Title: Convergence Properties for Optimised Adaptive Importance Samplers

Abstract: In this talk, I will consider an adaptation strategy for importance sampling that allows us to obtain theoretical guarantees of some adaptive importance sampling (AIS) schemes. First, I will demonstrate the case of exponential family proposals which lead to an adaptation procedure that is based on convex optimization with explicit convergence rates in terms of the number of iterations and Monte Carlo samples. Then, we will move on to the case of general proposals and discuss nonasymptotic guarantees of resulting AIS procedures.