Reinforcement Learning based Sequential Batch-sampling for Bayesian Optimal Experimental Design

Engineering problems that are modeled using sophisticated mathematical methods or by expensive experiments, are usually encumbered with limited resources. Moreover, practical scenarios in the industry, impose restrictions, based on logistics and preference, on the manner in which the experiments can be conducted. For example, material supply may enable only a handful of experiments in a single-shot or in the case of computational models one may face significant wait-time based on shared computational resources. In such scenarios, one usually resorts to performing experiments in a manner that allows for maximizing one's state-of-knowledge while satisfying the above mentioned practical constraints. Sequential design of experiments (SDOE) is a popular suite of methods, that has yielded promising results in recent years across different engineering and practical problems. A common strategy, that leverages Bayesian formalism is the Bayesian SDOE, which usually works best in the one-step-ahead or myopic scenario of selecting a single experiment at each step of a sequence of experiments. In this work, we aim to extend the SDOE strategy, to query the information source on a batch of inputs. To this end, we leverage deep reinforcement learning (RL) based policy gradient methods, to propose batches of queries that are selected taking into account entire budget in hand. The algorithm retains the sequential nature while incorporating elements of reward from the domain of deep RL. We demonstrate the performance of the proposed algorithm on a synthetic problem, and a challenging high-dimensional engineering problem.