Semi Bandit dynamics in Congestion Games: Convergence to Nash Equilibrium and No-Regret Guarantees.

Ioannis Panageas, Stratis Skoulakis, Luca Viano, Xiao Wang, Volkan Cevher
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:26904-26930, 2023.

Abstract

In this work, we propose introduce a variant of online stochastic gradient descent and prove it converges to Nash equilibria and simultaneously it has sublinear regret for the class of congestion games in the semi-bandit feedback setting. Our proposed method admits convergence rates depending only polynomially on the number of players and the number of facilities, but not on the size of the action set, which can be exponentially large in terms of the number of facilities. Moreover, the running time of our method has polynomial-time dependence on the implicit description of the game. Our analysis exploits techniques from convex geometry, in particular Caratheodory’s theorem and recent advances in non-convex stochastic optimization. This work improves upon and answers an open question from (Cui et al 2022).

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-panageas23a, title = {Semi Bandit dynamics in Congestion Games: Convergence to {N}ash Equilibrium and No-Regret Guarantees.}, author = {Panageas, Ioannis and Skoulakis, Stratis and Viano, Luca and Wang, Xiao and Cevher, Volkan}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {26904--26930}, 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/panageas23a/panageas23a.pdf}, url = {https://proceedings.mlr.press/v202/panageas23a.html}, abstract = {In this work, we propose introduce a variant of online stochastic gradient descent and prove it converges to Nash equilibria and simultaneously it has sublinear regret for the class of congestion games in the semi-bandit feedback setting. Our proposed method admits convergence rates depending only polynomially on the number of players and the number of facilities, but not on the size of the action set, which can be exponentially large in terms of the number of facilities. Moreover, the running time of our method has polynomial-time dependence on the implicit description of the game. Our analysis exploits techniques from convex geometry, in particular Caratheodory’s theorem and recent advances in non-convex stochastic optimization. This work improves upon and answers an open question from (Cui et al 2022).} }
Endnote
%0 Conference Paper %T Semi Bandit dynamics in Congestion Games: Convergence to Nash Equilibrium and No-Regret Guarantees. %A Ioannis Panageas %A Stratis Skoulakis %A Luca Viano %A Xiao Wang %A Volkan Cevher %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-panageas23a %I PMLR %P 26904--26930 %U https://proceedings.mlr.press/v202/panageas23a.html %V 202 %X In this work, we propose introduce a variant of online stochastic gradient descent and prove it converges to Nash equilibria and simultaneously it has sublinear regret for the class of congestion games in the semi-bandit feedback setting. Our proposed method admits convergence rates depending only polynomially on the number of players and the number of facilities, but not on the size of the action set, which can be exponentially large in terms of the number of facilities. Moreover, the running time of our method has polynomial-time dependence on the implicit description of the game. Our analysis exploits techniques from convex geometry, in particular Caratheodory’s theorem and recent advances in non-convex stochastic optimization. This work improves upon and answers an open question from (Cui et al 2022).
APA
Panageas, I., Skoulakis, S., Viano, L., Wang, X. & Cevher, V.. (2023). Semi Bandit dynamics in Congestion Games: Convergence to Nash Equilibrium and No-Regret Guarantees.. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:26904-26930 Available from https://proceedings.mlr.press/v202/panageas23a.html.

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