Global Convergence of Multi-Agent Policy Gradient in Markov Potential Games
summary
Defines a new class called Markov Potential Games and proves independent policy gradient converges to Nash policies: deterministic updates reach an ε‑Nash in O(1/ε^2) iterations with Lipschitz gradients and a gradient‑domination argument, while stochastic updates (with an alpha‑greedy parametrization to bound variance and an unbiased estimator) yield O(1/ε^6) sample complexity. Shows MPGs can include per‑state zero‑sum games, that per‑state potentiality doesn’t imply an MPG, and that transitions can create competition.
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chapters (16)
- 0:00Introduction to the topic
- 1:55Formal framework
- 7:51Policy gradient methods
- 9:27Motivation for the research
- 10:50Markov potential games
- 14:40Game examples
- 17:30Ordinal potential games
- 17:53Main results and convergence
- 22:37Proof insights
- 24:02Gradient domination property
- 26:21Deterministic convergence
- 26:52Stochastic case analysis
- 29:49Addressing variance issues
- 30:31Greedy parameterization
- 31:55Related literature
- 32:45Future work and Q&A
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