Ron Benchetrit

Idan Lev-Yehudi, Michael Novitsky, Moran Barenboim et al.

Autonomous systems that operate in continuous state, action, and observation spaces require planning and reasoning under uncertainty. Existing online planning methods for such POMDPs are almost exclusively sample-based, yet they forego the power of high-dimensional gradient optimization as combining it into Monte Carlo Tree Search (MCTS) has proved difficult, especially in non-parametric settings. We close this gap with three contributions. First, we derive a novel action-gradient theorem for both MDPs and POMDPs in terms of transition likelihoods, making gradient information accessible during tree search. Second, we introduce the Multiple Importance Sampling (MIS) tree, that re-uses samples for changing action branches, yielding consistent value estimates that enable in-search gradient steps. Third, we derive exact transition probability computation via the area formula for smooth generative models common in physical domains, a result of independent interest. These elements combine into Action-Gradient Monte Carlo Tree Search (AGMCTS), the first planner to blend non-parametric particle search with online gradient refinement in POMDPs. Across several challenging continuous MDP and POMDP benchmarks, AGMCTS outperforms widely-used sample-only solvers in solution quality.

Ron Benchetrit, Idan Lev-Yehudi, Andrey Zhitnikov et al.

Partially Observable Markov Decision Processes (POMDPs) provide a robust framework for decision-making under uncertainty in applications such as autonomous driving and robotic exploration. Their extension, $ρ$POMDPs, introduces belief-dependent rewards, enabling explicit reasoning about uncertainty. Existing online $ρ$POMDP solvers for continuous spaces rely on fixed belief representations, limiting adaptability and refinement - critical for tasks such as information-gathering. We present $ρ$POMCPOW, an anytime solver that dynamically refines belief representations, with formal guarantees of improvement over time. To mitigate the high computational cost of updating belief-dependent rewards, we propose a novel incremental computation approach. We demonstrate its effectiveness for common entropy estimators, reducing computational cost by orders of magnitude. Experimental results show that $ρ$POMCPOW outperforms state-of-the-art solvers in both efficiency and solution quality.