Problem
Research questions and friction points this paper is trying to address.
Continuous-time Mean-Field Games
Discounting
Entropy Regularization
Contraction Property
Finite Horizon
Horizon-Independent Contraction for Continuous-Time Discounted Regularized Mean-Field Games
🤖 AI Summary
研究了折扣和熵正则化下非平稳连续时间平均场博弈的收缩性质，提出了一种与时间范围无关的收缩条件，并得到了有限与无限时间范围均衡之间的收敛率。
📝 Abstract
We study contraction properties of non-stationary continuous-time mean-field games (MFGs) under discounting and entropy regularization. The state of the representative agent evolves according to a controlled continuous-time Markov chain, and both the state and action spaces are finite. In contrast to the undiscounted case, we show that, under a sufficiently large discount rate, finite-horizon MFGs admit a horizon-independent contraction condition, which also coincides with the corresponding infinite-horizon non-stationary contraction condition. As a byproduct, we obtain an explicit convergence rate between finite- and infinite-horizon mean-field equilibria. For each finite horizon, we further derive a refined contraction criterion from the spectral radius of a positive operator that majorizes the propagation of policy errors, and show that its large-horizon limit agrees with the horizon-independent contraction factor. Finally, we provide an explicit error bound between discounted and undiscounted finite-horizon regularized equilibria.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Horizon-Independent Contraction
Discounted Mean-Field Games
Entropy Regularization
Spectral Radius
Convergence Rate
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2023-09-30International Symposium on Games, Automata, Logics and Formal VerificationCitations: 0
