Michael H. Lim

Michael H. Lim, Tyler J. Becker, Mykel J. Kochenderfer et al.

Partially observable Markov decision processes (POMDPs) provide a flexible representation for real-world decision and control problems. However, POMDPs are notoriously difficult to solve, especially when the state and observation spaces are continuous or hybrid, which is often the case for physical systems. While recent online sampling-based POMDP algorithms that plan with observation likelihood weighting have shown practical effectiveness, a general theory characterizing the approximation error of the particle filtering techniques that these algorithms use has not previously been proposed. Our main contribution is bounding the error between any POMDP and its corresponding finite sample particle belief MDP (PB-MDP) approximation. This fundamental bridge between PB-MDPs and POMDPs allows us to adapt any sampling-based MDP algorithm to a POMDP by solving the corresponding particle belief MDP, thereby extending the convergence guarantees of the MDP algorithm to the POMDP. Practically, this is implemented by using the particle filter belief transition model as the generative model for the MDP solver. While this requires access to the observation density model from the POMDP, it only increases the transition sampling complexity of the MDP solver by a factor of $\mathcal{O}(C)$, where $C$ is the number of particles. Thus, when combined with sparse sampling MDP algorithms, this approach can yield algorithms for POMDPs that have no direct theoretical dependence on the size of the state and observation spaces. In addition to our theoretical contribution, we perform five numerical experiments on benchmark POMDPs to demonstrate that a simple MDP algorithm adapted using PB-MDP approximation, Sparse-PFT, achieves performance competitive with other leading continuous observation POMDP solvers.

Sampada Deglurkar, Michael H. Lim, Johnathan Tucker et al.

The Partially Observable Markov Decision Process (POMDP) is a powerful framework for capturing decision-making problems that involve state and transition uncertainty. However, most current POMDP planners cannot effectively handle high-dimensional image observations prevalent in real world applications, and often require lengthy online training that requires interaction with the environment. In this work, we propose Visual Tree Search (VTS), a compositional learning and planning procedure that combines generative models learned offline with online model-based POMDP planning. The deep generative observation models evaluate the likelihood of and predict future image observations in a Monte Carlo tree search planner. We show that VTS is robust to different types of image noises that were not present during training and can adapt to different reward structures without the need to re-train. This new approach significantly and stably outperforms several baseline state-of-the-art vision POMDP algorithms while using a fraction of the training time.

Michael H. Lim, Andy Zeng, Brian Ichter et al.

Enabling robots to solve multiple manipulation tasks has a wide range of industrial applications. While learning-based approaches enjoy flexibility and generalizability, scaling these approaches to solve such compositional tasks remains a challenge. In this work, we aim to solve multi-task learning through the lens of sequence-conditioning and weighted sampling. First, we propose a new suite of benchmark specifically aimed at compositional tasks, MultiRavens, which allows defining custom task combinations through task modules that are inspired by industrial tasks and exemplify the difficulties in vision-based learning and planning methods. Second, we propose a vision-based end-to-end system architecture, Sequence-Conditioned Transporter Networks, which augments Goal-Conditioned Transporter Networks with sequence-conditioning and weighted sampling and can efficiently learn to solve multi-task long horizon problems. Our analysis suggests that not only the new framework significantly improves pick-and-place performance on novel 10 multi-task benchmark problems, but also the multi-task learning with weighted sampling can vastly improve learning and agent performances on individual tasks.

Michael H. Lim, Claire J. Tomlin, Zachary N. Sunberg

This paper introduces Voronoi Progressive Widening (VPW), a generalization of Voronoi optimistic optimization (VOO) and action progressive widening to partially observable Markov decision processes (POMDPs). Tree search algorithms can use VPW to effectively handle continuous or hybrid action spaces by efficiently balancing local and global action searching. This paper proposes two VPW-based algorithms and analyzes them from theoretical and simulation perspectives. Voronoi Optimistic Weighted Sparse Sampling (VOWSS) is a theoretical tool that justifies VPW-based online solvers, and it is the first algorithm with global convergence guarantees for continuous state, action, and observation POMDPs. Voronoi Optimistic Monte Carlo Planning with Observation Weighting (VOMCPOW) is a versatile and efficient algorithm that consistently outperforms state-of-the-art POMDP algorithms in several simulation experiments.

Michael H. Lim, Claire J. Tomlin, Zachary N. Sunberg

Partially observable Markov decision processes (POMDPs) with continuous state and observation spaces have powerful flexibility for representing real-world decision and control problems but are notoriously difficult to solve. Recent online sampling-based algorithms that use observation likelihood weighting have shown unprecedented effectiveness in domains with continuous observation spaces. However there has been no formal theoretical justification for this technique. This work offers such a justification, proving that a simplified algorithm, partially observable weighted sparse sampling (POWSS), will estimate Q-values accurately with high probability and can be made to perform arbitrarily near the optimal solution by increasing computational power.