Information gathering in a partially observable environment can be formulated as a reinforcement learning (RL), problem where the reward depends on the agent's uncertainty. For example, the reward can be the negative entropy of the agent's belief over an unknown (or hidden) variable. Typically, the rewards of an RL agent are defined as a function of the state-action pairs and not as a function of the belief of the agent; this hinders the direct application of deep RL methods for such tasks. This paper tackles the challenge of using belief-based rewards for a deep RL agent, by offering a simple insight that maximizing any convex function of the belief of the agent can be approximated by instead maximizing a prediction reward: a reward based on prediction accuracy. In particular, we derive the exact error between negative entropy and the expected prediction reward. This insight provides theoretical motivation for several fields using prediction rewards---namely visual attention, question answering systems, and intrinsic motivation---and highlights their connection to the usually distinct fields of active perception, active sensing, and sensor placement. Based on this insight we present deep anticipatory networks (DANs), which enables an agent to take actions to reduce its uncertainty without performing explicit belief inference. We present two applications of DANs: building a sensor selection system for tracking people in a shopping mall and learning discrete models of attention on fashion MNIST and MNIST digit classification.

In active perception tasks, an agent aims to select sensory actions that reduce its uncertainty about one or more hidden variables. For example, a mobile robot takes sensory actions to efficiently navigate in a new environment. While partially observable Markov decision processes (POMDPs) provide 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. Furthermore, as the number of sensors available to the agent grows, the computational cost of POMDP planning grows exponentially with it, making POMDP planning infeasible with traditional methods. In this article, we address a twofold challenge of modeling and planning for active perception tasks. We analyze rhoPOMDP and POMDP-IR, two frameworks for modeling active perception tasks, that restore the PWLC property of the value function. We show the mathematical equivalence of these two frameworks by showing that given a rhoPOMDP along with a policy, they can be reduced to a POMDP-IR and an equivalent policy (and vice-versa). We prove that the value function for the given rhoPOMDP (and the given policy) and the reduced POMDP-IR (and the reduced policy) is the same. To efficiently plan for active perception tasks, we identify and exploit the independence properties of POMDP-IR to reduce the computational cost of solving POMDP-IR (and rhoPOMDP). We propose greedy point-based value iteration (PBVI), a new POMDP planning method that uses greedy maximization to greatly improve scalability in the action space of an active perception POMDP. Furthermore, we show that, under certain conditions, including submodularity, the value function computed using greedy PBVI is guaranteed to have bounded error with respect to the optimal value function. We establish the conditions under which the value function of an active perception POMDP is guaranteed to be submodular. Finally, we present a detailed empirical analysis on a dataset collected from a multi-camera tracking system employed in a shopping mall. Our method achieves similar performance to existing methods but at a fraction of the computational cost leading to better scalability for solving active perception tasks.