Seminar Details
2015-11-17 (14:00) : Dynamical behavior of a stochastic proximal point algorithm
At Euler building (A002)
Organized by Mathematical Engineering
Speaker :
Pascal Bianchi (Télécom ParisTech)
Abstract :
Maximal monotone operators are set-valued mappings which extend (but are not limited to) the notion of subdifferential of a convex function.
The proximal point algorithm and the forward-backward algorithm are amongst the most studied algorithms for finding iteratively a zero of a sum
of two maximal monotone operators A and B. The purpose of this talk is to investigate the case where operators A and B are either unobserved
or difficult to handle numerically. We propose an online version of the forward-backward algorithm where at each iteration, A and B are replaced
with one realization of some random maximal monotone operators whose expectations (in the Aumann sense) coincide with A and B respectively.
Under the assumption of a decreasing step size, we prove that the iterates "shadow" the behavior of a continuous-time differential inclusion
and converge almost surely to a zero of A+B provided some conditions. Applications to constrained convex optimization are considered.