Convergence to Nash Equilibrium and No-regret Guarantee in (Markov) Potential Games
This work addresses the challenge of efficient learning in multi-agent game theory, offering incremental improvements in regret bounds for Markov potential games.
The paper tackles the problem of achieving convergence to Nash equilibrium and sublinear regret in potential and Markov potential games under stochastic cost and bandit feedback, proposing a Frank-Wolfe variant that attains O(T^{4/5}) regret bounds, matching or improving prior results without requiring game knowledge.
In this work, we study potential games and Markov potential games under stochastic cost and bandit feedback. We propose a variant of the Frank-Wolfe algorithm with sufficient exploration and recursive gradient estimation, which provably converges to the Nash equilibrium while attaining sublinear regret for each individual player. Our algorithm simultaneously achieves a Nash regret and a regret bound of $O(T^{4/5})$ for potential games, which matches the best available result, without using additional projection steps. Through carefully balancing the reuse of past samples and exploration of new samples, we then extend the results to Markov potential games and improve the best available Nash regret from $O(T^{5/6})$ to $O(T^{4/5})$. Moreover, our algorithm requires no knowledge of the game, such as the distribution mismatch coefficient, which provides more flexibility in its practical implementation. Experimental results corroborate our theoretical findings and underscore the practical effectiveness of our method.