On the projected Aubry set of the rate function associated with large deviations for stochastic approximations

Sandeep K Juneja
Monday, 22 Jan 2024, 14:30 to 15:30
A-201 (STCS Seminar Room)

We consider the problem of minimizing an action potential that arises from large deviation theory for stochastic approximations. The solutions to the minimizing problem satisfy, in the sense of a viscosity solution, a Hamilton-Jacobi equation. From weak KAM theory, we know that these viscosity solutions are characterised by the projected Aubry set. The main result of this paper is that, for a specific rate function corresponding to a stochastic approximation algorithm, we prove that the projected Aubry set is equal to the forward limit set to the limit ODE.