Trajectory Optimization (TO) and Reinforcement Learning (RL) are powerful and complementary tools to solve optimal control problems. On the one hand, TO can efficiently compute locally-optimal solutions, but it tends to get stuck in local minima if the problem is not convex. On the other hand, RL is typically less sensitive to non-convexity, but it requires a much higher computational effort. Recently, we have proposed CACTO (Continuous Actor-Critic with Trajectory Optimization), an algorithm that uses TO to guide the exploration of an actor-critic RL algorithm. In turns, the policy encoded by the actor is used to warm-start TO, closing the loop between TO and RL. In this work, we present an extension of CACTO exploiting the idea of Sobolev learning. To make the training of the critic network faster and more data efficient, we enrich it with the gradient of the Value function, computed via a backward pass of the differential dynamic programming algorithm. Our results show that the new algorithm is more efficient than the original CACTO, reducing the number of TO episodes by a factor ranging from 3 to 10, and consequently the computation time. Moreover, we show that CACTO-SL helps TO to find better minima and to produce more consistent results.

本研究提出了一种基于轨迹优化和强化学习的算法CACTO-SL，通过使用梯度和值函数来加速批评网络的训练，实验证明该算法比原始的CACTO更高效，能够减少计算时间和寻找更好的极小值，同时产生更一致的结果。

CACTO-SL：使用Sobolev学习优化连续的Actor-Critic和轨迹优化