Related papers: On Monte-Carlo methods in convex stochastic optimi…
This paper focuses on the distributed optimization of stochastic saddle point problems. The first part of the paper is devoted to lower bounds for the centralized and decentralized distributed methods for smooth (strongly) convex-(strongly)…
In this paper, we generalize the chance optimization problems and introduce constrained volume optimization where enables us to obtain convex formulation for challenging problems in systems and control. We show that many different problems…
We adapt the quasi-monotone method from [2] for composite convex minimization in the stochastic setting. For the proposed numerical scheme we derive the optimal convergence rate in terms of the last iterate, rather than on average as it is…
This paper presents a piecewise convexification method for solving non-convex multi-objective optimization problems with box constraints. Based on the ideas of the $\alpha$-based Branch and Bound (${\rm \alpha BB}$) method of global…
Optimal values and solutions of empirical approximations of stochastic optimization problems can be viewed as statistical estimators of their true values. From this perspective, it is important to understand the asymptotic behavior of these…
This paper proves, in very general settings, that convex risk minimization is a procedure to select a unique conditional probability model determined by the classification problem. Unlike most previous work, we give results that are general…
We present an exact algorithm for mean-risk optimization subject to a budget constraint, where decision variables may be continuous or integer. The risk is measured by the covariance matrix and weighted by an arbitrary monotone function,…
We propose a new estimator for the high-dimensional linear regression model with observation error in the design where the number of coefficients is potentially larger than the sample size. The main novelty of our procedure is that the…
Partial differential equation is a powerful tool to characterize various physics systems. In practice, measurement errors are often present and probability models are employed to account for such uncertainties. In this paper, we present a…
To study the nonlinear properties of complex natural phenomena, the evolution of the quantity of interest can be often represented by systems of coupled nonlinear stochastic differential equations (SDEs). These SDEs typically contain…
We study global optimization of non-convex functions through optimal control theory. Our main result establishes that (quasi-)optimal trajectories of a discounted control problem converge globally and practically asymptotically to the set…
This manuscript presents a framework for using multilevel quadrature formulae to compute the solution of optimal control problems constrained by random partial differential equations. Our approach consists in solving a sequence of optimal…
Multi-stage stochastic optimization is a well-known quantitative tool for decision-making under uncertainty. It is broadly used in financial and investment planning, inventory control, and also natural disaster risk management. Theoretical…
Optimizing highly complex cost/energy functions over discrete variables is at the heart of many open problems across different scientific disciplines and industries. A major obstacle is the emergence of many-body effects among certain…
We consider the constrained sampling problem where the goal is to sample from a target distribution $\pi(x)\propto e^{-f(x)}$ when $x$ is constrained to lie on a convex body $\mathcal{C}$. Motivated by penalty methods from continuous…
High-dimensional linear regression under heavy-tailed noise or outlier corruption is challenging, both computationally and statistically. Convex approaches have been proven statistically optimal but suffer from high computational costs,…
This paper presents a novel stochastic optimisation methodology to perform empirical Bayesian inference in semi-blind image deconvolution problems. Given a blurred image and a parametric class of possible operators, the proposed…
A decision rule is epsilon-minimax if it is minimax up to an additive factor epsilon. We present an algorithm for provably obtaining epsilon-minimax solutions for a class of statistical decision problems. In particular, we are interested in…
We propose and analyze a novel Multi-Index Monte Carlo (MIMC) method for weak approximation of stochastic models that are described in terms of differential equations either driven by random measures or with random coefficients. The MIMC…
Consider the problem of estimating the mean of a Gaussian random vector when the mean vector is assumed to be in a given convex set. The most natural solution is to take the Euclidean projection of the data vector on to this convex set; in…