Muhammad Suhail Saleem, Rishi Veerapaneni, Maxim Likhachev

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

Introduction

Lazy heuristic search for solving pomdps with expensive-to-compute belief transitions. Lazy heuristic search (Lazy RTDP-Bel, Lazy LAO*) solves POMDPs with expensive belief transitions. Dramatically cuts robotics planning time by deferring costly computations.

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. These algorithms are specific instantiations of the broader idea of lazy search for POMDPs. 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.

Review

This paper addresses a critical practical limitation in solving Partially Observable Markov Decision Processes (POMDPs) using heuristic search methods like RTDP-Bel and LAO*. While these algorithms are effective for computing optimal or bounded sub-optimal solutions for belief MDPs, their application often falters when belief state transitions become prohibitively expensive to compute. The authors astutely point out that this is a common and severe challenge in robotics domains, where underlying physics simulations, raycasting, or expensive collision checks for transition and observation models incur significant computational costs, leading to unacceptably long planning times. The core problem identified is the high cost of Bayesian updates for successor beliefs, which the proposed work aims to alleviate. To mitigate the described computational bottleneck, the authors introduce novel algorithms: Lazy RTDP-Bel and Lazy LAO*. These methods are presented as specific instantiations of a broader "lazy search" paradigm for POMDPs, fundamentally deferring the expensive computation of belief state transitions. The key innovation lies in leveraging Q-value estimation to circumvent the immediate need for full belief propagation, thereby streamlining the search process. A significant practical contribution mentioned is the discussion of concrete Q-value estimation techniques tailored for commonly encountered problem classes, which promises to make the proposed lazy planners more accessible and broadly applicable. This strategic postponement of costly computations is central to achieving the promised reduction in planning time. The effectiveness of the proposed Lazy RTDP-Bel and Lazy LAO* algorithms is reportedly demonstrated across a diverse set of challenging robotics domains. The abstract highlights applications in contact-rich manipulation for pose estimation, outdoor navigation in rough terrain, and indoor navigation with a 1-D Lidar sensor, all scenarios where expensive simulations and checks are prevalent. The results reportedly show "superior performance" and a "dramatic improvement" in planning speed, critically, *while maintaining solution quality*. This work represents a significant advance for practical POMDP planning, offering a compelling solution to a long-standing computational hurdle. Its implications for deploying POMDPs in real-world robotic systems, particularly those requiring complex physical interactions or sophisticated sensing, are substantial, making this a highly valuable contribution to the field.

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