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Partially Observable Markov Decision Processes (POMDPs) offer a promisingworld representation for autonomous agents, as they can model both transitionaland perceptual uncertainties. Calculating the optimal solution to POMDPproblems can be computationally expensive as they require reasoning over the(possibly infinite) space of beliefs. Several approaches have been proposed toovercome this difficulty, such as discretizing the belief space, point-basedbelief sampling, and Monte Carlo tree search. The Real-Time Dynamic Programmingapproach of the RTDP-Bel algorithm approximates the value function by storingit in a hashtable with discretized belief keys. We propose an extension to theRTDP-Bel algorithm which we call Belief Branch and Bound RTDP (B$^3$RTDP). Ouralgorithm uses a bounded value function representation and takes advantage ofthis in two novel ways: a search-bounding technique based on action selectionconvergence probabilities, and a method for leveraging early action convergencecalled the \textit{Convergence Frontier}. Lastly, we empirically demonstratethat B$^3$RTDP can achieve greater returns in less time than thestate-of-the-art SARSOP solver on known POMDP problems.

B$^3$RTDP: A Belief Branch and Bound Real-Time Dynamic Programming Approach to Solving POMDPs