51. Sample Complexity of Kernel-Based Q-Learning
- Author
-
Yeh, Sing-Yuan, Chang, Fu-Chieh, Yueh, Chang-Wei, Wu, Pei-Yuan, Bernacchia, Alberto, and Vakili, Sattar
- Subjects
Computer Science - Machine Learning ,Computer Science - Artificial Intelligence ,Statistics - Machine Learning - Abstract
Modern reinforcement learning (RL) often faces an enormous state-action space. Existing analytical results are typically for settings with a small number of state-actions, or simple models such as linearly modeled Q-functions. To derive statistically efficient RL policies handling large state-action spaces, with more general Q-functions, some recent works have considered nonlinear function approximation using kernel ridge regression. In this work, we derive sample complexities for kernel based Q-learning when a generative model exists. We propose a nonparametric Q-learning algorithm which finds an $\epsilon$-optimal policy in an arbitrarily large scale discounted MDP. The sample complexity of the proposed algorithm is order optimal with respect to $\epsilon$ and the complexity of the kernel (in terms of its information gain). To the best of our knowledge, this is the first result showing a finite sample complexity under such a general model.
- Published
- 2023