相关论文: Primal-Dual Rates and Certificates

We consider convex-concave saddle point problems with a separable structure and non-strongly convex functions. We propose an efficient stochastic block coordinate descent method using adaptive primal-dual updates, which enables flexible…

We consider the penalized distributionally robust optimization (DRO) problem with a closed, convex uncertainty set, a setting that encompasses learning using $f$-DRO and spectral/$L$-risk minimization. We present Drago, a stochastic…

We consider decision-making problems that are formulated as non-convex optimization programs where uncertainty enters the constraints through an additive term, independent of the decision variables, and robustness is imposed using a finite…

Primal-dual methods in online optimization give several of the state-of-the art results in both of the most common models: adversarial and stochastic/random order. Here we try to provide a more unified analysis of primal-dual algorithms to…

We propose smoothed primal-dual algorithms for solving stochastic and smooth nonconvex optimization problems with linear inequality constraints. Our algorithms are single-loop and only require a single stochastic gradient based on one…

In this paper we consider a general, challenging distributed optimization set-up arising in several important network control applications. Agents of a network want to minimize the sum of local cost functions, each one depending on a local…

We propose a primal--dual technique that applies to infinite dimensional equality constrained problems, in particular those arising from optimal control. As an application of our general framework, we solve a control-constrained double…

The growing reliance on artificial intelligence in safety- and security-critical applications is raising concerns about the robustness of neural networks to erroneous or adversarial input. Certification is a methodology for ensuring model…

The Primal-Dual (PD) algorithm is widely used in convex optimization to determine saddle points. While the stability of the PD algorithm can be easily guaranteed, strict contraction is nontrivial to establish in most cases. This work…

We study theoretical runtime guarantees for a class of optimization problems that occur in a wide variety of inference problems. these problems are motivated by the lasso framework and have applications in machine learning and computer…

We propose a modified primal-dual method for general convex optimization problems with changing constraints. We obtain properties of Lagrangian saddle points for these problems which enable us to establish convergence of the proposed…

We consider large-scale Markov decision processes with an unknown cost function and address the problem of learning a policy from a finite set of expert demonstrations. We assume that the learner is not allowed to interact with the expert…

Despite the non-convexity of most modern machine learning parameterizations, Lagrangian duality has become a popular tool for addressing constrained learning problems. We revisit Augmented Lagrangian methods, which aim to mitigate the…

Discrete diffusion models generate structured sequences by progressively unmasking tokens, but enforcing global property constraints during generation remains an open challenge. We propose primal-dual guided decoding, an inference-time…

This paper shows that the implicit bias of gradient descent on linearly separable data is exactly characterized by the optimal solution of a dual optimization problem given by a smoothed margin, even for general losses. This is in contrast…

This article develops a duality principle applicable to a large class of variational problems. Firstly, we apply the results to a Ginzburg-Landau type model. In a second step, we develop another duality principle and related primal dual…

In this paper we present complexity certification results for a distributed Augmented Lagrangian (AL) algorithm used to solve convex optimization problems involving globally coupled linear constraints. Our method relies on the Accelerated…

In this note, we provide an overarching analysis of primal-dual dynamics associated to linear equality-constrained optimization problems using contraction analysis. For the well-known standard version of the problem: we establish…

A Tikhonov regularized inertial primal\mbox{-}dual dynamical system with time scaling and vanishing damping is proposed for solving a linearly constrained convex optimization problem in Hilbert spaces. The system under consideration…

In this article we develop a new primal dual variational formulation suitable for a large class of non-convex problems in the calculus of variations. The results are obtained through basic tools of convex analysis, duality theory, the…