Related papers: Strong Duality Relations in Nonconvex Risk-Constra…

We study the problem of differentially-private (DP) stochastic (convex-concave) saddle-points in the $\ell_1$ setting. We propose $(\varepsilon, \delta)$-DP algorithms based on stochastic mirror descent that attain nearly…

We develop an approach for solving time-consistent risk-sensitive stochastic optimization problems using model-free reinforcement learning (RL). Specifically, we assume agents assess the risk of a sequence of random variables using dynamic…

The main goal of this paper is to investigate strong duality of non-convex semidefinite programming problems (SDPs). In the optimization community, it is well-known that a convex optimization problem satisfies strong duality if the Slater's…

Nonlinear regression has been extensively employed in many computer vision problems (e.g., crowd counting, age estimation, affective computing). Under the umbrella of deep learning, two common solutions exist i) transforming nonlinear…

We introduce a robust optimization model consisting in a family of perturbation functions giving rise to certain pairs of dual optimization problems in which the dual variable depends on the uncertainty parameter. The interest of our…

A fruitful idea, when providing subdifferential formulae and dual representations for convex risk measures, is to make use of the conjugate duality theory in convex optimization. In this paper we underline the outstanding role played by the…

Bilevel optimization problems embed the optimality of a subproblem as a constraint of another optimization problem. We introduce the concept of near-optimality robustness for bilevel optimization, protecting the upper-level solution…

In this article we dwell into the class of so called ill posed Linear Inverse Problems (LIP) in machine learning, which has become almost a classic in recent times. The fundamental task in an LIP is to recover the entire signal / data from…

Large learning rates, when applied to gradient descent for nonconvex optimization, yield various implicit biases including the edge of stability (Cohen et al., 2021), balancing (Wang et al., 2022), and catapult (Lewkowycz et al., 2020).…

The effectiveness of supervised learning techniques has made them ubiquitous in research and practice. In high-dimensional settings, supervised learning commonly relies on dimensionality reduction to improve performance and identify the…

This article introduces an innovative mathematical framework designed to tackle non-linear convex variational problems in reflexive Banach spaces. Our approach employs a versatile technique that can handle a broad range of variational…

We consider the problem of learning functions within the $\mathcal{F}_{p,\pi}$ and Barron spaces, which play crucial roles in understanding random feature models (RFMs), two-layer neural networks, as well as kernel methods. Leveraging tools…

This work studies the strong duality of non-convex matrix factorization problems: we show that under certain dual conditions, these problems and its dual have the same optimum. This has been well understood for convex optimization, but…

We present a general technique for the analysis of first-order methods. The technique relies on the construction of a duality gap for an appropriate approximation of the objective function, where the function approximation improves as the…

We revisit the classical dual ascent algorithm for minimization of convex functionals in the presence of linear constraints, and give convergence results which apply even for non-convex functionals. We describe limit points in terms of the…

We study the universal closest refinement problem on measurable bipartite relations over standard Borel spaces. Given prescribed side measures, the feasible class consists of finite refinement plans concentrated on the relation and carrying…

In this paper we explore the role of duality principles within the problem of rotation averaging, a fundamental task in a wide range of computer vision applications. In its conventional form, rotation averaging is stated as a minimization…

Using convex combination and linesearch techniques, we introduce a novel primal-dual algorithm for solving structured convex-concave saddle point problems with a generic smooth nonbilinear coupling term. Our adaptive linesearch strategy…

We present a novel approach for constrained Bayesian inference. Unlike current methods, our approach does not require convexity of the constraint set. We reduce the constrained variational inference to a parametric optimization over the…

Solving non-convex, NP-hard optimization problems is crucial for training machine learning models, including neural networks. However, non-convexity often leads to black-box machine learning models with unclear inner workings. While convex…