Title: Myopic Bayesian Design of Experiments via Posterior Sampling and Probabilistic Programming,
Abstract: We design a new myopic strategy for a wide class of sequential design of
experiment (DOE) problems, where the goal is to collect data in order to to
fulfil a certain problem specific goal. Our approach, Myopic Posterior Sampling
(MPS), is inspired by the classical posterior (Thompson) sampling algorithm for
multi-armed bandits and leverages the flexibility of probabilistic programming
and approximate Bayesian inference to address a broad set of problems.
Empirically, this general-purpose strategy is competitive with more specialised
methods in a wide array of DOE tasks, and more importantly, enables addressing
complex DOE goals where no existing method seems applicable. On the theoretical
side, we leverage ideas from adaptive submodularity and reinforcement learning
to derive conditions under which MPS achieves sublinear regret against natural
benchmark policies.