Nonparametric Infinite Horizon Kullback-Leibler Stochastic Control

We present two nonparametric approaches to Kullback-Leibler (KL) control, or linearly-solvable Markov decision problem (LMDP) based on Gaussian processes (GP) and Nystr\"{o}m approximation. Compared to recently developed parametric methods, the proposed data-driven frameworks feature accurate function approximation and efficient on-line operations. Theoretically, we derive the mathematical connection of KL control based on dynamic programming with earlier work in control theory which relies on information theoretic dualities for the infinite time horizon case. Algorithmically, we give explicit optimal control policies in nonparametric forms, and propose on-line update schemes with budgeted computational costs. Numerical results demonstrate the effectiveness and usefulness of the proposed frameworks

A phase-1 approach for the generalized simplex algorithm

AbstractA new simplex variant allowing basis deficiency has recently been proposed to attack the degeneracy [1]. As a generalization of the simplex algorithm, it uses a Phase-1 procedure, solving an auxiliary problem with piecewise-linear sums of infeasibilities as its objective. In this paper, we develop another Phase-1 approach that only introduces a single artificial variable. Unlike the former, which needs a crash procedure to supply an initial basis, the proposed Phase-1 is able to get itself started from scratch, with an artificial basis having a single column. Computational results with a set of standard test problems from NETLIB are also reported

Agile Autonomous Driving using End-to-End Deep Imitation Learning

We present an end-to-end imitation learning system for agile, off-road autonomous driving using only low-cost sensors. By imitating a model predictive controller equipped with advanced sensors, we train a deep neural network control policy to map raw, high-dimensional observations to continuous steering and throttle commands. Compared with recent approaches to similar tasks, our method requires neither state estimation nor on-the-fly planning to navigate the vehicle. Our approach relies on, and experimentally validates, recent imitation learning theory. Empirically, we show that policies trained with online imitation learning overcome well-known challenges related to covariate shift and generalize better than policies trained with batch imitation learning. Built on these insights, our autonomous driving system demonstrates successful high-speed off-road driving, matching the state-of-the-art performance.Comment: 13 pages, Robotics: Science and Systems (RSS) 201