Value Gradients with Action Adaptive Search Trees in Continuous (PO)MDPs

Solving Partially Observable Markov Decision Processes (POMDPs) in continuous state, action and observation spaces is key for autonomous planning in many real-world mobility and robotics applications. Current approaches are mostly sample based, and cannot hope to reach near-optimal solutions in reasonable time. We propose two complementary theoretical contributions. First, we formulate a novel Multiple Importance Sampling (MIS) tree for value estimation, that allows to share value information between sibling action branches. The novel MIS tree supports action updates during search time, such as gradient-based updates. Second, we propose a novel methodology to compute value gradients with online sampling based on transition likelihoods. It is applicable to MDPs, and we extend it to POMDPs via particle beliefs with the application of the propagated belief trick. The gradient estimator is computed in practice using the MIS tree with efficient Monte Carlo sampling. These two parts are combined into a new planning algorithm Action Gradient Monte Carlo Tree Search (AGMCTS). We demonstrate in a simulated environment its applicability, advantages over continuous online POMDP solvers that rely solely on sampling, and we discuss further implications.

Anytime Incremental $ρ$POMDP Planning in Continuous Spaces

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, $\rho$POMDPs, introduces belief-dependent rewards, enabling explicit reasoning about uncertainty. Existing online $\rho$POMDP solvers for continuous spaces rely on fixed belief representations, limiting adaptability and refinement - critical for tasks such as information-gathering. We present $\rho$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 $\rho$POMCPOW outperforms state-of-the-art solvers in both efficiency and solution quality.