Related papers: Oracle-Based Robust Optimization via Online Learni…
Most existing distance metric learning methods assume perfect side information that is usually given in pairwise or triplet constraints. Instead, in many real-world applications, the constraints are derived from side information, such as…
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…
In this dissertation we study statistical and online learning problems from an optimization viewpoint.The dissertation is divided into two parts : I. We first consider the question of learnability for statistical learning problems in the…
The efficacy of robust optimization spans a variety of settings with uncertainties bounded in predetermined sets. In many applications, uncertainties are affected by decisions and cannot be modeled with current frameworks. This paper takes…
Robust optimization (RO) tackles data uncertainty by optimizing for the worst-case scenario of an uncertain parameter and, in its basic form, is sometimes criticized for producing overly-conservative solutions. To reduce the level of…
We investigate a data-driven quasiconcave maximization problem where information about the objective function is limited to a finite sample of data points. We begin by defining an ambiguity set for admissible objective functions based on…
Feedback-based online optimization algorithms have gained traction in recent years because of their simple implementation, their ability to reject disturbances in real time, and their increased robustness to model mismatch. While the…
Distributionally robust offline reinforcement learning (RL) aims to find a policy that performs the best under the worst environment within an uncertainty set using an offline dataset collected from a nominal model. While recent advances in…
Constrained non-convex optimization is fundamentally challenging, as global solutions are generally intractable and constraint qualifications may not hold. However, in many applications, including safe policy optimization in control and…
Robust optimization (RO) is a common approach to tractably obtain safeguarding solutions for optimization problems with uncertain constraints. In this paper, we study a statistical framework to integrate data into RO, based on learning a…
We derive computationally tractable formulations of the robust counterparts of convex quadratic and conic quadratic constraints that are concave in matrix-valued uncertain parameters. We do this for a broad range of uncertainty sets. In…
Applying robust optimization often requires selecting an appropriate uncertainty set both in shape and size, a choice that directly affects the trade-off between average-case and worst-case performances. In practice, this calibration is…
In this paper, a robust optimization framework is developed to train shallow neural networks based on reachability analysis of neural networks. To characterize noises of input data, the input training data is disturbed in the description of…
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…
We investigate robust optimization problems defined for maximizing convex functions. For finite uncertainty set, we develop a geometric branch-and-bound algorithmic approach to solve this problem. The geometric branch-and-bound algorithm…
Robust PCA has drawn significant attention in the last decade due to its success in numerous application domains, ranging from bio-informatics, statistics, and machine learning to image and video processing in computer vision. Robust PCA…
In this work we study binary two-stage robust optimization problems with objective uncertainty. We present an algorithm to calculate efficiently lower bounds for the binary two-stage robust problem by solving alternately the underlying…
Data-driven decision-making is performed by solving a parameterized optimization problem, and the optimal decision is given by an optimal solution for unknown true parameters. We often need a solution that satisfies true constraints even…
The field of portfolio selection is an active research topic, which combines elements and methodologies from various fields, such as optimization, decision analysis, risk management, data science, forecasting, etc. The modeling and…
It is well-known that given a smooth, bounded-from-below, and possibly nonconvex function, standard gradient-based methods can find $\epsilon$-stationary points (with gradient norm less than $\epsilon$) in $\mathcal{O}(1/\epsilon^2)$…