Uncoupled and Convergent Learning in Two-Player Zero-Sum Markov Games with Bandit Feedback
This provides a more practical solution for multi-agent reinforcement learning in competitive settings, though it is incremental as it builds on existing entropy regularization techniques.
The paper tackles the problem of learning in two-player zero-sum Markov games with bandit feedback, developing an uncoupled algorithm that achieves non-asymptotic last-iterate convergence rates, such as O(t^{-1/8}) for stateless games and O(t^{-1/(9+ε)}) for irreducible Markov games, without requiring coordination or prior knowledge.
We revisit the problem of learning in two-player zero-sum Markov games, focusing on developing an algorithm that is uncoupled, convergent, and rational, with non-asymptotic convergence rates. We start from the case of stateless matrix game with bandit feedback as a warm-up, showing an $O(t^{-\frac{1}{8}})$ last-iterate convergence rate. To the best of our knowledge, this is the first result that obtains finite last-iterate convergence rate given access to only bandit feedback. We extend our result to the case of irreducible Markov games, providing a last-iterate convergence rate of $O(t^{-\frac{1}{9+\varepsilon}})$ for any $\varepsilon>0$. Finally, we study Markov games without any assumptions on the dynamics, and show a path convergence rate, which is a new notion of convergence we defined, of $O(t^{-\frac{1}{10}})$. Our algorithm removes the coordination and prior knowledge requirement of [Wei et al., 2021], which pursued the same goals as us for irreducible Markov games. Our algorithm is related to [Chen et al., 2021, Cen et al., 2021] and also builds on the entropy regularization technique. However, we remove their requirement of communications on the entropy values, making our algorithm entirely uncoupled.