Related papers: Adopting Robustness and Optimality in Fitting and …
In classical inverse linear optimization, one assumes a given solution is a candidate to be optimal. Real data is imperfect and noisy, so there is no guarantee this assumption is satisfied. Inspired by regression, this paper presents a…
In this work we solve the problem of robustly learning a high-dimensional Gaussian mixture model with $k$ components from $\epsilon$-corrupted samples up to accuracy $\widetilde{O}(\epsilon)$ in total variation distance for any constant $k$…
The goal of robust constrained reinforcement learning (RL) is to optimize an agent's performance under the worst-case model uncertainty while satisfying safety or resource constraints. In this paper, we demonstrate that strong duality does…
In the context of structured nonconvex optimization, we estimate the increase in minimum value for a decision that is robust to parameter perturbations as compared to the value of a nominal problem. The estimates rely on detailed…
We study reinforcement learning with linear function approximation where the transition probability and reward functions are linear with respect to a feature mapping $\boldsymbol{\phi}(s,a)$. Specifically, we consider the episodic…
We study the problem of optimizing a function under a \emph{budgeted number of evaluations}. We only assume that the function is \emph{locally} smooth around one of its global optima. The difficulty of optimization is measured in terms of…
Many estimation problems in robotics, computer vision, and learning require estimating unknown quantities in the face of outliers. Outliers are typically the result of incorrect data association or feature matching, and it is common to have…
Machine learning models are often required to perform well across several pre-defined settings, such as a set of user groups. Worst-case performance is a common metric to capture this requirement, and is the objective of group…
This paper concerns the central issues of model robustness and sample efficiency in offline reinforcement learning (RL), which aims to learn to perform decision making from history data without active exploration. Due to uncertainties and…
Robust optimization is becoming increasingly important in machine learning applications. In this paper, we study a unified framework of robust submodular optimization. We study this problem both from a minimization and maximization…
Submodular functions have applications throughout machine learning, but in many settings, we do not have direct access to the underlying function $f$. We focus on stochastic functions that are given as an expectation of functions over a…
In many machine learning tasks, a common approach for dealing with large-scale data is to build a small summary, {\em e.g.,} coreset, that can efficiently represent the original input. However, real-world datasets usually contain outliers…
Robust estimators of large covariance matrices are considered, comprising regularized (linear shrinkage) modifications of Maronna's classical M-estimators. These estimators provide robustness to outliers, while simultaneously being…
Distributionally robust optimization (DRO) is a widely used framework for optimizing objective functionals in the presence of both randomness and model-form uncertainty. A key step in the practical solution of many DRO problems is a…
Training large-scale neural networks requires solving nonconvex optimization where the choice of optimizer fundamentally determines both convergence behavior and computational efficiency. While adaptive methods like Adam have long dominated…
This paper proposes a theoretical and computational framework for training and robustness verification of implicit neural networks based upon non-Euclidean contraction theory. The basic idea is to cast the robustness analysis of a neural…
We examine robust output feedback control of discrete-time nonlinear systems with bounded uncertainties affecting the dynamics and measurements. Specifically, we demonstrate how to construct semi-infinite programs that produce gains to…
We consider minimizing a function consisting of a quadratic term and a proximable term which is possibly nonconvex and nonsmooth. This problem is also known as scaled proximal operator. Despite its simple form, existing methods suffer from…
We propose a minimum distance estimation method for robust regression in sparse high-dimensional settings. The traditional likelihood-based estimators lack resilience against outliers, a critical issue when dealing with high-dimensional…
The robust adjustment of nonlinear models to data is considered in this paper. When data comes from real experiments, it is possible that measurement errors cause the appearance of discrepant values, which should be ignored when adjusting…