Adaptive Smoothing Path Integral Control

In Path Integral control problems a representation of an optimally controlled dynamical system can be formally computed and serve as a guidepost to learn a parametrized policy. The Path Integral Cross-Entropy (PICE) method tries to exploit this, but is hampered by poor sample efficiency. We propose a model-free algorithm called ASPIC (Adaptive Smoothing of Path Integral Control) that applies an inf-convolution to the cost function to speedup convergence of policy optimization. We identify PICE as the infinite smoothing limit of such technique and show that the sample efficiency problems that PICE suffers disappear for finite levels of smoothing. For zero smoothing this method becomes a greedy optimization of the cost, which is the standard approach in current reinforcement learning. We show analytically and empirically that intermediate levels of smoothing are optimal, which renders the new method superior to both PICE and direct cost-optimization.