Gehui Xu

Guanpu Chen, Gehui Xu, Fengxiang He et al.

Wide machine learning tasks can be formulated as non-convex multi-player games, where Nash equilibrium (NE) is an acceptable solution to all players, since no one can benefit from changing its strategy unilaterally. Attributed to the non-convexity, obtaining the existence condition of global NE is challenging, let alone designing theoretically guaranteed realization algorithms. This paper takes conjugate transformation to the formulation of non-convex multi-player games, and casts the complementary problem into a variational inequality (VI) problem with a continuous pseudo-gradient mapping. We then prove the existence condition of global NE: the solution to the VI problem satisfies a duality relation. Based on this VI formulation, we design a conjugate-based ordinary differential equation (ODE) to approach global NE, which is proved to have an exponential convergence rate. To make the dynamics more implementable, we further derive a discretized algorithm. We apply our algorithm to two typical scenarios: multi-player generalized monotone game and multi-player potential game. In the two settings, we prove that the step-size setting is required to be $\mathcal{O}(1/k)$ and $\mathcal{O}(1/\sqrt k)$ to yield the convergence rates of $\mathcal{O}(1/ k)$ and $\mathcal{O}(1/\sqrt k)$, respectively. Extensive experiments in robust neural network training and sensor localization are in full agreement with our theory.

Mengda Ji, Genjiu Xu, Liying Wang

This work focuses on the credit assignment problem in cooperative multi-agent reinforcement learning (MARL). Sharing the global advantage among agents often leads to suboptimal policy updates as it fails to account for the distinct contributions of agents. Although numerous methods consider global or individual contributions for credit assignment, a detailed analysis at the coalition level remains lacking in many approaches. This work analyzes the over-updating problem during multi-agent policy updates from a coalition-level perspective. To address this issue, we propose a credit assignment method called Coalitional Rational Advantage Decomposition (CORA). CORA evaluates coalitional advantages via marginal contributions from all possible coalitions and decomposes advantages using the core solution from cooperative game theory, ensuring coalitional rationality. To reduce computational overhead, CORA employs random coalition sampling. Experiments on matrix games, differential games, and multi-agent collaboration benchmarks demonstrate that CORA outperforms strong baselines, particularly in tasks with multiple local optima. These findings highlight the importance of coalition-aware credit assignment for improving MARL performance.