Value iteration for streaming data on a continuous space with gradient method in an RKHS.

Area of Science:

• Machine Learning
• Reinforcement Learning Theory
• Computational Statistics

Background:

• Classical reinforcement learning theory is limited to tabular or linear settings.
• Generalizing to continuous state and action spaces requires advanced function approximation and complexity analysis.
• Stochastic gradient descent (SGD) is a common iterative update method.

Purpose of the Study:

• To establish theoretical guarantees for reinforcement learning in continuous state and action spaces.
• To analyze the sample complexity of reinforcement learning prediction problems with streaming data.
• To demonstrate the efficiency of gradient descent in this setting.

Main Methods:

• Utilizing reproducing kernel Hilbert spaces (RKHS) for function representation.
• Applying gradient descent for value function updates.
• Analyzing sample complexity considering function smoothness.

Main Results:

• Established polynomial sample complexity for reinforcement learning in continuous spaces.
• Proved that gradient descent achieves efficient computation of the value function.
• Demonstrated convergence rates close to the optimal 1/N for parametric SGD.

Conclusions:

• Gradient descent is an efficient and computationally convenient algorithm for reinforcement learning with streaming data.
• The proposed framework provides theoretical support for using gradient descent in continuous reinforcement learning settings.
• The findings offer a significant advancement in understanding reinforcement learning theory for complex environments.