Entropy-Regularized Backward Stochastic Control System With Partial Information: Optimality and Algorithm Implementation

In this paper, we study the optimal exploratory control for entropy regularized backward stochastic control system with partial information. The stochastic maximum principle is given for the concerned nonlinear system. Then the existence and uniqueness of optimal control for the entropy regularized linear quadratic control problem with partial information is proved. Based on theoretical results, we design an efficient iterative algorithm for optimal control of linear-convex stochastic systems with partial information in the case that the state variable and the control variable are separated in cost functional, and moreover, we prove that the algorithm has an 1/n-order convergence rate. Finally, numerical examples are given to demonstrate the effectiveness of our proposed algorithm.