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A well-studied generalization of the standard online convex optimization (OCO) framework is constrained online convex optimization (COCO). In COCO, on every round, a convex cost function and a convex constraint function are revealed to the…
Aligning partially overlapping point sets where there is no prior information about the value of the transformation is a challenging problem in computer vision. To achieve this goal, we first reduce the objective of the robust point…
In many sequential decision making applications, the change of decision would bring an additional cost, such as the wear-and-tear cost associated with changing server status. To control the switching cost, we introduce the problem of online…
In this paper, we propose a new constraint, called shift-consistency, for solving matrix/tensor completion problems in the context of recommender systems. Our method provably guarantees several key mathematical properties: (1) satisfies a…
In recent years, the success of deep learning has inspired many researchers to study the optimization of general smooth non-convex functions. However, recent works have established pessimistic worst-case complexities for this class…
Generalizing both mixed-integer linear optimization and convex optimization, mixed-integer convex optimization possesses broad modeling power but has seen relatively few advances in general-purpose solvers in recent years. In this paper, we…
We consider the problem of sequential decision making under uncertainty in which the loss caused by a decision depends on the following binary observation. In competitive on-line learning, the goal is to design decision algorithms that are…
We study Online Convex Optimization (OCO) with adversarial constraints, where an online algorithm must make sequential decisions to minimize both convex loss functions and cumulative constraint violations. We focus on a setting where the…
We propose a new framework for black-box convex optimization which is well-suited for situations where gradient computations are expensive. We derive a new method for this framework which leverages several concepts from convex optimization,…
Low rank tensor learning, such as tensor completion and multilinear multitask learning, has received much attention in recent years. In this paper, we propose higher order matching pursuit for low rank tensor learning problems with a convex…
In this paper, we consider the problem of minimizing a difference-of-convex objective over a nonlinear conic constraint, where the cone is closed, convex, pointed and has a nonempty interior. We assume that the support function of a compact…
In this paper, we extend our previous results and formally propose the SCvx-fast algorithm, a new addition to the Successive Convexification algorithmic framework. The said algorithm solves non-convex optimal control problems with specific…
We consider the setting of online computation with advice, and study the bin packing problem and a number of scheduling problems. We show that it is possible, for any of these problems, to arbitrarily approach a competitive ratio of $1$…
The task of approximating an arbitrary convex function arises in several learning problems such as convex regression, learning with a difference of convex (DC) functions, and learning Bregman or $f$-divergences. In this paper, we develop…
Decision-makers often have access to machine-learned predictions about future demand that can help guide online resource allocation decisions. However, such predictions may be inaccurate. We develop a framework for online resource…
We address the problem of \emph{convex optimization with dueling feedback}, where the goal is to minimize a convex function given a weaker form of \emph{dueling} feedback. Each query consists of two points and the dueling feedback returns a…
We propose a novel white-box approach to hyper-parameter optimization. Motivated by recent work establishing a relationship between flat minima and generalization, we first establish a relationship between the strong convexity of the loss…
Recent focus on robustness to adversarial attacks for deep neural networks produced a large variety of algorithms for training robust models. Most of the effective algorithms involve solving the min-max optimization problem for training…
Recent efforts on solving inverse problems in imaging via deep neural networks use architectures inspired by a fixed number of iterations of an optimization method. The number of iterations is typically quite small due to difficulties in…
We study online learning problems in which a decision maker has to take a sequence of decisions subject to $m$ long-term constraints. The goal of the decision maker is to maximize their total reward, while at the same time achieving small…