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We study Markov potential games under the infinite horizon average reward criterion. Most previous studies have been for discounted rewards. We prove that both algorithms based on independent policy gradient and independent natural policy gradient converge globally to a Nash equilibrium for the average reward criterion. To set the stage for gradient-based methods, we first establish that the average reward is a smooth function of policies and provide sensitivity bounds for the differential value functions, under certain conditions on ergodicity and the second largest eigenvalue of the underlying Markov decision process (MDP). We prove that three algorithms, policy gradient, proximal-Q, and natural policy gradient (NPG), converge to an ϵ-Nash equilibrium with time complexity O(1ϵ2), given a gradient/differential Q function oracle. When policy gradients have to be estimated, we propose an algorithm with ~O(1mins,aπ(a|s)δ) sample complexity to achieve δ approximation error w.r.t~the ℓ2 norm. Equipped with the estimator, we derive the first sample complexity analysis for a policy gradient ascent algorithm, featuring a sample complexity of ~O(1/ϵ5). Simulation studies are presented.
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This content will become publicly available on June 1, 2026
POTEC: Off-Policy Contextual Bandits for Large Action Spaces via Policy Decomposition
We study off-policy learning (OPL) of contextual bandit policies in large discrete action spaces where existing methods – most of which rely crucially on reward-regression models or importance-weighted policy gradients – fail due to excessive bias or variance. To overcome these issues in OPL, we propose a novel two-stage algorithm, called Policy Optimization via Two-Stage Policy Decomposition (POTEC). It leverages clustering in the action space and learns two different policies via policy- and regression-based approaches, respectively. In particular, we derive a novel low-variance gradient estimator that enables to learn a first-stage policy for cluster selection efficiently via a policy-based approach. To select a specific action within the cluster sampled by the first-stage policy, POTEC uses a second-stage policy derived from a regression-based approach within each cluster. We show that a local correctness condition, which only requires that the regression model preserves the relative expected reward differences of the actions within each cluster, ensures that our policy-gradient estimator is unbiased and the second-stage policy is optimal. We also show that POTEC provides a strict generalization of policyand regression-based approaches and their associated assumptions. Comprehensive experiments demonstrate that POTEC provides substantial improvements in OPL effectiveness particularly in large and structured action spaces.
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- Award ID(s):
- 2311521
- PAR ID:
- 10660106
- Publisher / Repository:
- International Conference on Representation Learning (ICLR)
- Date Published:
- Edition / Version:
- 2025
- Page Range / eLocation ID:
- 57640--57664
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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