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.

@article{liu2025_2409.08422,
  title={ Fitted Q-Iteration via Max-Plus-Linear Approximation },
  author={ Y. Liu and M. A. S. Kolarijani },
  journal={arXiv preprint arXiv:2409.08422},
  year={ 2025 }
}