Tata Institute of Fundamental Research
On the projected Aubry set of the rate function associated with large deviations for stochastic approximations
STCS Seminar
Speaker:
Prof. Henrik Hult (Professor in Mathematical Statistics)
Organiser:
Sandeep K Juneja
Date:
Monday, 22 Jan 2024, 14:30 to 15:30
Venue:
A-201 (STCS Seminar Room)
(Scan to add to calendar)
Abstract:
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.
| Speaker: | Prof. Henrik Hult (Professor in Mathematical Statistics) |
| Organiser: | Sandeep K Juneja |
| Date: | Monday, 22 Jan 2024, 14:30 to 15:30 |
| Venue: | A-201 (STCS Seminar Room) |
(Scan to add to calendar)
Abstract:
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.