Related papers: Robust Metric Learning by Smooth Optimization
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 $k$…
Many metric learning tasks, such as triplet learning, nearest neighbor retrieval, and visualization, are treated primarily as embedding tasks where the ultimate metric is some variant of the Euclidean distance (e.g., cosine or Mahalanobis),…
We consider the problem of learning a graph from a finite set of noisy graph signal observations, the goal of which is to find a smooth representation of the graph signal. Such a problem is motivated by the desire to infer relational…
We consider a distributionally robust stochastic optimization problem and formulate it as a stochastic two-level composition optimization problem with the use of the mean--semideviation risk measure. In this setting, we consider a single…
We consider the problem of learning from training data obtained in different contexts, where the underlying context distribution is unknown and is estimated empirically. We develop a robust method that takes into account the uncertainty of…
Distance metric learning is a branch of machine learning that aims to learn distances from the data, which enhances the performance of similarity-based algorithms. This tutorial provides a theoretical background and foundations on this…
In this paper, we propose an improved numerical algorithm for solving minimax problems based on nonsmooth optimization, quadratic programming and iterative process. We also provide a rigorous proof of convergence for our algorithm under…
This paper presents a novel method for reformulating non-differentiable collision avoidance constraints into smooth nonlinear constraints using strong duality of convex optimization. We focus on a controlled object whose goal is to avoid…
Interesting theoretical associations have been established by recent papers between the fields of active learning and stochastic convex optimization due to the common role of feedback in sequential querying mechanisms. In this paper, we…
In reinforcement learning, robust policies for high-stakes decision-making problems with limited data are usually computed by optimizing the percentile criterion, which minimizes the probability of a catastrophic failure. Unfortunately,…
This paper presents a new deep learning-based framework for robust nonlinear estimation and control using the concept of a Neural Contraction Metric (NCM). The NCM uses a deep long short-term memory recurrent neural network for a global…
The goal of ordinal embedding is to represent items as points in a low-dimensional Euclidean space given a set of constraints in the form of distance comparisons like "item $i$ is closer to item $j$ than item $k$". Ordinal constraints like…
Distance metric learning aims to learn from the given training data a valid distance metric, with which the similarity between data samples can be more effectively evaluated for classification. Metric learning is often formulated as a…
Distance-based classification is among the most competitive classification methods for time series data. The most critical component of distance-based classification is the selected distance function. Past research has proposed various…
We propose a distributionally robust approach to learning hyperparameters for first-order methods in convex optimization. Given a dataset of problem instances, we minimize a Wasserstein distributionally robust version of the performance…
This paper explores the challenges of PAC learning in semi-enclosed environments that face persistent disruptive noise and demonstrates the weaknesses of traditional learning models based on noise-free data. We present a novel algorithm…
A common goal in statistics and machine learning is to learn models that can perform well against distributional shifts, such as latent heterogeneous subpopulations, unknown covariate shifts, or unmodeled temporal effects. We develop and…
When deploying machine learning solutions, they must satisfy multiple requirements beyond accuracy, such as fairness, robustness, or safety. These requirements are imposed during training either implicitly, using penalties, or explicitly,…
We propose a data-driven technique to automatically learn contextual uncertainty sets in robust optimization, resulting in excellent worst-case and average-case performance while also guaranteeing constraint satisfaction. Our method…
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…