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Continuous POMDPs with general belief-dependent rewards are notoriouslydifficult to solve online. In this paper, we present a complete provable theoryof adaptive multilevel simplification for the setting of a given externallyconstructed belief tree and MCTS that constructs the belief tree on the flyusing an exploration technique. Our theory allows to accelerate POMDP planningwith belief-dependent rewards without any sacrifice in the quality of theobtained solution. We rigorously prove each theoretical claim in the proposedunified theory. Using the general theoretical results, we present threealgorithms to accelerate continuous POMDP online planning with belief-dependentrewards. Our two algorithms, SITH-BSP and LAZY-SITH-BSP, can be utilized on topof any method that constructs a belief tree externally. The third algorithm,SITH-PFT, is an anytime MCTS method that permits to plug-in any explorationtechnique. All our methods are guaranteed to return exactly the same optimalaction as their unsimplified equivalents. We replace the costly computation ofinformation-theoretic rewards with novel adaptive upper and lower bounds whichwe derive in this paper, and are of independent interest. We show that they areeasy to calculate and can be tightened by the demand of our algorithms. Ourapproach is general; namely, any bounds that monotonically converge to thereward can be easily plugged-in to achieve significant speedup without any lossin performance. Our theory and algorithms support the challenging setting ofcontinuous states, actions, and observations. The beliefs can be parametric orgeneral and represented by weighted particles. We demonstrate in simulation asignificant speedup in planning compared to baseline approaches with guaranteedidentical performance.

No Compromise in Solution Quality: Speeding Up Belief-dependent Continuous POMDPs via Adaptive Multilevel Simplification