Open Problem: Optimal Instance-Dependent Sample Complexity for finding Nash Equilibrium in Two Player Zero-Sum Matrix games

Arnab Maiti
Proceedings of Thirty Eighth Conference on Learning Theory, PMLR 291:6230-6234, 2025.

Abstract

Optimal instance-dependent sample complexity is a well-studied topic in the multi-armed bandit literature. However, the analogous question in the setting of two-player zero-sum matrix games, where the payoff matrix can only be accessed through noisy samples, remains largely unexplored despite being a natural generalization of the multi-armed bandit problem. In this write-up, we pose a simple open question: What is the optimal instance-dependent sample complexity to find an approximate Nash equilibrium in two-player zero-sum matrix games?

Cite this Paper

BibTeX
@InProceedings{pmlr-v291-maiti25b, title = {Open Problem: Optimal Instance-Dependent Sample Complexity for finding Nash Equilibrium in Two Player Zero-Sum Matrix games}, author = {Maiti, Arnab}, booktitle = {Proceedings of Thirty Eighth Conference on Learning Theory}, pages = {6230--6234}, year = {2025}, editor = {Haghtalab, Nika and Moitra, Ankur}, volume = {291}, series = {Proceedings of Machine Learning Research}, month = {30 Jun--04 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v291/main/assets/maiti25b/maiti25b.pdf}, url = {https://proceedings.mlr.press/v291/maiti25b.html}, abstract = {Optimal instance-dependent sample complexity is a well-studied topic in the multi-armed bandit literature. However, the analogous question in the setting of two-player zero-sum matrix games, where the payoff matrix can only be accessed through noisy samples, remains largely unexplored despite being a natural generalization of the multi-armed bandit problem. In this write-up, we pose a simple open question: What is the optimal instance-dependent sample complexity to find an approximate Nash equilibrium in two-player zero-sum matrix games?} }
Endnote
%0 Conference Paper %T Open Problem: Optimal Instance-Dependent Sample Complexity for finding Nash Equilibrium in Two Player Zero-Sum Matrix games %A Arnab Maiti %B Proceedings of Thirty Eighth Conference on Learning Theory %C Proceedings of Machine Learning Research %D 2025 %E Nika Haghtalab %E Ankur Moitra %F pmlr-v291-maiti25b %I PMLR %P 6230--6234 %U https://proceedings.mlr.press/v291/maiti25b.html %V 291 %X Optimal instance-dependent sample complexity is a well-studied topic in the multi-armed bandit literature. However, the analogous question in the setting of two-player zero-sum matrix games, where the payoff matrix can only be accessed through noisy samples, remains largely unexplored despite being a natural generalization of the multi-armed bandit problem. In this write-up, we pose a simple open question: What is the optimal instance-dependent sample complexity to find an approximate Nash equilibrium in two-player zero-sum matrix games?
APA
Maiti, A.. (2025). Open Problem: Optimal Instance-Dependent Sample Complexity for finding Nash Equilibrium in Two Player Zero-Sum Matrix games. Proceedings of Thirty Eighth Conference on Learning Theory, in Proceedings of Machine Learning Research 291:6230-6234 Available from https://proceedings.mlr.press/v291/maiti25b.html.

Related Material