Related papers: On Robustness in Nonconvex Optimization with Appli…
Applications involving dictionary learning, non-negative matrix factorization, subspace clustering, and parallel factor tensor decomposition tasks motivate well algorithms for per-block-convex and non-smooth optimization problems. By…
We consider robust counterparts of uncertain combinatorial optimization problems, where the difference to the best possible solution over all scenarios is to be minimized. Such minmax regret problems are typically harder to solve than their…
Minimax optimization problems arises from both modern machine learning including generative adversarial networks, adversarial training and multi-agent reinforcement learning, as well as from tradition research areas such as saddle point…
The pooling problem has applications, e.g., in petrochemical refining, water networks, and supply chains and is widely studied in global optimization. To date, it has largely been treated deterministically, neglecting the influence of…
Reduced-order simulation is an emerging method for accelerating physical simulations with high DOFs, and recently developed neural-network-based methods with nonlinear subspaces have been proven effective in diverse applications as more…
We address reinforcement learning problems with finite state and action spaces where the underlying MDP has some known structure that could be potentially exploited to minimize the exploration rates of suboptimal (state, action) pairs. For…
In this paper, we analyze the mirror descent algorithm for non-smooth optimization problems in which the objective function is relatively strongly convex, without relying on the standard Lipschitz continuity assumption commonly used in the…
Stochastic optimization has found wide applications in minimizing objective functions in machine learning, which motivates a lot of theoretical studies to understand its practical success. Most of existing studies focus on the convergence…
Recently there were proposed some innovative convex optimization concepts, namely, relative smoothness [1] and relative strong convexity [2,3]. These approaches have significantly expanded the class of applicability of gradient-type methods…
We study the impact of nonconvexity on the complexity of nonsmooth optimization, emphasizing objectives such as piecewise linear functions, which may not be weakly convex. We focus on a dimension-independent analysis, slightly modifying a…
A broad class of optimization problems can be cast in composite form, that is, considering the minimization of the composition of a lower semicontinuous function with a differentiable mapping. This paper investigates the versatile template…
We consider a distributionally robust formulation of stochastic optimization problems arising in statistical learning, where robustness is with respect to uncertainty in the underlying data distribution. Our formulation builds on…
This paper concerns the problem of learning control policies for an unknown linear dynamical system to minimize a quadratic cost function. We present a method, based on convex optimization, that accomplishes this task robustly: i.e., we…
In practical optimization problems, we typically model uncertainty as a random variable though its true probability distribution is unobservable to the decision maker. Historical data provides some information of this distribution that we…
We consider the problem of minimizing the composition of a smooth (nonconvex) function and a smooth vector mapping, where the inner mapping is in the form of an expectation over some random variable or a finite sum. We propose a stochastic…
This paper considers an online proximal-gradient method to track the minimizers of a composite convex function that may continuously evolve over time. The online proximal-gradient method is inexact, in the sense that: (i) it relies on an…
For statistical decision problems with finite parameter space, it is well-known that the upper value (minimax value) agrees with the lower value (maximin value). Only under a generalized notion of prior does such an equivalence carry over…
Machine learning algorithms in high-dimensional settings are highly susceptible to the influence of even a small fraction of structured outliers, making robust optimization techniques essential. In particular, within the…
We show that when a high-dimensional data matrix is the sum of a low-rank matrix and a random error matrix with independent entries, the low-rank component can be consistently estimated by solving a convex minimization problem. We develop a…
Many fundamental problems in machine learning can be formulated by the convex program \[ \min_{\theta\in R^d}\ \sum_{i=1}^{n}f_{i}(\theta), \] where each $f_i$ is a convex, Lipschitz function supported on a subset of $d_i$ coordinates of…