Instance-dependent optimality in statistical decision-making: Why useful and how to achieve it? (Wenlong Mou -- UC Berkeley)

Data-driven methodology for decision-making requires theoretically sound procedures for choosing between estimators, tuning their parameters, and understanding bias/variance trade-offs. In many settings, asymptotic and/or worst-case theory fails to provide the relevant guidance. In this talk, I discuss some recent advances that involve a more refined approach, one that leads to non-asymptotic and instance-optimal guarantees. First, focusing on function approximation methods for policy evaluation in reinforcement learning, I describe a novel class of optimal oracle inequalities for projected Bellman equations. In contrast to corresponding results for ordinary regression, the approximation pre-factor depends on the geometry of the problem, and can be much larger than unity. Second, I discuss optimal procedures for estimating linear functionals from observational data. Our theory reveals a rich spectrum of behavior beyond the asymptotic semi-parametric efficiency bound. It also highlights the fundamental roles of geometry, and provides concrete guidance on practical procedures and parameter choices.