Measurement Simplification in \rho-POMDP with Performance Guarantees

Decision making under uncertainty is at the heart of any autonomous system acting with imperfect information. The cost of solving the decision making problem is exponential in the action and observation spaces, thus rendering it unfeasible for many online systems. This paper introduces a novel approach to efficient decision-making, by partitioning the high-dimensional observation space. Using the partitioned observation space, we formulate analytical bounds on the expected information-theoretic reward, for general belief distributions. These bounds are then used to plan efficiently while keeping performance guarantees. We show that the bounds are adaptive, computationally efficient, and that they converge to the original solution. We extend the partitioning paradigm and present a hierarchy of partitioned spaces that allows greater efficiency in planning. We then propose a specific variant of these bounds for Gaussian beliefs and show a theoretical performance improvement of at least a factor of 4. Finally, we compare our novel method to other state of the art algorithms in active SLAM scenarios, in simulation and in real experiments. In both cases we show a significant speed-up in planning with performance guarantees

Online algorithms for POMDPs with continuous state, action, and observation spaces

Online solvers for partially observable Markov decision processes have been applied to problems with large discrete state spaces, but continuous state, action, and observation spaces remain a challenge. This paper begins by investigating double progressive widening (DPW) as a solution to this challenge. However, we prove that this modification alone is not sufficient because the belief representations in the search tree collapse to a single particle causing the algorithm to converge to a policy that is suboptimal regardless of the computation time. This paper proposes and evaluates two new algorithms, POMCPOW and PFT-DPW, that overcome this deficiency by using weighted particle filtering. Simulation results show that these modifications allow the algorithms to be successful where previous approaches fail.Comment: Added Multilane sectio