Extends robust MDPs to continuous time with policy gradient derivations using differential equation methods and proposes optimizers achieving linear convergence and specific sample complexities.
Mirror Mean-Field Langevin Dynamics
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abstract
The mean-field Langevin dynamics (MFLD) minimizes an entropy-regularized nonlinear convex functional on the Wasserstein space over $\mathbb{R}^d$, and has gained attention recently as a model for the gradient descent dynamics of interacting particle systems such as infinite-width two-layer neural networks. However, many problems of interest have constrained domains, which are not solved by existing mean-field algorithms due to the global diffusion term. We study the optimization of probability measures constrained to a convex subset of $\mathbb{R}^d$ by proposing the \emph{mirror mean-field Langevin dynamics} (MMFLD), an extension of MFLD to the mirror Langevin framework. We obtain linear convergence guarantees for the continuous MMFLD via a uniform log-Sobolev inequality, and uniform-in-time propagation of chaos results for its time- and particle-discretized counterpart.
fields
cs.LG 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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Policy Gradient for Continuous-Time Robust Markov Decision Processes
Extends robust MDPs to continuous time with policy gradient derivations using differential equation methods and proposes optimizers achieving linear convergence and specific sample complexities.