CACTO-SL: Using Sobolev Learning to improve Continuous Actor-Critic with Trajectory Optimization
This work addresses computational efficiency in optimal control algorithms for robotics or autonomous systems, but it is incremental as it builds directly on the existing CACTO method.
The authors tackled the problem of improving the efficiency and performance of the CACTO algorithm, which combines trajectory optimization and reinforcement learning for optimal control, by incorporating Sobolev learning to accelerate critic network training. The result was a reduction in the number of trajectory optimization episodes by a factor of 3 to 10, leading to faster computation and better minima.
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.