Research map / Optimization / Nonconvex and smooth optimization
Can We Find Nash Equilibria at a Linear Rate in Markov Games?
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use Homotopy-PO with Averaging OGDA as Global-Slow and OGDA as Local-Fast | Two-player zero-sum discounted Markov games · Random zero-sum Markov games, 10 trials | Nash gap: less than $10^{-5}$ after $2\times 10^5$ iterations | Helped |
| Replace the comparison algorithm with Homotopy-PO | Random zero-sum Markov games, $\gamma = 0.5$ · Random zero-sum Markov games, $\gamma = 0.5$ | Nash gap | Helped |
| Use $2^k$ Global-Slow iterations followed by $\ceil{2.1^k}$ Local-Fast iterations instead of $2^k$ and $4^k$ (ablation) | Homotopy-PO · Random zero-sum Markov games | Nash gap: less than $10^{-3}$ after $2\times 10^5$ iterations; less than $10^{-6}$ or even $10^{-8}$ in about $2\times 10^5$ itera | Helped |
| Run Averaging OGDA during a Global-Slow segment instead of OGDA | Homotopy-PO · Random zero-sum Markov games | Nash gap | Mixed |
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