Lazy Heuristic Search for Solving POMDPs with Expensive-to-Compute Belief Transitions

TL;DR

This paper introduces lazy heuristic search algorithms for POMDPs that defer costly belief transition computations, significantly reducing planning time in robotics applications while maintaining solution quality.

Contribution

The paper proposes Lazy RTDP-Bel and Lazy LAO* algorithms that postpone expensive belief updates using Q-value estimation, enhancing efficiency in robotics POMDPs.

Findings

Lazy planners outperform traditional methods in planning speed.

They maintain solution quality despite deferred belief computations.

Effective Q-value estimation techniques are discussed for practical use.

Abstract

Heuristic search solvers like RTDP-Bel and LAO* have proven effective for computing optimal and bounded sub-optimal solutions for Partially Observable Markov Decision Processes (POMDPs), which are typically formulated as belief MDPs. A belief represents a probability distribution over possible system states. Given a parent belief and an action, computing belief state transitions involves Bayesian updates that combine the transition and observation models of the POMDP to determine successor beliefs and their transition probabilities. However, there is a class of problems, specifically in robotics, where computing these transitions can be prohibitively expensive due to costly physics simulations, raycasting, or expensive collision checks required by the underlying transition and observation models, leading to long planning times. To address this challenge, we propose Lazy RTDP-Bel and Lazy LAO*, which defer computing expensive belief state transitions by leveraging Q-value estimation, significantly reducing planning time. We demonstrate the superior performance of the proposed lazy planners in domains such as contact-rich manipulation for pose estimation, outdoor navigation in rough terrain, and indoor navigation with a 1-D LiDAR sensor. Additionally, we discuss practical Q-value estimation techniques for commonly encountered problem classes that our lazy planners can leverage. Our results show that lazy heuristic search methods dramatically improve planning speed by postponing expensive belief transition evaluations while maintaining solution quality.