We present four new reinforcement learning algorithms based on actor-critic and natural-gradient ideas, and provide their convergence proofs. Actor-critic rein- forcement learning methods are online approximations to policy iteration in which the value-function parameters are estimated using temporal difference learning and the policy parameters are updated by stochastic gradient descent. Methods based on policy gradients in this way are of special interest because of their com- patibility with function approximation methods, which are needed to handle large or in(cid:2)nite state spaces. The use of temporal difference learning in this way is of interest because in many applications it dramatically reduces the variance of the gradient estimates. The use of the natural gradient is of interest because it can produce better conditioned parameterizations and has been shown to further re- duce variance in some cases.

Simulated annealing is a popular method for approaching the solution of a global optimization problem. Existing results on its performance apply to discrete com- binatorial optimization where the optimization variables can assume only a finite set of possible values. We introduce a new general formulation of simulated an- nealing which allows one to guarantee finite-time performance in the optimiza- tion of functions of continuous variables. The results hold universally for any optimization problem on a bounded domain and establish a connection between simulated annealing and up-to-date theory of convergence of Markov chain Monte Carlo methods on continuous domains. This work is inspired by the concept of finite-time learning with known accuracy and confidence developed in statistical learning theory.

In this paper we focus on training deep neural networks for visual recognition tasks. One challenge is the lack of an informative regularization on the network parameters, to imply a meaningful control on the computed function. We propose a training strategy that takes advantage of kernel methods, where an existing kernel function represents useful prior knowledge about the learning task of interest. We derive an efficient algorithm using stochastic gradient descent, and demonstrate very positive results in a wide range of visual recognition tasks.

It has been established that the second-order stochastic gradient descent (2SGD) method can potentially achieve generalization performance as well as empirical optimum in a single pass (i.e., epoch) through the training examples. However, 2SGD requires computing the inverse of the Hessian matrix of the loss function, which is prohibitively expensive. This paper presents Periodic Step-size Adaptation (PSA), which approximates the Jacobian matrix of the mapping function and explores a linear relation between the Jacobian and Hessian to approximate the Hessian periodically and achieve near-optimal results in experiments on a wide variety of models and tasks.

With the increase in available data parallel machine learning has become an increasingly pressing problem. In this paper we present the first parallel stochastic gradient descent algorithm including a detailed analysis and experimental evidence. Unlike prior work on parallel optimization algorithms our variant comes with parallel acceleration guarantees and it poses no overly tight latency constraints, which might only be available in the multicore setting. Our analysis introduces a novel proof technique --- contractive mappings to quantify the speed of convergence of parameter distributions to their asymptotic limits. As a side effect this answers the question of how quickly stochastic gradient descent algorithms reach the asymptotically normal regime.

We present a fast online solver for large scale maximum-flow problems as they occur in portfolio optimization, inventory management, computer vision, and logistics. Our algorithm solves an integer linear program in an online fashion. It exploits total unimodularity of the constraint matrix and a Lagrangian relaxation to solve the problem as a convex online game. The algorithm generates approximate solutions of max-flow problems by performing stochastic gradient descent on a set of flows. We apply the algorithm to optimize tier arrangement of over 80 Million web pages on a layered set of caches to serve an incoming query stream optimally.

A common approach for handling the complexity and inherent ambiguities of 3D human pose estimation is to use pose priors learned from training data. Existing approaches however, are either too simplistic (linear), too complex to learn, or can only learn latent spaces from "simple data", i.e., single activities such as walking or running. In this paper, we present an efficient stochastic gradient descent algorithm that is able to learn probabilistic non-linear latent spaces composed of multiple activities. Furthermore, we derive an incremental algorithm for the online setting which can update the latent space without extensive relearning. We demonstrate the effectiveness of our approach on the task of monocular and multi-view tracking and show that our approach outperforms the state-of-the-art.

Many real-world networks are described by both connectivity information and features for every node. To better model and understand these networks, we present structure preserving metric learning (SPML), an algorithm for learning a Mahalanobis distance metric from a network such that the learned distances are tied to the inherent connectivity structure of the network. Like the graph embedding algorithm structure preserving embedding, SPML learns a metric which is structure preserving, meaning a connectivity algorithm such as k-nearest neighbors will yield the correct connectivity when applied using the distances from the learned metric. We show a variety of synthetic and real-world experiments where SPML predicts link patterns from node features more accurately than standard techniques. We further demonstrate a method for optimizing SPML based on stochastic gradient descent which removes the running-time dependency on the size of the network and allows the method to easily scale to networks of thousands of nodes and millions of edges.

We consider the minimization of a convex objective function defined on a Hilbert space, which is only available through unbiased estimates of its gradients. This problem includes standard machine learning algorithms such as kernel logistic regression and least-squares regression, and is commonly referred to as a stochastic approximation problem in the operations research community. We provide a non-asymptotic analysis of the convergence of two well-known algorithms, stochastic gradient descent (a.k.a. Robbins-Monro algorithm) as well as a simple modification where iterates are averaged (a.k.a. Our analysis suggests that a learning rate proportional to the inverse of the number of iterations, while leading to the optimal convergence rate in the strongly convex case, is not robust to the lack of strong convexity or the setting of the proportionality constant.

Stochastic Gradient Descent (SGD) is a popular algorithm that can achieve state-of-the-art performance on a variety of machine learning tasks. Several researchers have recently proposed schemes to parallelize SGD, but all require performance-destroying memory locking and synchronization. This work aims to show using novel theoretical analysis, algorithms, and implementation that SGD can be implemented without any locking. We present an update scheme called Hogwild which allows processors access to shared memory with the possibility of overwriting each other's work. We show that when the associated optimization problem is sparse, meaning most gradient updates only modify small parts of the decision variable, then Hogwild achieves a nearly optimal rate of convergence.