Related papers: Constrained and Preconditioned Stochastic Gradient…
Stochastic Gradient Descent has been widely studied with classification accuracy as a performance measure. However, these stochastic algorithms cannot be directly used when non-decomposable pairwise performance measures are used such as…
We study nonlinearly preconditioned gradient methods for smooth nonconvex optimization problems, focusing on sigmoid preconditioners that inherently perform a form of gradient clipping akin to the widely used gradient clipping technique.…
In this paper, we proposed a new technique, {\em variance controlled stochastic gradient} (VCSG), to improve the performance of the stochastic variance reduced gradient (SVRG) algorithm. To avoid over-reducing the variance of gradient by…
The proximal stochastic gradient method (PSGD) is one of the state-of-the-art approaches for stochastic composite-type problems. In contrast to its deterministic counterpart, PSGD has been found to have difficulties with the correct…
Interior point methods solve small to medium sized problems to high accuracy in a reasonable amount of time. However, for larger problems as well as stochastic problems, one needs to use first-order methods such as stochastic gradient…
In this paper, a sample-based procedure for obtaining simple and computable approximations of chance-constrained sets is proposed. The procedure allows to control the complexity of the approximating set, by defining families of…
We propose randomized subspace gradient methods for high-dimensional constrained optimization. While there have been similarly purposed studies on unconstrained optimization problems, there have been few on constrained optimization problems…
This paper introduces a new proximal stochastic gradient method with variance reduction and stabilization for minimizing the sum of a convex stochastic function and a group sparsity-inducing regularization function. Since the method may be…
We present two stochastic descent algorithms that apply to unconstrained optimization and are particularly efficient when the objective function is slow to evaluate and gradients are not easily obtained, as in some PDE-constrained…
We consider the problem of optimizing the sum of a smooth convex function and a non-smooth convex function using proximal-gradient methods, where an error is present in the calculation of the gradient of the smooth term or in the proximity…
We propose a novel study of the stochastic proximal gradient method for minimizing the sum of two convex functions, one of which is smooth. Under suitable assumptions and without requiring any boundedness or control of the variance of the…
Scalable algorithms of posterior approximation allow Bayesian nonparametrics such as Dirichlet process mixture to scale up to larger dataset at fractional cost. Recent algorithms, notably the stochastic variational inference performs local…
In this manuscript, we analyze the sparse signal recovery (compressive sensing) problem from the perspective of convex optimization by stochastic proximal gradient descent. This view allows us to significantly simplify the recovery analysis…
Gradient clipping is a popular modification to standard (stochastic) gradient descent, at every iteration limiting the gradient norm to a certain value $c >0$. It is widely used for example for stabilizing the training of deep learning…
Probabilistic graphical models (PGMs) are tools for solving complex probabilistic relationships. However, suboptimal PGM structures are primarily used in practice. This dissertation presents three contributions to the PGM literature. The…
Stochastic gradients have been widely integrated into Langevin-based methods to improve their scalability and efficiency in solving large-scale sampling problems. However, the proximal sampler, which exhibits much faster convergence than…
A recent article introduced thecontinuous stochastic gradient method (CSG) for the efficient solution of a class of stochastic optimization problems. While the applicability of known stochastic gradient type methods is typically limited to…
Stochastic versions of proximal methods have gained much attention in statistics and machine learning. These algorithms tend to admit simple, scalable forms, and enjoy numerical stability via implicit updates. In this work, we propose and…
Stochastic gradient descent (SGD) is a prevalent optimization technique for large-scale distributed machine learning. While SGD computation can be efficiently divided between multiple machines, communication typically becomes a bottleneck…
Stochastic optimization algorithms with variance reduction have proven successful for minimizing large finite sums of functions. Unfortunately, these techniques are unable to deal with stochastic perturbations of input data, induced for…