Federated Online and Bandit Convex Optimization

Kumar Kshitij Patel, Lingxiao Wang, Aadirupa Saha, Nathan Srebro
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:27439-27460, 2023.

Abstract

We study the problems of distributed online and bandit convex optimization against an adaptive adversary. We aim to minimize the average regret on $M$ machines working in parallel over $T$ rounds with $R$ intermittent communications. Assuming the underlying cost functions are convex and can be generated adaptively, our results show that collaboration is not beneficial when the machines have access to the first-order gradient information at the queried points. This is in contrast to the case for stochastic functions, where each machine samples the cost functions from a fixed distribution. Furthermore, we delve into the more challenging setting of federated online optimization with bandit (zeroth-order) feedback, where the machines can only access values of the cost functions at the queried points. The key finding here is identifying the high-dimensional regime where collaboration is beneficial and may even lead to a linear speedup in the number of machines. We further illustrate our findings through federated adversarial linear bandits by developing novel distributed single and two-point feedback algorithms. Our work is the first attempt towards a systematic understanding of federated online optimization with limited feedback, and it attains tight regret bounds in the intermittent communication setting for both first and zeroth-order feedback. Our results thus bridge the gap between stochastic and adaptive settings in federated online optimization.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-patel23a, title = {Federated Online and Bandit Convex Optimization}, author = {Patel, Kumar Kshitij and Wang, Lingxiao and Saha, Aadirupa and Srebro, Nathan}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {27439--27460}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/patel23a/patel23a.pdf}, url = {https://proceedings.mlr.press/v202/patel23a.html}, abstract = {We study the problems of distributed online and bandit convex optimization against an adaptive adversary. We aim to minimize the average regret on $M$ machines working in parallel over $T$ rounds with $R$ intermittent communications. Assuming the underlying cost functions are convex and can be generated adaptively, our results show that collaboration is not beneficial when the machines have access to the first-order gradient information at the queried points. This is in contrast to the case for stochastic functions, where each machine samples the cost functions from a fixed distribution. Furthermore, we delve into the more challenging setting of federated online optimization with bandit (zeroth-order) feedback, where the machines can only access values of the cost functions at the queried points. The key finding here is identifying the high-dimensional regime where collaboration is beneficial and may even lead to a linear speedup in the number of machines. We further illustrate our findings through federated adversarial linear bandits by developing novel distributed single and two-point feedback algorithms. Our work is the first attempt towards a systematic understanding of federated online optimization with limited feedback, and it attains tight regret bounds in the intermittent communication setting for both first and zeroth-order feedback. Our results thus bridge the gap between stochastic and adaptive settings in federated online optimization.} }
Endnote
%0 Conference Paper %T Federated Online and Bandit Convex Optimization %A Kumar Kshitij Patel %A Lingxiao Wang %A Aadirupa Saha %A Nathan Srebro %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-patel23a %I PMLR %P 27439--27460 %U https://proceedings.mlr.press/v202/patel23a.html %V 202 %X We study the problems of distributed online and bandit convex optimization against an adaptive adversary. We aim to minimize the average regret on $M$ machines working in parallel over $T$ rounds with $R$ intermittent communications. Assuming the underlying cost functions are convex and can be generated adaptively, our results show that collaboration is not beneficial when the machines have access to the first-order gradient information at the queried points. This is in contrast to the case for stochastic functions, where each machine samples the cost functions from a fixed distribution. Furthermore, we delve into the more challenging setting of federated online optimization with bandit (zeroth-order) feedback, where the machines can only access values of the cost functions at the queried points. The key finding here is identifying the high-dimensional regime where collaboration is beneficial and may even lead to a linear speedup in the number of machines. We further illustrate our findings through federated adversarial linear bandits by developing novel distributed single and two-point feedback algorithms. Our work is the first attempt towards a systematic understanding of federated online optimization with limited feedback, and it attains tight regret bounds in the intermittent communication setting for both first and zeroth-order feedback. Our results thus bridge the gap between stochastic and adaptive settings in federated online optimization.
APA
Patel, K.K., Wang, L., Saha, A. & Srebro, N.. (2023). Federated Online and Bandit Convex Optimization. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:27439-27460 Available from https://proceedings.mlr.press/v202/patel23a.html.

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