Bayesian Optimization for Continuous-time Optimal Control Problem with Unknown Cost Function
Bayesian Optimization for Continuous-time Optimal Control Problem with Unknown Cost Function
复制标题
DOI：
10.9746/sicetr.55.100
复制
发表时间：
2019
期刊：
影响因子：
--
通讯作者：
Mitsuru Toyoda
中科院分区：
文献类型：
--
作者：
Mitsuru Toyoda
本文将贝叶斯学习方法扩展为高斯过程回归，重点研究阶段成本函数未知的连续时间最优控制问题。应用控制参数化方法，将最优控制问题近似化为非线性规划问题，并分析了高斯过程回归估计的代价函数的统计性。为了求解贝叶斯优化问题，提出了一种有效的基于变分法的梯度计算方法。此外，通过对强盗问题的最优性分析，给出了算法实现的后悔界的阶数。
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.