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## Solving $K$ -MDPs

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Jonathan Ferrer-Mestres
• Function : Author
• PersonId : 1086331
Thomas G. Dietterich
• Function : Author
• PersonId : 1086332
Olivier Buffet

#### Abstract

Markov Decision Processes (MDPs) are employed to model sequential decision-making problems under uncertainty. Traditionally, algorithms to solve MDPs have focused on solving large state or action spaces. With increasing applications of MDPs to human-operated domains such as conservation of biodiversity and health, developing easy-to-interpret solutions is of paramount importance to increase uptake of MDP policies. Here, we define the problem of solving K-MDPs, i.e., given an original MDP and a constraint on the number of states (K), generate a reduced state space MDP that minimizes the difference between the original optimal MDP value function and the reduced optimal K-MDP value function. Building on existing non-transitive and transitive approximate state abstraction functions, we propose a family of three algorithms based on binary search with sub-optimality bounded polynomially in a precision parameter: ϕQ*εK-MDP-ILP, ϕQ*dK-MDP and ϕa*dK-MDP. We compare these algorithms to a greedy algorithm (ϕQ*ε Greedy K-MDP) and clustering approach (k-means++ K-MDP). On randomly generated MDPs and two computational sustainability MDPs, ϕa*dK-MDP outperformed all algorithms when it could find a feasible solution. While numerous state abstraction problems have been proposed in the literature, this is the first time that the general problem of solving K-MDPs is suggested. We hope that our work will generate future research aiming at increasing the interpretability of MDP policies in human-operated domains.

### Dates and versions

hal-03080154 , version 1 (17-12-2020)

### Identifiers

• HAL Id : hal-03080154 , version 1

### Cite

Jonathan Ferrer-Mestres, Thomas G. Dietterich, Olivier Buffet, Iadine Chadès. Solving $K$ -MDPs. ICAPS 2020 - International Conference on Automated Planning and Scheduling, Oct 2020, Nancy / Virtual, France. ⟨hal-03080154⟩

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