Motivated by recent advances in Deep Learning for robot control, this paper considers two learning algorithms in terms of how they acquire demonstrations. "Human-Centric" (HC) sampling is the standard supervised learning algorithm, where a human supervisor demonstrates the task by teleoperating the robot to provide trajectories consisting of state-control pairs. "Robot-Centric" (RC) sampling is an increasingly popular alternative used in algorithms such as DAgger, where a human supervisor observes the robot executing a learned policy and provides corrective control labels for each state visited. RC sampling can be challenging for human supervisors and prone to mislabeling. RC sampling can also induce error in policy performance because it repeatedly visits areas of the state space that are harder to learn. Although policies learned with RC sampling can be superior to HC sampling for standard learning models such as linear SVMs, policies learned with HC sampling may be comparable with highly-expressive learning models such as deep learning and hyper-parametric decision trees, which have little model error. We compare HC and RC using a grid world and a physical robot singulation task, where in the latter the input is a binary image of a connected set of objects on a planar worksurface and the policy generates a motion of the gripper to separate one object from the rest. We observe in simulation that for linear SVMs, policies learned with RC outperformed those learned with HC but that with deep models this advantage disappears. We also find that with RC, the corrective control labels provided by humans can be highly inconsistent. We prove there exists a class of examples where in the limit, HC is guaranteed to converge to an optimal policy while RC may fail to converge.
@cite_1 analyzed RC sampling as online optimization. They propose DAgger, an RC sampling algorithm, and show that the error for the robot’s policy is linear in @math for strongly convex losses (e.g. regularized linear or kernelized regression). However, the error also depends on the expected loss on the data collected during RC, which may be high due to observing complex recovery behaviors. We analyze this effect and show how it can prevent RC from converging to the supervisor's policy in Section V-A.
@cite_1
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Recovering low-rank and sparse matrices from incomplete or corrupted observations is an important problem in statistics, machine learning, computer vision, as well as signal and image processing. In theory, this problem can be solved by the natural convex joint mixed relaxations (i.e., l 1 -norm and trace norm) under certain conditions. However, all current provable algorithms suffer from superlinear per-iteration cost, which severely limits their applicability to large-scale problems. In this paper, we propose a scalable, provable and structured robust bilinear factorization (RBF) method to recover low-rank and sparse matrices from missing and grossly corrupted data, i.e., robust matrix completion (RMC), or incomplete and grossly corrupted measurements, i.e., compressive principal component pursuit (CPCP). Specifically, we first present two small-scale matrix trace norm regularized bilinear factorization models for RMC and CPCP problems, in which repetitively calculating SVD of a large-scale matrix is replaced by updating two much smaller factor matrices. Then, we apply the alternating direction method of multipliers (ADMM) to efficiently solve the RMC problems. Finally, we provide the convergence analysis of our algorithm, and extend it to address general CPCP problems. Experimental results verified both the efficiency and effectiveness of our method compared with the state-of-the-art methods. We demonstrate a simple greedy algorithm that can reliably recover a vector v ∈ R from incomplete and inaccurate measurements x = Φv + e. Here Φ is a N × d measurement matrix with N ≪ d, and e is an error vector. Our algorithm, Regularized Orthogonal Matching Pursuit (ROMP), seeks to close the gap between two major approaches to sparse recovery. It combines the speed and ease of implementation of the greedy methods with the strong guarantees of the convex programming methods. For any measurement matrix Φ that satisfies a Uniform Uncertainty Principle, ROMP recovers a signal v with O(n) nonzeros from its inaccurate measurements x in at most n iterations, where each iteration amounts to solving a Least Squares Problem. The noise level of the recovery is proportional to √ logn‖e‖2. In particular, if the error term e vanishes the reconstruction is exact. This stability result extends naturally to the very accurate recovery of approximately sparse signals. Randomized coordinate descent (RCD) methods are state-of-the-art algorithms for training linear predictors via minimizing regularized empirical risk. When the number of examples ( @math ) is much larger than the number of features ( @math ), a common strategy is to apply RCD to the dual problem. On the other hand, when the number of features is much larger than the number of examples, it makes sense to apply RCD directly to the primal problem. In this paper we provide the first joint study of these two approaches when applied to L2-regularized ERM. First, we show through a rigorous analysis that for dense data, the above intuition is precisely correct. However, we find that for sparse and structured data, primal RCD can significantly outperform dual RCD even if @math , and vice versa, dual RCD can be much faster than primal RCD even if @math . Moreover, we show that, surprisingly, a single sampling strategy minimizes both the (bound on the) number of iterations and the overall expected complexity of RCD. Note that the latter complexity measure also takes into account the average cost of the iterations, which depends on the structure and sparsity of the data, and on the sampling strategy employed. We confirm our theoretical predictions using extensive experiments with both synthetic and real data sets. We consider distributed convex optimization problems originating from sample average approximation of stochastic optimization, or empirical risk minimization in machine learning. We assume that each machine in the distributed computing system has access to a local empirical loss function, constructed with i.i.d. data sampled from a common distribution. We propose a communication-efficient distributed algorithm to minimize the overall empirical loss, which is the average of the local empirical losses. The algorithm is based on an inexact damped Newton method, where the inexact Newton steps are computed by a distributed preconditioned conjugate gradient method. We analyze its iteration complexity and communication efficiency for minimizing self-concordant empirical loss functions, and discuss the results for ridge regression, logistic regression and binary classification with a smoothed hinge loss. In a standard setting for supervised learning where the condition number of the problem grows with square root of the sample size, the required number of communication rounds of the algorithm does not increase with the sample size, and only grows slowly with the number of machines.