Welfare Maximization Algorithm for Solving Budget-Constrained Multi-Component POMDPs
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866913467543322624 |
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| author | Vora, Manav Thangeda, Pranay Grussing, Michael N. Ornik, Melkior |
| author_facet | Vora, Manav Thangeda, Pranay Grussing, Michael N. Ornik, Melkior |
| contents | Partially Observable Markov Decision Processes (POMDPs) provide an efficient way to model real-world sequential decision making processes. Motivated by the problem of maintenance and inspection of a group of infrastructure components with independent dynamics, this paper presents an algorithm to find the optimal policy for a multi-component budget-constrained POMDP. We first introduce a budgeted-POMDP model (b-POMDP) which enables us to find the optimal policy for a POMDP while adhering to budget constraints. Next, we prove that the value function or maximal collected reward for a b-POMDP is a concave function of the budget for the finite horizon case. Our second contribution is an algorithm to calculate the optimal policy for a multi-component budget-constrained POMDP by finding the optimal budget split among the individual component POMDPs. The optimal budget split is posed as a welfare maximization problem and the solution is computed by exploiting the concave nature of the value function. We illustrate the effectiveness of the proposed algorithm by proposing a maintenance and inspection policy for a group of real-world infrastructure components with different deterioration dynamics, inspection and maintenance costs. We show that the proposed algorithm vastly outperforms the policy currently used in practice. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_10302 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Welfare Maximization Algorithm for Solving Budget-Constrained Multi-Component POMDPs Vora, Manav Thangeda, Pranay Grussing, Michael N. Ornik, Melkior Optimization and Control Artificial Intelligence Partially Observable Markov Decision Processes (POMDPs) provide an efficient way to model real-world sequential decision making processes. Motivated by the problem of maintenance and inspection of a group of infrastructure components with independent dynamics, this paper presents an algorithm to find the optimal policy for a multi-component budget-constrained POMDP. We first introduce a budgeted-POMDP model (b-POMDP) which enables us to find the optimal policy for a POMDP while adhering to budget constraints. Next, we prove that the value function or maximal collected reward for a b-POMDP is a concave function of the budget for the finite horizon case. Our second contribution is an algorithm to calculate the optimal policy for a multi-component budget-constrained POMDP by finding the optimal budget split among the individual component POMDPs. The optimal budget split is posed as a welfare maximization problem and the solution is computed by exploiting the concave nature of the value function. We illustrate the effectiveness of the proposed algorithm by proposing a maintenance and inspection policy for a group of real-world infrastructure components with different deterioration dynamics, inspection and maintenance costs. We show that the proposed algorithm vastly outperforms the policy currently used in practice. |
| title | Welfare Maximization Algorithm for Solving Budget-Constrained Multi-Component POMDPs |
| topic | Optimization and Control Artificial Intelligence |
| url | https://arxiv.org/abs/2303.10302 |