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An informative measurement is the most efficient way to gain informationabout an unknown state. We present a first-principles derivation of ageneral-purpose dynamic programming algorithm that returns an optimal sequenceof informative measurements by sequentially maximizing the entropy of possiblemeasurement outcomes. This algorithm can be used by an autonomous agent orrobot to decide where best to measure next, planning a path corresponding to anoptimal sequence of informative measurements. The algorithm is applicable tostates and controls that are either continuous or discrete, and agent dynamicsthat is either stochastic or deterministic; including Markov decision processesand Gaussian processes. Recent results from the fields of approximate dynamicprogramming and reinforcement learning, including on-line approximations suchas rollout and Monte Carlo tree search, allow the measurement task to be solvedin real time. The resulting solutions include non-myopic paths and measurementsequences that can generally outperform, sometimes substantially, commonly usedgreedy approaches. This is demonstrated for a global search task, where on-lineplanning for a sequence of local searches is found to reduce the number ofmeasurements in the search by approximately half. A variant of the algorithm isderived for Gaussian processes for active sensing.

A Dynamic Programming Algorithm for Finding an Optimal Sequence of Informative Measurements