Related papers: Optimal variance-reduced stochastic approximation …
This paper considers an $N$-player stochastic Nash game in which the $i$th player minimizes a composite objective $f_i(x) + r_i(x_i)$, where $f_i$ is expectation-valued and $r_i$ has an efficient prox-evaluation. In this context, we make…
In this paper, we introduce new implicit and explicit iterative schemes which converge strongly to a unique solution of variational inequality problems for strongly accretive operators over a common fixed point set of finite family of…
Stochastic approximation (SA) is a key method used in statistical learning. Recently, its non-asymptotic convergence analysis has been considered in many papers. However, most of the prior analyses are made under restrictive assumptions…
The analysis in Part I revealed interesting properties for subgradient learning algorithms in the context of stochastic optimization when gradient noise is present. These algorithms are used when the risk functions are non-smooth and…
This paper considers a general framework for the study of the existence of quasi-variational and variational solutions to a class of nonlinear evolution systems in convex sets of Banach spaces describing constraints on a linear combination…
Price determination is a central research topic of revenue management in marketing. The important aspect in pricing is controlling the stochastic behavior of demand, and the previous studies have tackled price optimization problems with…
We consider the least-squares regression problem and provide a detailed asymptotic analysis of the performance of averaged constant-step-size stochastic gradient descent (a.k.a. least-mean-squares). In the strongly-convex case, we provide…
This paper investigates probabilistic robustness of nonconvex-nonconcave minimax problems via the scenario approach. Specifically, under convex strategy sets for all players, inspired by recent advances in scenario optimization, we first…
Constructing or learning a function from a finite number of sampled data points (measurements) is a fundamental problem in science and engineering. This is often formulated as a minimum norm interpolation problem, regularized learning…
This paper is dedicated to the investigation of a new numerical method to approximate the optimal stopping problem for a discrete-time continuous state space Markov chain under partial observations. It is based on a two-step discretization…
The paper concerns foundations of sensitivity and stability analysis in optimization and related areas, being primarily addressed truncated constrained systems. We consider general models, which are described by multifunctions between…
Contextual stochastic optimization is an advanced methodology to model uncertainty in the presence of contextual information during decision planning processes. Although classical methodologies focus on minimizing the expectation of a…
In this paper we completely characterize the norm attainment set of a bounded linear operator on a Hilbert space. This partially answers a question raised recently in [\textit{D. Sain, On the norm attainment set of a bounded linear…
We introduce a class of stochastic algorithms for minimizing weakly convex functions over proximally smooth sets. As their main building blocks, the algorithms use simplified models of the objective function and the constraint set, along…
In this paper, we develop stochastic variance reduced algorithms for solving a class of finite-sum hemivariational inequality (HVI) problem. In this HVI problem, the associated function is assumed to be differentiable, and both the vector…
Recently, there has been a surge in interest in safe and robust techniques within reinforcement learning (RL). Current notions of risk in RL fail to capture the potential for systemic failures such as abrupt stoppages from system failures…
We consider a class of hierarchical noncooperative $N$-player games where the $i$th player solves a parametrized stochastic mathematical program with equilibrium constraints (MPEC) with the caveat that the implicit form of the $i$th…
We investigate the Stochastic Krasnoselskii-Mann iterations for expected nonexpansive fixed-point problems in a real Hilbert space. We establish convergence guarantees under significantly weaker assumptions on the variance than those…
We adopt an operator-theoretic perspective to analyze a class of nonlinear fixed-point iterations and discrete-time dynamical systems. Specifically, we study the Krasnoselskij iteration - at the heart of countless algorithmic schemes and…
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…