相关论文: On Smoothing, Regularization and Averaging in Stoc…

When measuring the value of a function to be minimized is not only expensive but also with noise, the popular simultaneous perturbation stochastic approximation (SPSA) algorithm requires only two function values in each iteration. In this…

Randomized matrix sparsification has proven to be a fruitful technique for producing faster algorithms in applications ranging from graph partitioning to semidefinite programming. In the decade or so of research into this technique, the…

This paper introduces a drift optimization model of stochastic optimization problems driven by regulated stochastic processes. A broad range of problems across operations research, machine learning, and statistics can be viewed as…

The modified Method of Successive Approximations (MSA) is an iterative scheme for approximating solutions to stochastic control problems in continuous time based on Pontryagin Optimality Principle which, starting with an initial open loop…

In the machine learning and optimization community, there are two main approaches for the convex risk minimization problem, namely, the Stochastic Approximation (SA) and the Sample Average Approximation (SAA). In terms of oracle complexity…

Over the past ten years, driven by large scale optimisation problems arising from machine learning, the development of stochastic optimisation methods have witnessed a tremendous growth. However, despite their popularity, the theoretical…

Stochastic approximation is a framework unifying many random iterative algorithms occurring in a diverse range of applications. The stability of the process is often difficult to verify in practical applications and the process may even be…

Stochastic variance reduced gradient (SVRG) is a popular variance reduction technique for accelerating stochastic gradient descent (SGD). We provide a first analysis of the method for solving a class of linear inverse problems in the lens…

We analyze two classical algorithms for solving additively composite convex optimization problems where the objective is the sum of a smooth term and a nonsmooth regularizer: proximal stochastic gradient method for a single regularizer; and…

We consider a class of stochastic smooth convex optimization problems under rather general assumptions on the noise in the stochastic gradient observation. As opposed to the classical problem setting in which the variance of noise is…

Forecasting entails a complex estimation challenge, as it requires balancing multiple, often conflicting, priorities and objectives. Traditional forecast optimization criteria typically focus on a single metric -- such as minimizing the…

Randomized Smoothing (RS) is a prominent technique for certifying the robustness of neural networks against adversarial perturbations. With RS, achieving high accuracy at small radii requires a small noise variance, while achieving high…

Stochastic approximation (SA) is a powerful and scalable computational method for iteratively estimating the solution of optimization problems in the presence of randomness, particularly well-suited for large-scale and streaming data…

Stochastic rounding (SR) is a probabilistic method used to round numbers to floating-point and fixed-point representations. In length $n$ summation, the worst-case error of SR grows as $\sqrt{n}$ with high probability, unlike for standard…

Stochastic non-smooth convex optimization constitutes a class of problems in machine learning and operations research. This paper considers minimization of a non-smooth function based on stochastic subgradients. When the function has a…

The growing prevalence of nonsmooth optimization problems in machine learning has spurred significant interest in generalized smoothness assumptions. Among these, the (L0, L1)-smoothness assumption has emerged as one of the most prominent.…

For many applications in signal processing and machine learning, we are tasked with minimizing a large sum of convex functions subject to a large number of convex constraints. In this paper, we devise a new random projection method (RPM) to…

We study finite-sum nonconvex optimization problems, where the objective function is an average of $n$ nonconvex functions. We propose a new stochastic gradient descent algorithm based on nested variance reduction. Compared with…

Presently the most successful approaches to semi-supervised learning are based on consistency regularization, whereby a model is trained to be robust to small perturbations of its inputs and parameters. To understand consistency…

This paper proposes a constrained stochastic successive convex approximation (CSSCA) algorithm to find a stationary point for a general non-convex stochastic optimization problem, whose objective and constraint functions are non-convex and…