Related papers: Learning Weakly Convex Sets in Metric Spaces

We present an efficient and practical algorithm for the online prediction of discrete-time linear dynamical systems with a symmetric transition matrix. We circumvent the non-convex optimization problem using improper learning: carefully…

Clustering is a fundamental problem in unsupervised learning. Popular methods like K-means, may suffer from poor performance as they are prone to get stuck in its local minima. Recently, the sum-of-norms (SON) model (also known as the…

We consider minimization of stochastic functionals that are compositions of a (potentially) non-smooth convex function $h$ and smooth function $c$ and, more generally, stochastic weakly-convex functionals. We develop a family of stochastic…

Recently, deep learning approaches with various network architectures have achieved significant performance improvement over existing iterative reconstruction methods in various imaging problems. However, it is still unclear why these deep…

In this paper we analyze several new methods for solving nonconvex optimization problems with the objective function formed as a sum of two terms: one is nonconvex and smooth, and another is convex but simple and its structure is known.…

Many meta-learning approaches for few-shot learning rely on simple base learners such as nearest-neighbor classifiers. However, even in the few-shot regime, discriminatively trained linear predictors can offer better generalization. We…

Constrained bilevel optimization tackles nested structures present in constrained learning tasks like constrained meta-learning, adversarial learning, and distributed bilevel optimization. However, existing bilevel optimization methods…

The rapid development of machine learning (ML) and artificial intelligence (AI) applications requires the training of large numbers of models. This growing demand highlights the importance of training models without human supervision, while…

We formalize and study the natural approach of designing convex surrogate loss functions via embeddings, for problems such as classification, ranking, or structured prediction. In this approach, one embeds each of the finitely many…

We consider the problem of adversarial bandit convex optimization, that is, online learning over a sequence of arbitrary convex loss functions with only one function evaluation for each of them. While all previous works assume known and…

Verifying the robustness of machine learning models against evasion attacks at test time is an important research problem. Unfortunately, prior work established that this problem is NP-hard for decision tree ensembles, hence bound to be…

In the field of machine unlearning, certified unlearning has been extensively studied in convex machine learning models due to its high efficiency and strong theoretical guarantees. However, its application to deep neural networks (DNNs),…

A fundamental question in reinforcement learning theory is: suppose the optimal value functions are linear in given features, can we learn them efficiently? This problem's counterpart in supervised learning, linear regression, can be solved…

In part \textit{I} we proposed a structure for a general Hypotheses Space $\mathcal{H}$, the Learning Space $\mathbb{L}(\mathcal{H})$, which can be employed to avoid \textit{overfitting} when estimating in a complex space with relative…

This manuscript studies statistical properties of linear classifiers obtained through minimization of an unregularized convex risk over a finite sample. Although the results are explicitly finite-dimensional, inputs may be passed through…

The Euclidean projection onto a convex set is an important problem that arises in numerous constrained optimization tasks. Unfortunately, in many cases, computing projections is computationally demanding. In this work, we focus on…

In many physical systems, inputs related by intrinsic system symmetries are mapped to the same output. When inverting such systems, i.e., solving the associated inverse problems, there is no unique solution. This causes fundamental…

The implicit convex feasibility problem attempts to find a point in the intersection of a finite family of convex sets, some of which are not explicitly determined but may vary. We develop simultaneous and sequential projection methods…

A good measure of similarity between data points is crucial to many tasks in machine learning. Similarity and metric learning methods learn such measures automatically from data, but they do not scale well respect to the dimensionality of…

Federated learning is an efficient machine learning tool for dealing with heterogeneous big data and privacy protection. Federated learning methods with regularization can control the level of communications between the central and local…