Solving the Linear Bellman Equation via Dual Kernel Embeddings

We introduce a data-efficient approach for solving the linear Bellman equation, which corresponds to a class of Markov decision processes (MDPs) and stochastic optimal control (SOC) problems. We show that this class of control problem can be cast as a stochastic composition optimization problem, which can be further reformulated as a saddle point problem and solved via dual kernel embeddings [1]. Our method is model-free and using only one sample per state transition from stochastic dynamical systems. Different from related work such as Z-learning [2, 3] based on temporal-difference learning [4], our method is an online algorithm following the true stochastic gradient. Numerical results are provided, showing that our method outperforms the Z-learning algorithm.