On Stochastic Gradient Langevin Dynamics with Dependent Data Streams: The Fully Nonconvex Case
Ngọc Huy Châu, Éric Moulines, Miklós Rásonyi, Sotirios Sabanis, Ying Zhang
Abstract
We consider the problem of sampling from a target distribution, which is not necessarily log-concave, in the context of empirical risk minimization and stochastic optimization as presented in [M. Raginsky, A. Rakhlin, and M. Telgarsky, Proc. Mach. Learn. Res., 65 (2017), pp. 1674--1703]. Non-asymptotic results are established in the $L^1$-Wasserstein distance for the behavior of stochastic gradient Langevin dynamics algorithms. We allow gradient estimates based on dependent data streams. Our convergence estimates are sharper and uniform in the number of iterations, in contrast to those in previous studies.
Topics & Concepts
Langevin dynamicsConvergence (economics)Computer scienceDynamics (music)Langevin equationStatistical physicsMathematical economicsMathematical optimizationApplied mathematicsOperations researchPhysicsMathematicsEconomicsEconomic growthAcousticsMarkov Chains and Monte Carlo MethodsStochastic processes and financial applicationsStochastic Gradient Optimization Techniques