Thomas Powell and Davide Barbarossa (Bath University) are visiting Swansea this week. This afternoon Thomas will give a talk on the "Rates of convergence for stochastic processes" as a part of our seminar series.
Abstract: I will present two ongoing projects in the new area of proof mining in stochastic optimization, each representing a distinct inroad into the area. First, I will give an account of recent work with Morenikeji Neri that focuses on convergence proofs based on martingales: This quantitative study of martingale convergence has resulted in several variants of the famous Robbins-Siegmund theorem that come equipped with numerical information, with applications including stochastic quasi-Fejer monotone sequences and gradient-descent type algorithms. Second, I will report on some work in progress with Nicholas Pischkeon a new stochastic alternating Halpern-Mann scheme with noise terms: In addition to new convergence results (both qualitative and quantitative), this project has led to an interesting application in reinforcement learning, demonstrating that the techniques of proof mining are relevant for current research in the mathematics of artificial intelligence.
