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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 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.
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POMDP inference and robust solution via deep reinforcement learning: an application to railway optimal maintenance
Abstract Partially Observable Markov Decision Processes (POMDPs) can model complex sequential decision-making problems under stochastic and uncertain environments. A main reason hindering their broad adoption in real-world applications is the unavailability of a suitable POMDP model or a simulator thereof. Available solution algorithms, such as Reinforcement Learning (RL), typically benefit from the knowledge of the transition dynamics and the observation generating process, which are often unknown and non-trivial to infer. In this work, we propose a combined framework for inference and robust solution of POMDPs via deep RL. First, all transition and observation model parameters are jointly inferred via Markov Chain Monte Carlo sampling of a hidden Markov model, which is conditioned on actions, in order to recover full posterior distributions from the available data. The POMDP with uncertain parameters is then solved via deep RL techniques with the parameter distributions incorporated into the solution via domain randomization, in order to develop solutions that are robust to model uncertainty. As a further contribution, we compare the use of Transformers and long short-term memory networks, which constitute model-free RL solutions and work directly on the observation space, with an approach termed the belief-input method, which works on the belief space by exploiting the learned POMDP model for belief inference. We apply these methods to the real-world problem of optimal maintenance planning for railway assets and compare the results with the current real-life policy. We show that the RL policy learned by the belief-input method is able to outperform the real-life policy by yielding significantly reduced life-cycle costs.
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- Award ID(s):
- 1751941
- PAR ID:
- 10552115
- Publisher / Repository:
- Springer
- Date Published:
- Journal Name:
- Machine Learning
- Volume:
- 113
- Issue:
- 10
- ISSN:
- 0885-6125
- Page Range / eLocation ID:
- 7967 to 7995
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1007/s10994-024-06559-2
