Related papers: A Lyapunov Analysis of Accelerated PDHG Algorithms

We study the convergence analysis of continuous-time dynamical systems associated with optimization methods for strongly convex functions. Recent works have proposed systematic constructions of Lyapunov functions for such analysis, while…

This paper addresses the bilinearly coupled minimax optimization problem: $\min_{x \in \mathbb{R}^{d_x}}\max_{y \in \mathbb{R}^{d_y}} \ f_1(x) + f_2(x) + y^{\top} Bx - g_1(y) - g_2(y)$, where $f_1$ and $g_1$ are smooth convex functions,…

Aligning large language models (LLMs) with human preferences is a critical challenge in AI research. While methods like Reinforcement Learning from Human Feedback (RLHF) and Direct Preference Optimization (DPO) are widely used, they often…

In this paper, we develop a unified framework able to certify both exponential and subexponential convergence rates for a wide range of iterative first-order optimization algorithms. To this end, we construct a family of parameter-dependent…

We introduce a novel primal-dual flow for affine constrained convex optimization problems. As a modification of the standard saddle-point system, our primal-dual flow is proved to possess the exponential decay property, in terms of a…

Convergence analysis of accelerated first-order methods for convex optimization problems are presented from the point of view of ordinary differential equation solvers. A new dynamical system, called Nesterov accelerated gradient flow, has…

Primal-dual interior-point methods solve constrained convex optimization problems to tight tolerances with speed and robustness. Their solutions are also efficiently differentiable with respect to the problem data through the implicit…

This paper deals with a new Tikhonov regularized primal-dual dynamical system with variable mass and Hessian-driven damping for solving a convex optimization problem with linear equality constraints. The system features several…

By time discretization of a second-order primal-dual dynamical system with damping $\alpha/t$ where an inertial construction in the sense of Nesterov is needed only for the primal variable, we propose a fast primal-dual algorithm for a…

In this paper, we adapt proximal incremental aggregated gradient methods to saddle point problems, which is motivated by decoupling linear transformations in regularized empirical risk minimization models. First, the Primal-Dual Proximal…

Multi-objective optimization (MOO) lies at the core of many machine learning (ML) applications that involve multiple, potentially conflicting objectives (e.g., multi-task learning, multi-objective reinforcement learning, among many others).…

The exponential growth of computational workloads is surpassing the capabilities of conventional architectures, which are constrained by fundamental limits. In-memory computing (IMC) with RRAM provides a promising alternative by providing…

The optimistic gradient method has seen increasing popularity for solving convex-concave saddle point problems. To analyze its iteration complexity, a recent work [arXiv:1906.01115] proposed an interesting perspective that interprets this…

We propose an inexact proximal augmented Lagrangian framework with explicit inner problem termination rule for composite convex optimization problems. We consider arbitrary linearly convergent inner solver including in particular stochastic…

We consider solving a convex, possibly stochastic optimization problem over a randomly time-varying multi-agent network. Each agent has access to some local objective function, and it only has unbiased estimates of the gradients of the…

The primal-dual algorithm recently proposed by Chambolle & Pock (abbreviated as CPA) for structured convex optimization is very efficient and popular. It was shown by Chambolle & Pock in \cite{CP11} and also by Shefi & Teboulle in…

Relying on fixed point techniques, Mahey, Oualibouch and Tao introduced the scaled proximal decomposition on the graph of a maximal monotone operator (SPDG) algorithm and analyzed its performance on inclusions for strongly monotone and…

DPO (Direct Preference Optimization) has become a widely used offline preference optimization algorithm due to its simplicity and training stability. However, DPO is prone to overfitting and collapse. To address these challenges, we propose…

The advent of parameter-efficient fine-tuning methods has significantly reduced the computational burden of adapting large-scale pretrained models to diverse downstream tasks. However, existing approaches often struggle to achieve robust…

The distributed nonconvex optimization problem of minimizing a global cost function formed by a sum of $n$ local cost functions by using local information exchange is considered. This problem is an important component of many machine…