Technical Report MSC-2021-38

Title: Online Partially Observable Markov Decision Process Planning via Simplification
Authors: Ori Sztyglic
Supervisors: Vadim Indelman
PDFCurrently accessibly only within the Technion network
Abstract: Partially Observable Markov Decision Process (POMDPs) are notoriously hard to solve. In this work we consider online planning in partially observable domains. Solving the corresponding POMDP problem is a very challenging task, particularly in an online setting.

Our key contribution is a novel algorithmic approach, Simplified Information Theoretic Belief Space Planning (SITH-BSP), which aims to speed up POMDP planning considering belief-dependent rewards, without compromising on the solution's accuracy. We do so by mathematically relating the simplified elements of the problem to the corresponding counterparts of the original problem. Specifically, we focus on belief simplification and use it to formulate bounds on the corresponding original belief-dependent rewards. These bounds in turn are used to perform branch pruning over the belief tree, in the process of calculating the optimal policy. We further introduce the notion of adaptive simplification, while re-using calculations between different simplification levels, and exploit it to prune, at each level in the belief tree, all branches but one.

Therefore, our approach is guaranteed to find the optimal solution of the original problem but with substantial speedup. As a second key contribution, we derive novel analytical bounds for differential entropy, considering a sampling-based belief representation, which we believe are of interest on their own. We validate our approach in simulation using these bounds and where simplification corresponds to reducing the number of samples, exhibiting a significant computational speedup while yielding the optimal solution. Finally, we embed the paradigm of simplification into the MCTS algorithm. In particular, we present Simplified Information-Theoretic Particle Filter Tree (SITH-PFT), a novel variant to the MCTS algorithm that considers information-theoretic rewards but avoids the need to calculate them completely. Our approach is general; namely, any converging to the reward bounds can be easily plugged-in to achieve substantial speedup without any loss in performance.

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