arXiv subjects

Gavin Taylor

Publications and source records attributed to Gavin Taylor.

23 records · Page 2Linked to original sources

arXiv2015

Layer-Specific Adaptive Learning Rates for Deep Networks

The increasing complexity of deep learning architectures is resulting in training time requiring weeks or even months. This slow training is due in part to vanishing gradients, in which the gradients used by back-propagation are extremely large for weights connecting deep layers (layers near the output layer), and extremely small for shallow layers (near the input layer); this results in slow learning in the shallow layers. Additionally, it has also been shown that in highly non-convex problems, such as deep neural networks, there is a proliferation of high-error low curvature saddle points, which slows down learning dramatically. In this paper, we attempt to overcome the two above problems by proposing an optimization method for training deep neural networks which uses learning rates which are both specific to each layer in the network and adaptive to the curvature of the function, increasing the learning rate at low curvature points. This enables us to speed up learning in the shallow layers of the network and quickly escape high-error low curvature saddle points. We test our method on standard image classification datasets such as MNIST, CIFAR10 and ImageNet, and demonstrate that our method increases accuracy as well as reduces the required training time over standard algorithms.

cs.CV↗

arXiv2015

Unwrapping ADMM: Efficient Distributed Computing via Transpose Reduction

Recent approaches to distributed model fitting rely heavily on consensus ADMM, where each node solves small sub-problems using only local data. We propose iterative methods that solve {\em global} sub-problems over an entire distributed dataset. This is possible using transpose reduction strategies that allow a single node to solve least-squares over massive datasets without putting all the data in one place. This results in simple iterative methods that avoid the expensive inner loops required for consensus methods. To demonstrate the efficiency of this approach, we fit linear classifiers and sparse linear models to datasets over 5 Tb in size using a distributed implementation with over 7000 cores in far less time than previous approaches.

cs.DC↗

arXiv2014

An Analysis of State-Relevance Weights and Sampling Distributions on L1-Regularized Approximate Linear Programming Approximation Accuracy

Recent interest in the use of $L_1$ regularization in the use of value function approximation includes Petrik et al.'s introduction of $L_1$-Regularized Approximate Linear Programming (RALP). RALP is unique among $L_1$-regularized approaches in that it approximates the optimal value function using off-policy samples. Additionally, it produces policies which outperform those of previous methods, such as LSPI. RALP's value function approximation quality is affected heavily by the choice of state-relevance weights in the objective function of the linear program, and by the distribution from which samples are drawn; however, there has been no discussion of these considerations in the previous literature. In this paper, we discuss and explain the effects of choices in the state-relevance weights and sampling distribution on approximation quality, using both theoretical and experimental illustrations. The results provide insight not only onto these effects, but also provide intuition into the types of MDPs which are especially well suited for approximation with RALP.

cs.AI↗

arXiv2012

Value Function Approximation in Noisy Environments Using Locally Smoothed Regularized Approximate Linear Programs

Recently, Petrik et al. demonstrated that L1Regularized Approximate Linear Programming (RALP) could produce value functions and policies which compared favorably to established linear value function approximation techniques like LSPI. RALP's success primarily stems from the ability to solve the feature selection and value function approximation steps simultaneously. RALP's performance guarantees become looser if sampled next states are used. For very noisy domains, RALP requires an accurate model rather than samples, which can be unrealistic in some practical scenarios. In this paper, we demonstrate this weakness, and then introduce Locally Smoothed L1-Regularized Approximate Linear Programming (LS-RALP). We demonstrate that LS-RALP mitigates inaccuracies stemming from noise even without an accurate model. We show that, given some smoothness assumptions, as the number of samples increases, error from noise approaches zero, and provide experimental examples of LS-RALP's success on common reinforcement learning benchmark problems.

cs.LG↗

arXiv2010

Feature Selection Using Regularization in Approximate Linear Programs for Markov Decision Processes

Approximate dynamic programming has been used successfully in a large variety of domains, but it relies on a small set of provided approximation features to calculate solutions reliably. Large and rich sets of features can cause existing algorithms to overfit because of a limited number of samples. We address this shortcoming using $L_1$ regularization in approximate linear programming. Because the proposed method can automatically select the appropriate richness of features, its performance does not degrade with an increasing number of features. These results rely on new and stronger sampling bounds for regularized approximate linear programs. We also propose a computationally efficient homotopy method. The empirical evaluation of the approach shows that the proposed method performs well on simple MDPs and standard benchmark problems.

cs.AI↗