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.