未知評価関数を有する連続時間最適制御問題におけるベイズ的最適化手法

抄録

This study presents an extension of Bayesian learning approach with Gaussian process regression focusing on continuous-time optimal control problem in which stage cost function is unknown. By applying control parametrization method, the optimal control problem can be approximately formulated as a nonlinear programming problem, and the statistics of the cost function estimated by Gaussian process regression is analyzed. To obtain a solution to Bayesian optimization problem, an effective gradient calculation based on variational method is developed. Furthermore, the analysis of optimality in the fashion of bandit problem provides the order of regret bound achieved by the proposed algorithm.