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Sampling from the Mean-Field Stationary Distribution
We study the complexity of sampling from the stationary distribution of a mean-field SDE, or equivalently, the complexity of minimizing a functional over the space of probability measures which includes an interaction term.
Convergence and Optimality of Policy Gradient Methods in Weakly Smooth Settings
Policy gradient methods have been frequently applied to problems in control and reinforcement learning with great success, yet existing convergence analysis still relies on non-intuitive, impractical and often opaque conditions.
Convergence of Langevin Monte Carlo in Chi-Squared and Renyi Divergence
We prove that, initialized with a Gaussian random vector that has sufficiently small variance, iterating the LMC algorithm for $\widetilde{\mathcal{O}}(\lambda^2 d\epsilon^{-1})$ steps is sufficient to reach $\epsilon$-neighborhood of the target in both Chi-squared and Renyi divergence, where $\lambda$ is the logarithmic Sobolev constant of $\nu_*$.
