Data-Efficient Quadratic Q-Learning Using LMIs
<|reference_start|>Data-Efficient Quadratic Q-Learning Using LMIs: Reinforcement learning (RL) has seen significant research and application results but often requires large amounts of training data. This paper proposes two data-efficient off-policy RL methods that use parametrized Q-learning. In these methods, the Q-function is chosen to be linear in the parameters and quadratic in selected basis functions in the state and control deviations from a base policy. A cost penalizing the $\ell_1$-norm of Bellman errors is minimized. We propose two methods: Linear Matrix Inequality Q-Learning (LMI-QL) and its iterative variant (LMI-QLi), which solve the resulting episodic optimization problem through convex optimization. LMI-QL relies on a convex relaxation that yields a semidefinite programming (SDP) problem with linear matrix inequalities (LMIs). LMI-QLi entails solving sequential iterations of an SDP problem. Both methods combine convex optimization with direct Q-function learning, significantly improving learning speed. A numerical case study demonstrates their advantages over existing parametrized Q-learning methods.<|reference_end|>
@article{van hulst2024data-efficient,
    title={Data-Efficient Quadratic Q-Learning Using LMIs},
    author={J.S. van Hulst, W.P.M.H. Heemels, D.J. Antunes},
    journal={arXiv preprint arXiv:2409.11986},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.11986},
    primaryClass={eess.SY cs.SY}
}