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math.OC2022
Deep Relaxation of Controlled Stochastic Gradient Descent via Singular Perturbations
Martino Bardi, Hicham Kouhkouh
We consider a singularly perturbed system of stochastic differential equations proposed by Chaudhari et al. (Res. Math. Sci. 2018) to approximate the Entropic Gradient Descent in t…
math.OC2022
Singular perturbations in stochastic optimal control with unbounded data
Martino Bardi, Hicham Kouhkouh
We study singular perturbations of a class of two-scale stochastic control systems with unbounded data. The assumptions are designed to cover some relaxation problems for deep neur…
math.OC2022
An Eikonal equation with vanishing Lagrangian arising in Global Optimization
Martino Bardi, Hicham Kouhkouh
We show a connection between global unconstrained optimization of a continuous function and weak KAM theory for an eikonal-type equation arising also in ergodic control. A solu…