Related papers: A Simple Analysis for Exp-concave Empirical Minimi…

Matrix completion has been well studied under the uniform sampling model and the trace-norm regularized methods perform well both theoretically and numerically in such a setting. However, the uniform sampling model is unrealistic for a…

Concave regularization methods provide natural procedures for sparse recovery. However, they are difficult to analyze in the high dimensional setting. Only recently a few sparse recovery results have been established for some specific local…

In this work we consider numerical efficiency and convergence rates for solvers of non-convex multi-penalty formulations when reconstructing sparse signals from noisy linear measurements. We extend an existing approach, based on reduction…

Dual averaging-type methods are widely used in industrial machine learning applications due to their ability to promoting solution structure (e.g., sparsity) efficiently. In this paper, we propose a novel accelerated dual-averaging…

This paper proposes an algorithm to calculate the maximal probability of unsafety with respect to trajectories of a stochastic process and a hazard set. The unsafe probability estimation problem is cast as a primal-dual pair of…

We analyze the performance of alternating minimization for loss functions optimized over two variables, where each variable may be restricted to lie in some potentially nonconvex constraint set. This type of setting arises naturally in…

We study a general class of convex submodular optimization problems with indicator variables. Many applications such as the problem of inferring Markov random fields (MRFs) with a sparsity or robustness prior can be naturally modeled in…

We consider robust empirical risk minimization (ERM), where model parameters are chosen to minimize the worst-case empirical loss when each data point varies over a given convex uncertainty set. In some simple cases, such problems can be…

Many applications require recovering a matrix of minimal rank within an affine constraint set, with matrix completion a notable special case. Because the problem is NP-hard in general, it is common to replace the matrix rank with the…

In this paper, we present an equivalent convex optimization formulation for discrete-time stochastic linear systems subject to linear chance constraints, alongside a tight convex relaxation for quadratic chance constraints. By lifting the…

This paper establishes bounds on the predictive performance of empirical risk minimization for principal component regression. Our analysis is nonparametric, in the sense that the relation between the prediction target and the predictors is…

We study the sample complexity of the best-case Empirical Risk Minimizer in the setting of stochastic convex optimization. We show that there exists an instance in which the sample size is linear in the dimension, learning is possible, but…

This article considers nonconvex global optimization problems subject to uncertainties described by continuous random variables. Such problems arise in chemical process design, renewable energy systems, stochastic model predictive control,…

We study the empirical measure associated to a sample of size $n$ and modified by $N$ iterations of the raking-ratio method. This empirical measure is adjusted to match the true probability of sets in a finite partition which changes each…

The problem of minimizing convex functionals of probability distributions is solved under the assumption that the density of every distribution is bounded from above and below. A system of sufficient and necessary first-order optimality…

In this paper, we propose new sequential randomized algorithms for convex optimization problems in the presence of uncertainty. A rigorous analysis of the theoretical properties of the solutions obtained by these algorithms, for full…

Recently there has been a surge of interest in understanding implicit regularization properties of iterative gradient-based optimization algorithms. In this paper, we study the statistical guarantees on the excess risk achieved by…

We study online convex optimization in the random order model, recently proposed by \citet{garber2020online}, where the loss functions may be chosen by an adversary, but are then presented to the online algorithm in a uniformly random…

This article presents a new method for computing guaranteed convex and concave relaxations of nonlinear stochastic optimal control problems with final-time expected-value cost functions. This method is motivated by similar methods for…

We analyze two classical algorithms for solving additively composite convex optimization problems where the objective is the sum of a smooth term and a nonsmooth regularizer: proximal stochastic gradient method for a single regularizer; and…