Summary of Provable Policy Gradient Methods For Average-reward Markov Potential Games, by Min Cheng et al.
Provable Policy Gradient Methods for Average-Reward Markov Potential Games
by Min Cheng, Ruida Zhou, P. R. Kumar, Chao Tian
First submitted to arxiv on: 9 Mar 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Computer Science and Game Theory (cs.GT)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary A novel study on Markov potential games under the infinite horizon average reward criterion is conducted. The research builds upon previous discounted reward-based studies and provides insights into the global convergence of algorithms based on independent policy gradient and natural policy gradient to a Nash equilibrium for the average reward criterion. The study establishes that the average reward is a smooth function of policies, providing sensitivity bounds for differential value functions under certain conditions. Three algorithms – policy gradient, proximal-Q, and natural policy gradient (NPG) – are shown to converge to an epsilon-Nash equilibrium with time complexity O(1/epsilon^2), given a gradient/differential Q function oracle. When estimating policy gradients, the study proposes an algorithm with sample complexity Õ(1/min_s,a_π(a|s)δ) achieving δ approximation error w.r.t. the ℓ_2 norm. The research also derives the first sample complexity analysis for a policy gradient ascent algorithm featuring a sample complexity of Õ(1/epsilon^5). Simulation studies are presented. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary A new study looks at how games with infinite rewards work when we want to find the best strategy in the long run. Most people have only looked at this problem when the rewards get smaller and smaller over time, but this research takes a different approach. It shows that two important algorithms for solving these kinds of problems can find the best solution if we use them correctly. The study also finds that another algorithm, which is used to improve our estimate of the best strategy, works well too. This means we can make good decisions in complex situations where we want to maximize our rewards over time. |
