深層微分値関数と行動制約を用いたHJB最適フィードバック制御
HJB Optimal Feedback Control with Deep Differential Value Functions and Action Constraints
Hamilton-Jacobi-Bellman方程式に深層微分ネットワークを組み込み、行動制約を自然に満たす連続時間の最適フィードバック制御則を学習する手法を提案した。再計画なしに任意の状態から最適軌道を生成できる。
著者: Michael Lutter, Boris Belousov, Kim Listmann, Debora Clever, Jan Peters
分類: cs.LG, cs.RO, stat.ML
原文アブストラクト
Learning optimal feedback control laws capable of executing optimal trajectories is essential for many robotic applications. Such policies can be learned using reinforcement learning or planned using optimal control. While reinforcement learning is sample inefficient, optimal control only plans an optimal trajectory from a specific starting configuration. In this paper we propose deep optimal feedback control to learn an optimal feedback policy rather than a single trajectory. By exploiting the inherent structure of the robot dynamics and strictly convex action cost, we can derive principled cost functions such that the optimal policy naturally obeys the action limits, is globally optimal and stable on the training domain given the optimal value function. The corresponding optimal value function is learned end-to-end by embedding a deep differential network in the Hamilton-Jacobi-Bellmann differential equation and minimizing the error of this equality while simultaneously decreasing the discounting from short- to far-sighted to enable the learning. Our proposed approach enables us to learn an optimal feedback control law in continuous time, that in contrast to existing approaches generates an optimal trajectory from any point in state-space without the need of replanning. The resulting approach is evaluated on non-linear systems and achieves optimal feedback control, where standard optimal control methods require frequent replanning.
