Anytime-Constrained Equilibria in Polynomial Time

Jeremy Mcmahan
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:43399-43416, 2025.

Abstract

We extend anytime constraints to the Markov game setting and the corresponding solution concept of anytime-constrained equilibrium (ACE). Then, we present a comprehensive theory of anytime-constrained equilibria that includes (1) a computational characterization of feasible policies, (2) a fixed-parameter tractable algorithm for computing ACE, and (3) a polynomial-time algorithm for approximately computing ACE. Since computing a feasible policy is NP-hard even for two-player zero-sum games, our approximation guarantees are the best possible so long as $P \neq NP$. We also develop the first theory of efficient computation for action-constrained Markov games, which may be of independent interest.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-mcmahan25a, title = {Anytime-Constrained Equilibria in Polynomial Time}, author = {Mcmahan, Jeremy}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {43399--43416}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/mcmahan25a/mcmahan25a.pdf}, url = {https://proceedings.mlr.press/v267/mcmahan25a.html}, abstract = {We extend anytime constraints to the Markov game setting and the corresponding solution concept of anytime-constrained equilibrium (ACE). Then, we present a comprehensive theory of anytime-constrained equilibria that includes (1) a computational characterization of feasible policies, (2) a fixed-parameter tractable algorithm for computing ACE, and (3) a polynomial-time algorithm for approximately computing ACE. Since computing a feasible policy is NP-hard even for two-player zero-sum games, our approximation guarantees are the best possible so long as $P \neq NP$. We also develop the first theory of efficient computation for action-constrained Markov games, which may be of independent interest.} }
Endnote
%0 Conference Paper %T Anytime-Constrained Equilibria in Polynomial Time %A Jeremy Mcmahan %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-mcmahan25a %I PMLR %P 43399--43416 %U https://proceedings.mlr.press/v267/mcmahan25a.html %V 267 %X We extend anytime constraints to the Markov game setting and the corresponding solution concept of anytime-constrained equilibrium (ACE). Then, we present a comprehensive theory of anytime-constrained equilibria that includes (1) a computational characterization of feasible policies, (2) a fixed-parameter tractable algorithm for computing ACE, and (3) a polynomial-time algorithm for approximately computing ACE. Since computing a feasible policy is NP-hard even for two-player zero-sum games, our approximation guarantees are the best possible so long as $P \neq NP$. We also develop the first theory of efficient computation for action-constrained Markov games, which may be of independent interest.
APA
Mcmahan, J.. (2025). Anytime-Constrained Equilibria in Polynomial Time. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:43399-43416 Available from https://proceedings.mlr.press/v267/mcmahan25a.html.

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