An Analysis of Piecewise−Linear and Convex Value Functions for Active Perception POMDPs

Abstract

In active perception tasks, an agent aims to select actions that reduce its uncertainty about a hidden state. While partially observable Markov decision processes (POMDPs) are a natural model for such problems, reward functions that directly penalize uncertainty in the agent’s belief can remove the piecewise-linear and convex (PWLC) property of the value function required by most POMDP planners. This paper analyses ρ-POMDP and POMDP-IR, two frameworks that restore the PWLC property in active perception tasks. We establish the mathematical equivalence of the two frameworks and show that both admit a decomposition of the maximization performed in the Bellman backup, yielding substantial computational savings. We also present an empirical analysis on data from real multi-camera tracking systems that illustrates these savings and analyzes the critical factors in the performance of POMDP planners in such tasks.