Related papers: Sample Average Approximation for Stochastic Optimi…

The sample average approximation (SAA) and the stochastic approximation (SA) are two popular schemes for solving the stochastic variational inequalities problem (SVIP). In the past decades, theories on the consistency of the SAA solutions…

The tuning of stochastic gradient algorithms (SGAs) for optimization and sampling is often based on heuristics and trial-and-error rather than generalizable theory. We address this theory--practice gap by characterizing the large-sample…

Several classical adaptive optimization algorithms, such as line search and trust region methods, have been recently extended to stochastic settings where function values, gradients, and Hessians in some cases, are estimated via stochastic…

Two-stage stochastic optimization is a framework for modeling uncertainty, where we have a probability distribution over possible realizations of the data, called scenarios, and decisions are taken in two stages: we make first-stage…

A key trait of stochastic optimizers is that multiple runs of the same optimizer in attempting to solve the same problem can produce different results. As a result, their performance is evaluated over several repeats, or runs, on the…

In this paper, a stochastic approximation (SA) based distributed algorithm is proposed to solve the resource allocation (RA) with uncertainties. In this problem, a group of agents cooperatively optimize a separable optimization problem with…

High-probability guarantees in stochastic optimization are often obtained only under strong noise assumptions such as sub-Gaussian tails. We show that such guarantees can also be achieved under the weaker assumption of bounded variance by…

Algorithmic stability is a central concept in statistics and learning theory that measures how sensitive an algorithm's output is to small changes in the training data. Stability plays a crucial role in understanding generalization,…

In this work, we introduce a learning model designed to meet the needs of applications in which computational resources are limited, and robustness and interpretability are prioritized. Learning problems can be formulated as constrained…

Any performance analysis based on stochastic simulation is subject to the errors inherent in misspecifying the modeling assumptions, particularly the input distributions. In situations with little support from data, we investigate the use…

We study the regret performance of Sample Average Approximation (SAA) for data-driven newsvendor problems with general convex inventory costs. In literature, the optimality of SAA has not been fully established under both \alpha-global…

Polyak-Ruppert averaging is a widely used technique to achieve the optimal asymptotic variance of stochastic approximation (SA) algorithms, yet its high-probability performance guarantees remain underexplored in general settings. In this…

Stochastic approximation (SA) that involves multiple coupled sequences, known as multiple-sequence SA (MSSA), finds diverse applications in the fields of signal processing and machine learning. However, existing theoretical understandings…

Stochastic optimization problems often involve data distributions that change in reaction to the decision variables. This is the case for example when members of the population respond to a deployed classifier by manipulating their features…

This paper investigates the stability and convergence properties of asynchronous stochastic approximation (SA) algorithms, with a focus on extensions relevant to average-reward reinforcement learning. We first extend a stability proof…

This paper studies linear stochastic approximation (SA) algorithms and their application to multi-agent systems in engineering and sociology. As main contribution, we provide necessary and sufficient conditions for convergence of linear SA…

This article describes a novel approach to chance-constrained programming based on the sample average approximation (SAA) method. Recent work focuses on heuristic approximations to the SAA problem and we introduce a novel approach which…

Two-time-scale Stochastic Approximation (SA) is an iterative algorithm with applications in reinforcement learning and optimization. Prior finite time analysis of such algorithms has focused on fixed point iterations with mappings…

Stochastic variance reduced methods have shown strong performance in solving finite-sum problems. However, these methods usually require the users to manually tune the step-size, which is time-consuming or even infeasible for some…

Theory and application of stochastic approximation (SA) have become increasingly relevant due in part to applications in optimization and reinforcement learning. This paper takes a new look at SA with constant step-size $\alpha>0$, defined…