Fitted Q-Iteration via Max-Plus-Linear Approximation
<|reference_start|>Fitted Q-Iteration via Max-Plus-Linear Approximation: In this study, we consider the application of max-plus-linear approximators for Q-function in offline reinforcement learning of discounted Markov decision processes. In particular, we incorporate these approximators to propose novel fitted Q-iteration (FQI) algorithms with provable convergence. Exploiting the compatibility of the Bellman operator with max-plus operations, we show that the max-plus-linear regression within each iteration of the proposed FQI algorithm reduces to simple max-plus matrix-vector multiplications. We also consider the variational implementation of the proposed algorithm which leads to a per-iteration complexity that is independent of the number of samples.<|reference_end|>
@article{liu2024fitted,
    title={Fitted Q-Iteration via Max-Plus-Linear Approximation},
    author={Y. Liu and M. A. S. Kolarijani},
    journal={arXiv preprint arXiv:2409.08422},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.08422},
    primaryClass={math.OC cs.AI cs.LG cs.SY eess.SY}
}