Sample Complexity of Kernel-Based Q-Learning
This provides a theoretical foundation for efficient RL in complex environments, though it is incremental as it builds on existing kernel methods.
The paper tackles the problem of reinforcement learning in large state-action spaces with general Q-functions by deriving sample complexities for kernel-based Q-learning, achieving an order-optimal sample complexity for finding an ε-optimal policy.
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 $ε$-optimal policy in an arbitrarily large scale discounted MDP. The sample complexity of the proposed algorithm is order optimal with respect to $ε$ 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.