. Chen, S.  2010\.  Hybrid association mining and refinement for affective mapping in emotional design Hybrid association mining and refinement for affective mapping in emotional design. Journal of Computing and Information Science in Engineering103.
  * Zhou, Jiao . (2011) zhou2011userZhou, F., Jiao, JR., Xu, Q. Takahashi, K.  2011\.  User experience modeling and simulation for product ecosystem design based on fuzzy reasoning Petri nets User experience modeling and simulation for product ecosystem design based on fuzzy reasoning petri nets. IEEE transactions on systems, man, and cybernetics-part A: Systems and humans421201–212.
  * Zhou, Kong . (2020) zhou2020fineZhou, F., Kong, S., Fowlkes, CC., Chen, T. Lei, B.  2020\.  Fine-grained facial expression analysis using dimensional emotion model Fine-grained facial expression analysis using dimensional emotion model. Neurocomputing.
  * Zhou . (2017) zhou2017affectiveZhou, F., Lei, B., Liu, Y. Jiao, JR.  2017\.  Affective parameter shaping in user experience prospect evaluation based on hierarchical Bayesian estimation Affective parameter shaping in user experience prospect evaluation based on hierarchical bayesian estimation. Expert Systems with Applications781–15.
  * Zhou, Qu . (2011) zhou2011affectZhou, F., Qu, X., Helander, MG. Jiao, JR.  2011\.  Affect prediction from physiological measures via visual stimuli Affect prediction from physiological measures via visual stimuli. International Journal of Human-Computer Studies6912801–819.
  * Zhou, Qu . (2014) zhou2014emotionZhou, F., Qu, X., Jiao, J. Helander, MG.  2014\.  Emotion prediction from physiological signals: A comparison study between visual and auditory elicitors Emotion prediction from physiological signals: A comparison study between visual and auditory elicitors. Interacting with computers263285–302.
  * Zhou, Xu Jiao (2011) zhou2011fundamentalsZhou, F., Xu, Q. Jiao, JR.  2011\.  Fundamentals of product ecosystem design for user experience Fundamentals of product ecosystem design for user experience. Research in Engineering Design22143–61.
  * Zhou, Yang Zhang (2020) zhou2020takeoverZhou, F., Yang, XJ. Zhang, X.  2020\.  Takeover transition in autonomous vehicles: a YouTube study Takeover transition in autonomous vehicles: a youtube study. International Journal of Human–Computer Interaction363295–306.


myequation

$\BODY$

# CASPER: Carbon-Aware Scheduling and Provisioning for Distributed Web
Services

Abel Souza, Shruti Jasoria, Basundhara Chakrabarty, David Irwin, Prashant
Shenoy  University of Massachusetts AmherstUSA and  Alexander Bridgwater, Axel
Lundberg, Filip Skogh, Ahmed Ali-Eldin  Chalmers University of
TechnologySweden

(2023; Date: October 28–29, 2023)

###### Abstract.

There has been a significant societal push towards sustainable practices,
including in computing. Modern interactive workloads such as geo-distributed
web-services exhibit various spatiotemporal and performance flexibility,
enabling the possibility to adapt the location, time, and intensity of
processing to align with the availability of renewable and low-carbon energy.
An example is a web application hosted across multiple cloud regions, each
with varying carbon intensity based on their local electricity mix.
Distributed load-balancing enables the exploitation of low-carbon energy
through load migration across regions, reducing web applications carbon
footprint. In this paper, we present CASPER, a carbon-aware scheduling and
provisioning system that primarily minimizes the carbon footprint of
distributed web services while also respecting their Service Level Objectives
(SLO). We formulate CASPER as an multi-objective optimization problem that
considers both the variable carbon intensity and latency constraints of the
network. Our evaluation reveals the significant potential of CASPER in
achieving substantial reductions in carbon emissions. Compared to baseline
methods, CASPER demonstrates improvements of up to 70% with no latency
performance degradation.

††copyright: acmcopyright=false††journalyear: 2023††copyright:
acmlicensed††conference: THE 14th international Green and Sustainable
Computing Conference; October 28–29, 2023; Toronto, ON, Canada††booktitle: THE
14th international Green and Sustainable Computing Conference (IGSC ’23),
October 28–29, 2023, Toronto, ON, Canada††ccs: Computer systems organization
Cloud computing††ccs: Computer systems organization Special purpose systems

##  1\. Introduction

Figure 1. _Grid carbon intensity in 2022 across six distinct cloud regions
showing 6 $\times$ spatial variations._

In recent years, the global focus on sustainability and environmental
responsibility has brought renewable energy to the forefront of the
discussions on energy systems, leading to an increased focus on reducing the
carbon footprint of cloud platforms in both research and industry (Strubell et
al., 2020; Souza et al., 2023; Gupta et al., 2021, 2022; Wu et al., 2022).
Although there has been substantial progress in improving efficiency, today’s
datacenter infrastructures consume around three to five percent of electricity
worldwide and in ten years, five times as much (Cook and Pomerantz, 2015;
Jones, 2018; Garcia, 2022). These estimations may be lower than reality, as
the growth of computing demand has been increasing exponentially for decades
(Denning and Lewis, 2017). Cloud datacenters have mainly relied on
enhancements in energy efficiency, which is unlikely to lead to significant
reductions in carbon emissions as modern datacenters have already achieved
high levels of optimization in energy efficiency. For instance, the Power
Usage Effectiveness (PUE), a measurement of the total operational efficiency
of most datacenters, is already near the optimal value of $1.0$. More
importantly, thesse trends are positioning cloud platforms as one of the
largest contributors to global emissions (Denning and Lewis, 2017). Therefore,
while energy efficiency improvements are important, they will be insufficient
to counterbalance the rising energy consumption from the rapidly growing
demand for cloud services. To effectively reduce carbon emissions, cloud
platforms must shift their focus towards low-carbon energy sources. This
entails harnessing energy derived from renewable sources such as wind, solar,
hydro, nuclear, geothermal, and other sustainable alternatives.

To reduce cloud platforms’ carbon emissions, many have suggested leveraging
computing workloads’ spatial and temporal flexibility, which is often
significant, to dynamically shift the location and time of execution to better
align with when and where low-carbon energy is available. Yet, despite the
prominence of such simple carbon-aware spatiotemporal workload shifting as an
abstract idea, prior work has only quantified its benefits in specific
settings such as batch workloads. Web applications, in particular, serve as an
excellent case for exploring the untapped potential of carbon-aware computing.
These applications are typically distributed across multiple cloud servers
located in different regions worldwide. Traditional approaches reduce latency
by forwarding user requests to the geographically closest replica server,
reducing load times and offering a better user experience. On the other hand,
different cloud regions have varying carbon costs associated with their
electricity sources, leading to different carbon footprints for user requests
depending on which replica server services them. Consequently, optimizing the
scheduling of user requests with respect to the carbon costs associated with
different replicas presents an intriguing opportunity to make web applications
more sustainable.

While renewable energy still continues to be unreliable due to its dependence
on natural factors, web applications can still benefit from it without
sacrificing performance. For instance, the inherent fault tolerance achieved
through replication and load-balancing mechanisms can safeguard web
applications against the intermittency and unpredictability of renewable
energy sources (Maji et al., 2023). By ensuring that replicas are spread
across diverse regions and backed by different energy sources, these
applications can maintain high availability while capitalizing on the
potential of cleaner energy. However, although cloud providers maintain the
information about the energy supply powering their servers, it is not readily
available at a software level to applications (Souza et al., 2023).
Consequently, resource provisioners and load balancers cannot leverage this
information to optimize the carbon efficiency of web workloads. Providing
these systems with more visibility into the carbon footprint across
datacenters enable the design of heuristics to provision resources and
schedule workloads towards replicas with low carbon intensities while
respecting applications Service Level Objectives (SLOs).

As such, we present CASPER, a carbon-aware scheduler and provisioner for
distributed web applications. We assume a setting where resource provisioning
and load balancing ought to happen in concert to minimize emissions while
meeting application SLO targets. This is formulated as a multi-objective
optimization problem, addressing both the carbon footprint resulting from
server provisioning and the latency caused by load balancing. We evaluate the
performance of spatial server provisioning and geo-distributed request
scheduling for distributed web applications by implementing CASPER as a
Kubernetes scheduler and submitting it to a real web workload. Our results
highlight CASPER’s significant potential in achieving considerable reductions
in carbon emissions while meeting all latency constrains. In comparison to
baseline methods, our approach demonstrates enhancements of up to 70% without
compromising latency performance. We release CASPER as an open-source tool
that can perform carbon optimizations for their distributed web applications:
https://github.com/carbonfirst/casper

##  2\. Background

This section provides background on the grid carbon intensity, cloud model,
and carbon-aware workload optimizations.

#### Carbon Intensity

The electric grid relies on a combination of generation sources to meet the
demand for electricity, and include fossil fuel-based generators using coal or
natural gas, low-carbon sources like hydro, wind, and solar, as well as non-
carbon sources such as nuclear. Since electricity demand fluctuates throughout
the day and follows diurnal patterns, the mix of generation sources and their
relative proportions also vary over time. It is worth noting that renewable
sources — such as wind and solar — are intermittent, which further impacts the
overall generation mix. The carbon intensity (CI) of electricity supply,
measured in grams of CO2 equivalent per watt or g$\cdot$CO2eq/kWh, represents
the average weighted carbon intensity of the generation sources used at any
given moment. As fossil-based sources have high, and renewable sources have
low or zero carbon weights, the average CI depends on the proportion of each
source in the overall generation mix. Figure 1 illustrates the average carbon
intensity of the grid electricity over the 2022 period for six different
geographical regions, revealing significant variations across locations. On
the vertical axis, the carbon intensity exhibits spatial variations between
regions, while the horizontal axis presents temporal variations within
regions. As shown, France has the lowest carbon-intensity due to its reliance
on nuclear power, while Germany and Singapore have the highest intensities due
to their reliance on fossil fuels. However, regions like California and
Germany have higher temporal variability due to increasing penetration of
renewables. These variations imply that the carbon footprint of a job can vary
by up to 40% depending on whether it is executed during a high or low carbon-
intensity period. Moreover, they indicate that executing the same job in
different cloud regions can lead to a 6-8x variation in emissions. This
underscores the potential for techniques that strategically schedule workloads
on clusters based on the current and projected carbon intensity of grid
electricity. While cluster managers can leverage temporal variations by
aligning job execution with low carbon periods (Souza et al., 2023; Wiesner et
al., 2021a), we focus on exploiting spatial characteristics that involves
distributing workloads across regions with both low carbon intensity and
sufficient latency performance. Finally, our work concentrates on scheduling
techniques aimed at reducing scope 2 emissions as defined by the GHG
(Greenhouse Gas) protocol (Protocol, 2024), in which the majority of
operational emissions are attributed to energy consumption (including scope
1). We do not consider embodied emissions (scope 3).

#### Workload Flexibility

The potential for a job to reduce emissions is a function of its type – batch
or interactive –, memory state, and the network latency and bandwidth across
locations. Additionally, there may be regulatory constraints, such as HIPPA
(Assistance, 2003) and GDPR (European Parliament and Council of the European
Union, 2016), that prevent spatially shifting a job outside of a specific
country, region or jurisdiction.

Figure 2. CASPER: CAP and CAS provision and coordinate user workloads.

While batch jobs such as AI and machine learning often have flexible
completion times and can accommodate temporal variations, interactive
workloads have strict low-latency requirements and limited temporal
flexibility. This is especially true in web-services environments where
requests pass through multiple microservices before a response is produced.
For instance, load balancing tools enable modern workloads with the ability to
shift their execution location to minimize latency and improve service
availability (Souza et al., 2018). These techniques work mostly with workloads
that have lightweight memory states and which do not need to transfer data
around locations. In this study, we consider lightweight web-requests –
specifically HTTP requests –, that can be seamlessly processed across various
locations. These requests have latency requirements that need to be limited
within a maximum threshold. Given that numerous services are highly optimized
for latency, minor deviations within a specified target are unlikely to impact
the overall user experience, and can enable the exercise of spatial shifting
to optimize for carbon.

##  3\. System Design and Implementation

This section outlines the design and architecture of CASPER, along with its
key components.

###  3.1. Architecture

CASPER is designed as a modular system that can be integrated into any
existing distributed resource manager. Figure 2 illustrates the overall system
architecture, highlighting its two main components: the Carbon-Aware
Provisioner (CAP) and the Carbon-Aware Scheduler (CAS). CASPER includes
various components for interfacing with interactive jobs, such as the resource
manager, monitoring, and the carbon-aware load-balancing and scheduling
policies.

#### Carbon-Aware Provisioner.

CAP acts as an intelligent provisioner that analyzes the inter-regional
network latency, the region’s (variable) carbon intensity, and the expected
application’s workload. Besides reducing carbon, CAP provides operators with
an important estimator: the optimal number of servers needed in each region
such that the expected workload is correctly handled for each time period and
lowest carbon intensity.

Parameter | Description
---|---
$x_{ij}$ | Requests redirected from region $i$ to region $j$
$\bar{x_{j}}$ | Requests not sent to region $j$
$s_{j}$ | Number of servers in region $j$
$n$ | Number of regions $\mathcal{R}$
$I_{j}$ | Carbon intensity in region $j$
$\alpha$ |  | Normalized weight for the carbon intensity
---
(in relation to number of servers $s_{j}$)
$\lambda_{i}$ | Incoming request rate at region $i$
$\ell_{ij}$ | Expected latency from region $i$ to $j$
$c_{j}$ | Resource capacity of region $j$ (in # of requests)
$L_{i}$ | Maximum tolerated latency for a request
$K$ | Maximum number of servers across all locations
$t_{j}$ | Number of requests submitted to region $j$

Table 1. List of parameters used by CAP.

This intuition leads us to formalize this provisioning problem as a multi-
objective formulation:

(1a) $\displaystyle\underset{x}{\min}\quad$
$\displaystyle\alpha\sum_{j}I_{j}\sum_{i}x_{ij}+(1-\alpha)\sum_{j}s_{j}$ (1b)
s.t. $\displaystyle\sum_{i}x_{ij}\leq s_{j}c_{j}$ (1c)
$\displaystyle\sum_{j}s_{j}\leq K$ (1d) $\displaystyle
x_{ij}\left(\ell_{ij}-L\right)\leq 0$ (1e)
$\displaystyle\sum_{i,j}x_{ij}=\mathbb{E}[\lambda_{i}],\forall i,j$ (1f)
$\displaystyle\alpha\in[0,1]$ (1g) $\displaystyle\bar{x}_{j}s_{j}=0$ (1h)
$\displaystyle x_{ij},s_{j}\in\mathbb{Z}_{\geq 0}$

We present CAP’s formulation in Equation 1, and Table 1 describes all of its
parameters. All indices $i,j$ represent the set of available regions
$\mathcal{R}$ for resource allocation, request processing and redirection
capacities. We let $\bar{x_{j}}\in\\{\,0,1\,\\}$ be the variable that
represents requests that are not sent to a region $j$, i.e.,
$\sum_{j}x_{ij}=0$. This constraint effectively means that if it is
anticipated that region $j$ won’t receive any requests, there should be no
server allocation in that region. Moreover, $x_{ij}$ represents the optimal
count of requests from region $i$ that is redirected to region $j$, while
$s_{j}$ is the number of servers provisioned in region $j$ to handle incoming
requests. Eq. 1a aims to minimize both the total carbon footprint of executing
requests (Eq. 1b) and the cumulative number of servers $s_{j}$ across all
regions (Eq. 1c) such that the minimum latency target is guaranteed (Eq. 1d).
Finally, the following assumptions are made. First, the problem is defined
within the scope of minimizing carbon emissions while simultaneously adhering
to application latency constraints. Second, since we consider cloud
datacenters, we ignore issues regarding resource limits, although we do
include a maximum amounr of servers (Eq. 1c) that CASPER can provision. We
also assume the load-balancers communication latency across regions (as seen
in Figure 2) is negligible when compared to the requests’ average service
(processing) times. Finally, the provisioner uses forecasts for carbon
intensity (Maji et al., 2022) and hourly workload request rates that are
expressed in terms of expected arrivals in region $i$ (Eq. 1e).

###  3.2. Carbon Aware Scheduler

ABC${{r_{1,j}}}$${{r_{2,j}}}$${{r_{3,j}}}$
(a) CAS Balancing

r_i,j = ∑ixij∑i∑jxij t_j

(b) Weight Factors

Figure 3. Illustration of CAS and weight calculation.

Figure 3 shows how the Carbon Aware Scheduler (CAS) distributes requests
between regions $x_{ij}$, which denotes the load of requests that need to be
redirected from region $i$ to $j$. It uses a vector as shown by Equation 3(b)
to model each region $r$’s weight, following the timely estimates obtained
from CAP (e.g., hourly). We implement CAS as a load-balancer module in CASPER,
whereas local incoming requests are redistributed across all regions according
to their proportional weights. More importantly, CAS ensures that unforeseen
workload events — e.g., load spikes, not accounted for in CAP’s optimization —
are effectively handled as best as possible.

###  3.3. Implementation

CASPER is implemented as a Kubernetes (K8S) scheduler with $s<K$ workers, each
representing a cloud region. Each deployment comprises of a single K8S pod
that runs the application. A prototype has been developed to emulate the
operations of a Wikipedia-like service across six distinct AWS regions, as
detailed in Table 2. These regions are selected as the closest regions to the
original Wikimedia servers (Foundation, 2024).

#### CAP

CASPER’s provisioner is developed using Python, while the optimizations are
solved using the PuLP library (Mitchell et al., 2011), an interface to the
Coin-or branch and cut (CBC) solver (Saltzman, 2002). The region wise server
deployment array obtained as an output of CAP is used to scale the size of
each regions using server collected metrics. Additionally, CAP computes the
optimal request distribution matrix, which is forwarded to CAS.

#### CAS

The scheduler coordinates a set of load balancers, one per-region, to
implement its logic. It timely forwards incoming requests to the appropriate
regions following the weights derived in the CAP’s optimal request
distribution matrix. Traefik (Vauge, 2016) is used to establish the cluster’s
load balancer layer, creating a HTTP proxy for every region to receive and
forward requests by routing the traffic to one of the corresponding backend
regions based on the hourly weights calculated by CAP.

##  4\. Evaluation

|  |  |
---|---|---|---
(a) Latency | (b) Carbon-20 | (c) Carbon-500 | (d) Resource Utilization
Figure 4. _Redirection rate (a, b and c) and resource provisioning per-region
and policies (d): Provisioning tends to increase in greener nearby regions._

In this section, we first discuss the real-world application, workload,
carbon, and network traces that are utilized to evaluate CASPER. Then, we
discuss the policies briefly introduced in the previous section. Finally, we
demonstrate and quantify the trade-offs between carbon savings and latency
performance for various targets.

Geographical Region | AWS Region
---|---
California | US-West-1
Virginia | US-East-1
Ohio | US-East-2
Germany | EU-Central-1
France | EU-West-3
Singapore | AP-SouthEast-2

Table 2. AWS Regions used in the evaluation.

###  4.1. Setup

#### Infrastructure.

CASPER runs on Ubuntu Linux 20.04, and it consists of a control plane and
worker nodes. The cluster compromises 16 servers with 16-cores Intel Xeon
processors and 32GB of memory. Each node runs a Kubernetes deployment
representing one region. For intra-cluster communication, an overlay network
is created using Flannel (CoreOS, 2016).

#### Application

To evaluate CASPER, we deploy Kiwix (Engelhart and Gaudin, 2007), a platform
to host and distribute compressed versions of the Wikipedia (Engelhart et al.,
2016). Specifically, we load Kiwix with the pre-built version of the German
Wikipedia from May 2023, which comprises a total of 32 GB of content
(Engelhart et al., 2023). Requests are directed through the CAS load balancer,
which interconnects all nodes in the cluster via a HTTP port.

#### Carbon Intensity.

Figure 1 illustrates the carbon intensity data for all the aforementioned
geographical regions (Table 2) at an hourly granularity. This data has been
collected from Electricity Maps (ElectricityMap, 2022) for 2022.

#### Workload and Network Traces.

We use the Wikimedia’s dataset (Foundation, 2023) covering six datacenters
across the USA, Europe, and Asia. For each region, the dataset includes the
request rates (requests per-second) and datacenter hourly utilization covering
2022. Since two of the AWS regions do not match those from Wikimedia’s – i.e.,
Netherlandas and Texas –, we select the two closest AWS regions i.e., Germany
and Ohio (Table 2). Average latency data (in milliseconds) across all AWS
regions are obtained from Cloudping (Adorjan, 2017) for 2022.

#### Telemetry.

Each region’s load-balancer exports their service-level metrics, specifically
the total count of HTTP requests served by each endpoint and their associated
service time. To calculate the carbon cost of request execution, this metric
is multiplied by the region’s current hour’s carbon intensity.

#### Policies

We conduct a comprehensive evaluation of CASPER throughout the entire year of
2022. The parameters for CAP are set as follows: $n=6$ (representing the AWS
regions), $\alpha$ = 0.5 (equal weights to both carbon and latency costs),
$c_{j}=100$ (one server can handle up to 1k requests), and $K=500$ (global
maximum number of servers). We also introduce several variations in the values
of $L_{i}$ (see below), which establish the maximum acceptable latency for
each request. CAP runs at the beginning of every hour to determine the
provisioning of servers at each location. The CAS weights are then calculated
based on the output of CAP. To assess the system’s performance, we execute a
real workload simulation spanning 24 hours. Metrics are collected at 10-minute
intervals and aggregated at the end of each hour. We conduct evaluations using
the following policies:

  1. (1)

Latency. This simulation serves as the baseline scenario without any carbon
optimization, where requests are solely served based on the lowest latency,
i.e., locally in the originating region, without any load balancing.

  2. (2)

Carbon-L Policies.  These runs focus on carbon optimization with various
latency $L$ threshold guarantees, ranging from 20 to 500ms. This approach
involves a trade-off in terms of performance, as requests can be redirected as
long as the latency requirements remain below $L$ ms.

These implementations strictly follow Mediawiki’s operations, in particular
the Latency policy that adheres to their stringent latency requirements
(Foundation, 2024). Among the carbon-aware policies, we set one with threshold
of $L=500$ ms as it represents the most flexible response time across all
regions. In this particular setting, the carbon cost of execution is minimized
by irrestrictive redirections that can reach very distant, lower carbon
regions capable of accommodating the redirected requests.

#### Workload Generation

A sample of the workload is represented in Figure 4(a), with incoming requests
in all regions. Each hour is divided into timesteps, and the request rate for
each timestep is selected from a set of values that follow an exponential
distribution. Parameters to generate the distributions are selected such that
the upper limit of the generated values is approximately 1.5$\times$ the
request rate for the hour.

###  4.2. Results

#### Effects on Request Redirection

Figures 4(a)-(c) present workload redirection results for Latency, Carbon-20,
and Carbon-500. As shown in Figure 1, Zone ”eu-west-3” (France) has the lowest
carbon intensity, followed by ”us-west-1” (California), ”us-east-[1,2]”
(Ohio/Virginia), ”eu-central-1” (Germany), and ”ap-southeast-2” (Singapore).
Figure 4(a) simply shows the original workload, where no redirection happens.
Notably in Figure 4(b), due to close proximity and low carbon intensity,
CASPER redirects as many requests as possible from Germany towards France. And
due to the latency constrains (20ms), Ohio and Virginia cannot induce savings.
This behavior is more evident in 4(c): As the latency constraint is relaxed
(500ms), France and California receive as many requests as possible from all
regions. However, eu-west-3 reaches capacity at various moments, triggering
CASPER to forward load to California (us-west-1).

#### Effects on Resource Provisioning

|  |
---|---|---
(a) Average Latency | (b) Hourly Latency |
|  |
(c) Average Emissions | (d) Hourly Emissions |
Figure 5. _Latency and carbon tradeoffs across policies._

Figure 4(d) illustrates the resource provisioning across the six AWS regions.
The Latency policy represents the original provisioning with no redirections.
As the latency constraints increase, the CASPER initiates re-provisioning of
servers from the German (”eu-central-1”) region to France due to its lower
carbon and lower network latency. Under Carbon-100, a significant portion of
the Ohio and Virginia workloads are redirected exclusively to France, as the
100ms latency requirement can be fulfilled. It is worth noting that requests
originating from Singapore are only directed to greener locations under the
Carbon-400 policy. This limitation arises from the end-to-end latency from
Singapore to any other region surpassing the 100ms threshold. Moreover, the
capacity in France reaches its limit under the Carbon-400 policy, prompting
redirections towards California, in addition to few towards Germany to meet
the latency requirements.

#### Effects on Carbon and Latency

Figures 5(a)-(d) present a comparative analysis of all policies. Figures 5(a)
and (c) clearly illustrate the primary tradeoff of CASPER, wherein the
relaxation of latency constraints leads to an increased potential for
emissions reduction. The Latency policy, despite achieving an average response
time as low as 6ms, exhibits the highest carbon emissions due to requests
remaining localized in high-intensity regions such as Germany and Singapore.
Notably, Carbon-20 demonstrates that even small relaxations in latency
constraints can result in a 25% carbon reductions. Carbon-100 achieves a 37%
reduction, while Carbon-400 reaches a point of diminishing returns with a 70%
reduction, similar to Carbon-500 which represents an unrestricted carbon
optimization scenario. Moreover, Figures 5(b) and (d) display the hourly
variations in average latency and emissions, respectively. In comparison to
the Latency policy, Carbon-20 shows a minimal increase in latency of 6ms while
simultaneously reducing emissions. Carbon-100 through Carbon-500 exhibit
latency increases ranging from 5-16$\times$, although delivering the most
substantial reductions. Finally, it is important to note that results would
change with other $\alpha$ values. This is primarily due to the fact that
CASPER would redirect requests differently due to the trade-off between carbon
emissions and the number of servers needed to satisfy latency SLOs.
Specifically, as $\alpha$ increases, CASPER would redirect more requests to
greener regions at the cost of latency because this would reduce the number of
servers in browner regions. In contrast, as $\alpha$ decreases, CASPER would
prioritize latency, opting to handle requests locally despite the carbon costs
of setting additional servers.

##  5\. Related Work

Recent efforts have concentrated on harnessing the flexibility in energy
demand for diverse workloads to diminish their carbon footprint by leveraging
the temporal and spatial flexibility of computing (Sukprasert et al., 2023;
Souza et al., 2023; Gupta et al., 2021, 2022; Wu et al., 2022; Radovanović et
al., 2023; Tabaeiaghdaei et al., 2023; Lin and Chien, 2023; Bashir et al.,
2021; Lechowicz et al., 2024; Wiesner et al., 2021a). Treehouse (Anderson et
al., 2023) proposes a software-centric approach to reduce the carbon intensity
of datacenter computing by making energy and carbon visible at the application
layer. CADRE focuses on carbon-aware data replication to reduce overall carbon
footprint, while leveraging load flexibility and interactions with the
electricity market to minimize carbon emissions (Xu et al., 2015). (Wiesner et
al., 2021b) investigates the potential of shifting computational workloads to
less carbon-intensive periods based on the fluctuating carbon intensity of
energy supply. (James and Schien, 2019) introduces a low-carbon extension to
the Kubernetes scheduler, sorting cloud regions by carbon intensity and
migrating workloads to regions with low carbon cost. However, the proposed
framework is evaluated primarily for batch jobs. On the other hand, numerous
works have employed integer programming techniques to devise new techniques
for low-carbon scheduling (Trevino-Martinez et al., 2022). Carbon-aware geo-
distributed scheduling is particularly relevant for Machine Learning (ML)
workloads requiring long periods of execution (Haghshenas et al., 2022).
(Zhang et al., 2023) proposes Cucumber, an admission control policy that
leverages load and energy forecasting techniques to determine scheduling
strategies to use renewables. Unlike the previous works, CASPER is the first
framework that seamlessly integrates server provisioning and request
scheduling for a geo-distributed web application, with a particular focus on
interactive web requests.

##  6\. Conclusion and Future Work

This paper introduced CASPER, a carbon-aware scheduler and provisioner
designed for distributed web applications. At the heart of CASPER lies a
multi-objective optimization that minimizes both resources and latency,
introducing a novel method to control the load balancing of web applications.
We observe substantial savings in the carbon footprint, reaching up to 70%
with controllable and negligible losses in performance while meeting all SLOs.
CASPER represents a crucial advancement in carbon-aware schedulers for
distributed and geo-distributed applications. Further analysis and exploration
of additional spatiotemporal carbon-aware strategies are warranted to enhance
the system’s efficiency. As a potential avenue for future work, the
implementation of auto-scaling policies that continuously monitors resource
utilization across regions to dynamically adapt allocations could be explored.

###### Acknowledgements.

We thank the reviewers for their valuable comments, which improved the quality
of this paper, and Electricity Maps for access to their carbon-intensity data.
This research is supported by NSF grants 2211302, 2211888, 2213636, 2105494,
and Army contract W911NF-17-2-0196.

## References

  * (1)
  * Adorjan (2017) Matt Adorjan. 2017\.  CloudPing.  www.cloudping.co.
  * Anderson et al. (2023) Thomas Anderson, Adam Belay, Mosharaf Chowdhury, Asaf Cidon, and Irene Zhang. 2023.  Treehouse: A case for carbon-aware datacenter software.  _ACM SIGENERGY Energy Informatics Review_ 3, 3 (2023), 64–70.
  * Assistance (2003) HIPAA Compliance Assistance. 2003\.  Summary of the hipaa privacy rule.  _Office for Civil Rights_ (2003).
  * Bashir et al. (2021) Noman Bashir, Tian Guo, Mohammad Hajiesmaili, David Irwin, Prashant Shenoy, Ramesh Sitaraman, Abel Souza, and Adam Wierman. 2021\.  Enabling Sustainable Clouds: The Case for Virtualizing the Energy System. In _Proceedings of the ACM Symposium on Cloud Computing_ _(SoCC ’21)_. Association for Computing Machinery, New York, NY, USA, 350–358.  https://doi.org/10.1145/3472883.3487009
  * Cook and Pomerantz (2015) Gary Cook and David Pomerantz. 2015.  Clicking clean: A guide to building the green Internet.  _Greenpeace International, Tech. Rep._ (2015).
  * CoreOS (2016) CoreOS. 2016.  Flannel.  https://github.com/flannel-io/flannel.
  * Denning and Lewis (2017) Peter J. Denning and Ted G. Lewis. 2017.  Exponential Laws of Computing Growth.  _Commun. ACM_ 60, 1 (January 2017), 54–65.
  * ElectricityMap (2022) ElectricityMap. 2022\.  ElectricityMap.  https://electricitymaps.com/.
  * Engelhart and Gaudin (2007) Emmanuel Engelhart and Renaud Gaudin. 2007.  Kiwix.  https://kiwix.org.
  * Engelhart et al. (2016) Emmanuel Engelhart, Tommi Makitalo, and Manuel Schneider. 2016\.  openZIM.  https://openzim.org.
  * Engelhart et al. (2023) Emmanuel Engelhart, Tommi Makitalo, and Manuel Schneider. 2023\.  Latest Wikipedia zim dump.  https://download.kiwix.org/zim/wikipedia/.
  * European Parliament and Council of the European Union (2016) European Parliament and Council of the European Union. 2016\.  Regulation (EU) 2016/679 of the European Parliament and of the Council.  https://data.europa.eu/eli/reg/2016/679/oj.
  * Foundation (2023) Wikimedia Foundation. 2023\.  Wikimedia’s Grafana installation.  https://grafana.wikimedia.org/.
  * Foundation (2024) Wikimedia Foundation. 2024\.  Wikimedia infrastructure.  https://wikitech.wikimedia.org/wiki/Wikimedia_infrastructure.
  * Garcia (2022) C. Garcia. 2022\.  AKCP, The Real Amount of Energy A Data Center Uses.  https://www.akcp.com/blog/the-real-amount-of-energy-a-data-center-use/.
  * Gupta et al. (2022) Udit Gupta, Mariam Elgamal, Gage Hills, Gu-Yeon Wei, Hsien-Hsin S. Lee, David Brooks, and Carole-Jean Wu. 2022.  ACT: Designing Sustainable Computer Systems with an Architectural Carbon Modeling Tool. In _Proceedings of the 49th Annual International Symposium on Computer Architecture_. 784–799.
  * Gupta et al. (2021) Udit Gupta, Young Geun Kim, Sylvia Lee, Jordan Tse, Hsien-Hsin S. Lee, Gu-Yeon Wei, David Brooks, and Carole-Jean Wu. 2021\.  Chasing Carbon: The Elusive Environmental Footprint of Computing. In _HPCA_. ACM.
  * Haghshenas et al. (2022) Kawsar Haghshenas, Brian Setz, and Marco Aiello. 2022\.  CO2 Emission Aware Scheduling for Deep Neural Network Training Workloads. In _2022 IEEE International Conference on Big Data (Big Data)_. 1542–1549.  https://doi.org/10.1109/BigData55660.2022.10020544
  * James and Schien (2019) Aled James and Daniel Schien. 2019.  A low carbon kubernetes scheduler. In _6th International Conference on ICT for Sustainability, ICT4S 2019_ _(CEUR Workshop Proceedings, Vol. 2382)_. CEUR-WS.  6th International Conference on ICT for Sustainability, ICT4S 2019 ; Conference date: 10-06-2019 Through 14-06-2019.
  * Jones (2018) Nicola Jones. 2018\.  How to stop data centres from gobbling up the world’s electricity.  _Nature_ 561, 7722 (2018), 163–167.
  * Lechowicz et al. (2024) Adam Lechowicz, Nicolas Christianson, Jinhang Zuo, Noman Bashir, Mohammad Hajiesmaili, Adam Wierman, and Prashant Shenoy. 2024.  The Online Pause and Resume Problem: Optimal Algorithms and An Application to Carbon-Aware Load Shifting. In _Proceedings of the ACM on Measurement and Analysis of Computing Systems_ _(SIGMETRICS 2024)_. ACM, New York, NY, USA, 35 pages.
  * Lin and Chien (2023) Liuzixuan Lin and Andrew A Chien. 2023.  Adapting Datacenter Capacity for Greener Datacenters and Grid. In _Proceedings of the ACM International Conference on Future Energy Systems (e-Energy)_. ACM, New York, NY, USA, 200–213.
  * Maji et al. (2023) Diptyaroop Maji, Ben Pfaff, Vipin PR, Rajagopal Sreenivasan, Victor Firoiu, Sreeram Iyer, Colleen Josephson, Zhelong Pan, and Ramesh K Sitaraman. 2023.  Bringing Carbon Awareness to Multi-cloud Application Delivery. In _Proceedings of the 2nd Workshop on Sustainable Computer Systems_. 1–6.
  * Maji et al. (2022) Diptyaroop Maji, Prashant Shenoy, and Ramesh K Sitaraman. 2022\.  CarbonCast: multi-day forecasting of grid carbon intensity. In _Proceedings of the 9th ACM International Conference on Systems for Energy-Efficient Buildings, Cities, and Transportation_. 198–207.
  * Mitchell et al. (2011) Stuart Mitchell, Michael OSullivan, and Iain Dunning. 2011\.  PuLP: a linear programming toolkit for python.  _The University of Auckland, Auckland, New Zealand_ 65 (2011).
  * Protocol (2024) Green Gas House Protocol. 2024\.  GHG Protocol Scope 2 Guidance.  https://ghgprotocol.org/scope-2-guidance.
  * Radovanović et al. (2023) Ana Radovanović, Ross Koningstein, Ian Schneider, Bokan Chen, Alexandre Duarte, Binz Roy, Diyue Xiao, Maya Haridasan, Patrick Hung, Nick Care, Saurav Talukdar, Eric Mullen, Kendal Smith, MariEllen Cottman, and Walfredo Cirne. 2023.  Carbon-Aware Computing for Datacenters.  _IEEE Transactions on Power Systems_ 38, 2 (2023), 1270–1280.
  * Saltzman (2002) Matthew J Saltzman. 2002\.  COIN-OR: an open-source library for optimization.  _Programming languages and systems in computational economics and finance_ (2002), 3–32.
  * Souza et al. (2023) Abel Souza, Noman Bashir, Jorge Murillo, Walid Hanafy, Qianlin Liang, David Irwin, and Prashant Shenoy. 2023.  Ecovisor: A Virtual Energy System for Carbon-Efficient Applications. In _ASPLOS_. ACM, New York, NY, USA, 252–265.
  * Souza et al. (2018) Abel Souza, Alessandro Vittorio Papadopoulos, Luis Tomas, David Gilbert, and Johan Tordsson. 2018.  Hybrid adaptive checkpointing for virtual machine fault tolerance. In _2018 IEEE International Conference on Cloud Engineering (IC2E)_. IEEE, 12–22.
  * Strubell et al. (2020) Emma Strubell, Ananya Ganesh, and Andrew McCallum. 2020\.  Energy and Policy Considerations for Modern Deep Learning Research. In _AAAI Conference on Artificial Intelligence (AAAI)_. ACM, New York, NY, USA, 13693–13696.
  * Sukprasert et al. (2023) Thanathorn Sukprasert, Abel Souza, Noman Bashir, David Irwin, and Prashant Shenoy. 2023\.  Quantifying the Benefits of Carbon-Aware Temporal and Spatial Workload Shifting in the Cloud.  _arXiv preprint arXiv:2306.06502_ (2023).
  * Tabaeiaghdaei et al. (2023) Seyedali Tabaeiaghdaei, Simon Scherrer, Jonghoon Kwon, and Adrian Perrig. 2023.  Carbon-Aware Global Routing in Path-Aware Networks. In _Proceedings of the ACM International Conference on Future Energy Systems (e-Energy)_. ACM, New York, NY, USA, 144–158.
  * Trevino-Martinez et al. (2022) Samuel Trevino-Martinez, Rapinder Sawhney, and Oleg Shylo. 2022\.  Energy-carbon footprint optimization in sequence-dependent production scheduling.  _Applied Energy_ 315 (2022), 118949.  https://doi.org/10.1016/j.apenergy.2022.118949
  * Vauge (2016) Emile Vauge. 2016\.  Traefik.  https://traefik.io/traefik/.
  * Wiesner et al. (2021a) Philipp Wiesner, Ilja Behnke, Dominik Scheinert, Kordian Gontarska, and Lauritz Thamsen. 2021a.  Let’s Wait Awhile: How Temporal Workload Shifting Can Reduce Carbon Emissions in the Cloud. In _Proceedings of the 22nd International Middleware Conference (Middleware)_. ACM, New York, NY, USA, 260–272.
  * Wiesner et al. (2021b) Philipp Wiesner, Ilja Behnke, Dominik Scheinert, Kordian Gontarska, and Lauritz Thamsen. 2021b.  Let’s wait awhile: How temporal workload shifting can reduce carbon emissions in the cloud. In _Proceedings of the 22nd International Middleware Conference_. 260–272.
  * Wu et al. (2022) Carole-Jean Wu, Ramya Raghavendra, Udit Gupta, Bilge Acun, Newsha Ardalani, Kiwan Maeng, Gloria Chang, Fiona Aga, Jinshi Huang, Charles Bai, et al. 2022\.  Sustainable AI: Environmental Implications, Challenges and Opportunities.  _Proceedings of Machine Learning and Systems_ 4, 795–813.
  * Xu et al. (2015) Zichen Xu, Nan Deng, Christopher Stewart, and Xiaorui Wang. 2015\.  Cadre: Carbon-aware data replication for geo-diverse services. In _2015 IEEE International Conference on Autonomic Computing_. IEEE, 177–186.
  * Zhang et al. (2023) Siyue Zhang, Minrui Xu, Wei Yang Bryan Lim, and Dusit Niyato. 2023\.  Sustainable AIGC Workload Scheduling of Geo-Distributed Data Centers: A Multi-Agent Reinforcement Learning Approach.  arXiv:2304.07948 [cs.AI]