With the recent proliferation of large-scale learning problems, there have been a lot of interest on distributed machine learning algorithms, particularly those that are based on stochastic gradient descent (SGD) and its variants. However, existing algorithms either suffer from slow convergence due to the inherent variance of stochastic gradients, or have a fast linear convergence rate but at t...

Randomized algorithms are central to modern machine learning. In the presence of massive datasets, researchers often turn to stochastic optimization to solve learning problems. Of particular interest is stochastic gradient descent (SGD), a first-order method that approximates the learning objective and gradient by a random point estimate. A classical question in learning theory is, if a randomi...

The success of deep learning has led to a rising interest in the generalization property of the stochastic gradient descent (SGD) method, and stability is one popular approach to study it. Existing works based on stability have studied nonconvex loss functions, but only considered the generalization error of the SGD in expectation. In this paper, we establish various generalization error bounds...

We propose a low-rank stochastic gradient descent (LR-SGD) method for solving a class of semidefinite programming (SDP) problems. LR-SGD has clear computational advantages over the standard SGD peers as its iterative projection step (a SDP problem) can be solved in an efficient manner. Specifically, LR-SGD constructs a low-rank stochastic gradient and computes an optimal solution to the project...

Uniform sampling of training data has been commonly used in traditional stochastic optimization algorithms such as Proximal Stochastic Gradient Descent (prox-SGD) and Proximal Stochastic Dual Coordinate Ascent (prox-SDCA). Although uniform sampling can guarantee that the sampled stochastic quantity is an unbiased estimate of the corresponding true quantity, the resulting estimator may have a ra...

We consider a discrete time, nite state Markov reward process that depends on a set of parameters. In earlier work, we proposed a class of (stochastic) gradient descent methods that tune the parameters in order to optimize the average reward, using a single (possibly simulated) sample path of the process of interest. The resulting algorithms can be implemented online, and have the property that...

In deterministic optimization problems, line search routines are a standard tool ensuring stability and efficiency. In the stochastic setting, no direct equivalent has so far been formulated, because uncertain gradients do not allow for a strict sequence of decisions collapsing the search space. We construct a probabilistic version of the line search paradigm, by combining the structure of exis...

In this project, we approach the problem of English-word hyphenation using a linear-chain conditional random field model. We measure the effectiveness of different feature combinations and two different learning methods: Collins perceptron and stochastic gradient following. We achieve the accuracy rate of 77.95% using stochastic gradient descent.

We consider the gradient method xt+1 = xt + γt(st + wt), where st is a descent direction of a function f : �n → � and wt is a deterministic or stochastic error. We assume that ∇f is Lipschitz continuous, that the stepsize γt diminishes to 0, and that st and wt satisfy standard conditions. We show that either f(xt) → −∞ or f(xt) converges to a finite value and ∇f(xt) → 0 (with probability 1 in t...

Reinforcement learning by direct policy gradient estimation is attractive in theory but in practice leads to notoriously ill-behaved optimization problems. We improve its robustness and speed of convergence with stochastic meta-descent, a gain vector adaptation method that employs fast Hessian-vector products. In our experiments the resulting algorithms outperform previously employed online sto...