Proves the first universal approximation theorems for k-times differentiable nonlinear operators between Banach spaces and their derivatives uniformly on compact sets in weighted Sobolev norms via encoder-decoder operator learning architectures.
Learning in mean field games: A survey
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Model-free DQN learning achieves suboptimality bounds of O(1/sqrt(Ns)) + O(1/N) in Karma DPGs at equilibrium, and deep RL combined with fictitious play empirically reaches near-Stationary Nash Equilibrium from scratch.
The authors propose actor-critic q-learning algorithms for mean-field control with common noise based on martingale orthogonality conditions and relaxed controls, establish convergence of inner iterations in the linear-quadratic case, and demonstrate performance on examples.
Mean-field game equilibrium calibrated to historical de-pegs attributes most peg recovery to primary-market arbitrage and identifies a nonlinear stress threshold for slow recovery.
Neural mean-field games integrate mean-field game theory with neural SDEs to learn strategic interactions from data in a model-free way, demonstrated on games and viral dynamics.
citing papers explorer
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Universal Approximation of Nonlinear Operators and Their Derivatives
Proves the first universal approximation theorems for k-times differentiable nonlinear operators between Banach spaces and their derivatives uniformly on compact sets in weighted Sobolev norms via encoder-decoder operator learning architectures.
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Towards Model-Free Learning in Dynamic Population Games: An Application to Karma Economies
Model-free DQN learning achieves suboptimality bounds of O(1/sqrt(Ns)) + O(1/N) in Karma DPGs at equilibrium, and deep RL combined with fictitious play empirically reaches near-Stationary Nash Equilibrium from scratch.
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Continuous-time q-learning for mean-field control with common noise, part-II: q-learning algorithms
The authors propose actor-critic q-learning algorithms for mean-field control with common noise based on martingale orthogonality conditions and relaxed controls, establish convergence of inner iterations in the linear-quadratic case, and demonstrate performance on examples.
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Who Restores the Peg? A Mean-Field Game Approach to Model Stablecoin Market Dynamics
Mean-field game equilibrium calibrated to historical de-pegs attributes most peg recovery to primary-market arbitrage and identifies a nonlinear stress threshold for slow recovery.
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Neural Mean-Field Games: Extending Mean-Field Game Theory with Neural Stochastic Differential Equations
Neural mean-field games integrate mean-field game theory with neural SDEs to learn strategic interactions from data in a model-free way, demonstrated on games and viral dynamics.
- Travel-time tomography from mean field game dynamics