Policy Design for Active Sequential Hypothesis Testing using Deep Learning

TL;DR

This paper introduces deep learning-based heuristics for active sequential hypothesis testing, aiming to efficiently identify the true hypothesis with fewer samples, outperforming existing methods in certain scenarios.

Contribution

It proposes two novel heuristics using deep reinforcement learning and KL-divergence games for POMDP-based hypothesis testing, improving over current solutions.

Findings

Deep RL heuristic outperforms traditional methods in sample efficiency.

KL-divergence game heuristic achieves better accuracy in specific scenarios.

Numerical experiments validate the effectiveness of proposed heuristics.

Abstract

Information theory has been very successful in obtaining performance limits for various problems such as communication, compression and hypothesis testing. Likewise, stochastic control theory provides a characterization of optimal policies for Partially Observable Markov Decision Processes (POMDPs) using dynamic programming. However, finding optimal policies for these problems is computationally hard in general and thus, heuristic solutions are employed in practice. Deep learning can be used as a tool for designing better heuristics in such problems. In this paper, the problem of active sequential hypothesis testing is considered. The goal is to design a policy that can reliably infer the true hypothesis using as few samples as possible by adaptively selecting appropriate queries. This problem can be modeled as a POMDP and bounds on its value function exist in literature. However, optimal policies have not been identified and various heuristics are used. In this paper, two new heuristics are proposed: one based on deep reinforcement learning and another based on a KL-divergence zero-sum game. These heuristics are compared with state-of-the-art solutions and it is demonstrated using numerical experiments that the proposed heuristics can achieve significantly better performance than existing methods in some scenarios.