Data-Efficient Quadratic Q-Learning Using LMIs
| Autor: | van Hulst, J. S., Heemels, W. P. M. H., Antunes, D. J. |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: Accepted for Presentation at 63rd IEEE Conference on Decision and Control, CDC 2024, Milan, Italy, 2024 |
| Databáze: | arXiv |
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