2 citations · 3 across the 16 of their papers we have counts for
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Asymptotic properties of non-coercive Hamiltonians with drift
Martino Bardi
We consider Hamiltonians associated to optimal control problems for affine systems on the torus. They are not coercive and are possibly unbounded from below in the direction of the…
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…
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…
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…
Convergence of some Mean Field Games systems to aggregation and flocking models
Martino Bardi, Pierre Cardaliaguet
For two classes of Mean Field Game systems we study the convergence of solutions as the interest rate in the cost functional becomes very large, modeling agents caring only about a…
Almost sure stability of controlled degenerate diffusions
Martino Bardi, Annalisa Cesaroni
We develop a direct Lyapunov method for the almost sure open-loop stabilizability and asymptotic stabilizability of controlled degenerate diffusion processes. The infinitesimal dec…