Stochastic Inertial Dynamics Via Time Scaling and Averaging

Understand

Our work is part of the close link between continuous-time dissipative dynamical systems and optimization algorithms, and more precisely here, in the stochastic setting.

• We aim to study stochastic convex minimization problems through the lens of stochastic inertial differential inclusions that are driven by the subgradient of a convex objective function.
• This will provide a general mathematical framework for analyzing the convergence properties of stochastic second-order inertial continuous-time dynamics involving vanishing viscous damping and measurable stochastic subgradient selections.
• Our chief goal in this paper is to develop a systematic and unified way that transfers the properties recently studied for first-order stochastic differential equations to second-order ones involving even subgradients in lieu of gradients.