Myopic Bayesian Design of Experiments via Posterior Sampling and Probabilistic Programming
This work addresses the challenge of efficiently collecting data to meet specific goals in DOE for researchers and practitioners, offering a flexible approach that is incremental in combining existing ideas like Thompson sampling and probabilistic programming.
The paper tackles the problem of sequential design of experiments (DOE) by proposing Myopic Posterior Sampling (MPS), a general-purpose strategy that is competitive with specialized methods across various tasks and enables handling complex DOE goals where no existing methods apply, with theoretical guarantees of sublinear regret under certain conditions.
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.