Related papers: Stochastic Monotone Inclusion with Closed Loop Dis…
We address the challenge of sequential data-driven decision-making under context distributional uncertainty. This problem arises in numerous real-world scenarios where the learner optimizes black-box objective functions in the presence of…
To solve convex optimization problems with a noisy gradient input, we analyze the global behavior of subgradient-like flows under stochastic errors. The objective function is composite, being equal to the sum of two convex functions, one…
We study the complexity of producing $(\delta,\epsilon)$-stationary points of Lipschitz objectives which are possibly neither smooth nor convex, using only noisy function evaluations. Recent works proposed several stochastic zero-order…
In this paper, we consider robust control using randomized algorithms. We extend the existing order statistics distribution theory to the general case in which the distribution of population is not assumed to be continuous and the order…
In this paper we investigate in a Hilbert space setting a second order dynamical system of the form $$\ddot{x}(t)+\g(t)\dot{x}(t)+x(t)-J_{\lambda(t) A}\big(x(t)-\lambda(t) D(x(t))-\lambda(t)\beta(t)B(x(t))\big)=0,$$ where $A:{\mathcal…
Distributionally-robust optimization is often studied for a fixed set of distributions rather than time-varying distributions that can drift significantly over time (which is, for instance, the case in finance and sociology due to…
This monograph develops a comprehensive statistical learning framework that is robust to (distributional) perturbations in the data using Distributionally Robust Optimization (DRO) under the Wasserstein metric. Beginning with fundamental…
We consider stochastic variational inequality problems where the mapping is monotone over a compact convex set. We present two robust variants of stochastic extragradient algorithms for solving such problems. Of these, the first scheme…
In binary classification and regression problems, it is well understood that Lipschitz continuity and smoothness of the loss function play key roles in governing generalization error bounds for empirical risk minimization algorithms. In…
Distributionally Robust Optimization (DRO) provides a framework for decision-making under distributional uncertainty, yet its effectiveness can be compromised by outliers in the training data. This paper introduces a principled approach to…
We analyze convergence rates of stochastic optimization procedures for non-smooth convex optimization problems. By combining randomized smoothing techniques with accelerated gradient methods, we obtain convergence rates of stochastic…
In this paper we study a robust expected utility maximization problem with random endowment in discrete time. We give conditions under which an optimal strategy exists and derive a dual representation for the optimal utility. Our approach…
Optimization under uncertainty and risk is indispensable in many practical situations. Our paper addresses stability of optimization problems using composite risk functionals which are subjected to measure perturbations. Our main focus is…
We investigate the stochastic optimization problem of minimizing population risk, where the loss defining the risk is assumed to be weakly convex. Compositions of Lipschitz convex functions with smooth maps are the primary examples of such…
In this paper we provide a splitting algorithm for solving coupled monotone inclusions in a real Hilbert space involving the sum of a normal cone to a vector subspace, a maximally monotone, a monotone-Lipschitzian, and a cocoercive…
Many iterative optimization algorithms involve compositions of special cases of Lipschitz continuous operators, namely firmly nonexpansive, averaged and nonexpansive operators. The structure and properties of the compositions are of…
We consider a stochastic version of the proximal point algorithm for optimization problems posed on a Hilbert space. A typical application of this is supervised learning. While the method is not new, it has not been extensively analyzed in…
In this paper, we propose a quantized learning equation with a monotone increasing resolution of quantization and stochastic analysis for the proposed algorithm. According to the white noise hypothesis for the quantization error with dense…
We analyze the global and local behavior of gradient-like flows under stochastic errors towards the aim of solving convex optimization problems with noisy gradient input. We first study the unconstrained differentiable convex case, using a…
We investigate the convergence properties of a stochastic primal-dual splitting algorithm for solving structured monotone inclusions involving the sum of a cocoercive operator and a composite monotone operator. The proposed method is the…