Related papers: The case for and against fixed step-size: Stochast…

This paper analyzes a (1, $\lambda$)-Evolution Strategy, a randomized comparison-based adaptive search algorithm, optimizing a linear function with a linear constraint. The algorithm uses resampling to handle the constraint. Two cases are…

This paper concerns a high-dimensional stochastic programming problem of minimizing a function of expected cost with a matrix argument. To this problem, one of the most widely applied solution paradigms is the sample average approximation…

The stochastic Auxiliary Problem Principle (APP) algorithm is a general Stochastic Approximation (SA) scheme that turns the resolution of an original optimization problem into the iterative resolution of a sequence of auxiliary problems.…

This paper studies the control-oriented identification problem of set-valued moving average systems with uniform persistent excitations and observation noises. A stochastic approximation-based (SA-based) algorithm without projections or…

Using tail bounds, we introduce a new probabilistic condition for function estimation in stochastic derivative-free optimization which leads to a reduction in the number of samples and eases algorithmic analyses. Moreover, we develop simple…

Traditionally, stochastic approximation schemes for SVIs have relied on strong monotonicity and Lipschitzian properties of the underlying map. In contrast, we consider monotone stochastic variational inequality (SVI) problems where the…

In this paper, we propose a proximal stochasitc gradient algorithm (PSGA) for solving composite optimization problems by incorporating variance reduction techniques and an adaptive step-size strategy. In the PSGA method, the objective…

We introduce a statistical physics inspired supervised machine learning algorithm for classification and regression problems. The method is based on the invariances or stability of predicted results when known data is represented as…

Stochastic approximation (SA) is a fundamental iterative framework with broad applications in reinforcement learning and optimization. Classical analyses typically rely on martingale difference or Markov noise with bounded second moments,…

We consider a Markov chain $(x_n)$ whose kernel is indexed by a scaling parameter $\gamma>0$, refered to as the step size. The aim is to analyze the behavior of the Markov chain in the doubly asymptotic regime where $n\to\infty$ then…

Acceleration is an increasingly common theme in the stochastic optimization literature. The two most common examples are Nesterov's method, and Polyak's momentum technique. In this paper two new algorithms are introduced for root finding…

StochAstic Recursive grAdient algoritHm (SARAH), originally proposed for convex optimization and also proven to be effective for general nonconvex optimization, has received great attention due to its simple recursive framework for updating…

Temporal difference (TD) learning is a fundamental algorithm for estimating value functions in reinforcement learning. Recent finite-time analyses of TD with linear function approximation quantify its theoretical convergence rate. However,…

An algorithm is proposed for solving stochastic and finite sum minimization problems. Based on a trust region methodology, the algorithm employs normalized steps, at least as long as the norms of the stochastic gradient estimates are within…

The progressive hedging algorithm (PHA) is a cornerstone among algorithms for large-scale stochastic programming problems. However, its traditional implementation is hindered by some limitations, including the requirement to solve all…

Under interpolation-type assumptions such as the strong growth condition, stochastic optimization methods can attain convergence rates comparable to full-batch methods, but their performance, particularly for SGD, remains highly sensitive…

This work develops new results for stochastic approximation algorithms. The emphases are on treating algorithms and limits with discontinuities. The main ingredients include the use of differential inclusions, set-valued analysis, and…

Classical probabilistic rounding error analysis is particularly well suited to stochastic rounding (SR), and it yields strong results when dealing with floating-point algorithms that rely heavily on summation. For many numerical linear…

We discuss numerical approximation methods for Random Time Change equations which possess a deterministic drift part and jump with state-dependent rates. It is first established that solutions to such equations are versions of certain…

Linear two-timescale stochastic approximation (SA) scheme is an important class of algorithms which has become popular in reinforcement learning (RL), particularly for the policy evaluation problem. Recently, a number of works have been…