“Efficient Nash Equilibrium Attainment in Stochastic Potential Games”
This work presents an interesting study on potential games and Markov potential games under stochastic cost and bandit feedback. The authors propose a variant of the Frank-Wolfe algorithm that incorporates sufficient exploration and recursive gradient estimation. The algorithm is proven to converge to the Nash equilibrium while achieving sublinear regret for each individual player.
One notable aspect of this algorithm is that it does not require additional projection steps, which sets it apart from existing methods. The algorithm achieves a Nash regret and a regret bound of O(T^(4/5)) for potential games, matching the best available result. This is a significant improvement and demonstrates the effectiveness of the proposed approach.
Furthermore, the authors extend their results to Markov potential games, where they improve the best available Nash regret from O(T^(5/6)) to O(T^(4/5)). This improvement is achieved by carefully balancing the reuse of past samples and exploration of new samples.
What is particularly interesting about this algorithm is that it does not require any prior knowledge of the game, such as the distribution mismatch coefficient. This provides more flexibility in practical implementation and makes the algorithm applicable to a wide range of scenarios.
The experimental results presented in this work confirm the theoretical findings and highlight the practical effectiveness of the proposed method. This lends further credibility to the algorithm and suggests its potential for real-world applications.
In conclusion, this work presents a novel algorithm for potential games and Markov potential games under stochastic cost and bandit feedback. The algorithm achieves impressive regret bounds and does not require prior knowledge of the game. It represents a valuable contribution to the field and opens up possibilities for further research and practical implementations.