Abstract: The Bayesian approach to inverse problems has become very popular in the last decade after seminal work by Andrew Stuart (2010) and collaborators. Particularly in non-linear applications with PDEs and when using Gaussian process priors, this can leverage powerful MCMC methodology to tackle difficult high-dimensional and non-convex inference problems. Little is known in terms of rigorous performance guarantees for such algorithms. After laying out the main ideas behind Bayesian inversion, we will discuss recent progress providing both statistical and…

Abstract: The contextual bandit is a sequential decision making problem in which a learner repeatedly selects an action (e.g., a news article to display) in response to a context (e.g., a user’s profile) and receives a reward, but only for the action they selected. Beyond the classic explore-exploit tradeoff, a fundamental challenge in contextual bandits is to develop algorithms that can leverage flexible function approximation to model similarity between contexts, yet have computational requirements comparable to classical supervised learning tasks…