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arXiv · 2410.23637

Anytime-Constrained Equilibria in Polynomial Time

Jeremy McMahan
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Abstract

We extend anytime constraints to the Markov game setting and the corresponding solution concept of an 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 optimal 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.

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Jeremy McMahan. 2024-10-31. Anytime-Constrained Equilibria in Polynomial Time. https://arxiv.org/abs/2410.23637

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