Research map / Optimization / Nonconvex and smooth optimization
Learning While Playing in Mean-Field Games: Convergence and Optimality
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Single-loop fictitious play (one PPO-style policy improvement step plus mean-field update per iteration) instead of double-loop solving of the MDP induced by each mean-field state | Mean-field game Nash equilibrium learning · Theoretical convergence (Theorem 1 / Corollary 1) | convergence rate to entropy-regularized Nash equilibrium | No clear effect |
| Entropy regularization with parameter lambda added to the MFG objective | Mean-field game policy optimization · Theoretical convergence (Theorem 1) | convergence rate bound scaling | Helped |
| Relaxing the l-infinity concentrability condition (Assumption 4) to an l2 condition | Fictitious play algorithm for MFG · Theoretical convergence (Theorem 2 / Corollary 2) | convergence rate exponent: T^-1/5 to T^-1/9 | Hurt |
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