Related papers: Accelerating Multi-Block Constrained Optimization …
The augmented Lagrangian method (ALM) is one of the most useful methods for constrained optimization. Its convergence has been well established under convexity assumptions or smoothness assumptions, or under both assumptions. ALM may…
Existing multi-objective preference alignment methods for large language models (LLMs) face limitations: (1) the inability to effectively balance various preference dimensions, and (2) reliance on auxiliary reward/reference models…
Continual learning is inherently a constrained learning problem. The goal is to learn a predictor under a no-forgetting requirement. Although several prior studies formulate it as such, they do not solve the constrained problem explicitly.…
In this paper, we consider solving multiple-block separable convex minimization problems using alternating direction method of multipliers (ADMM). Motivated by the fact that the existing convergence theory for ADMM is mostly limited to the…
We present a numerical method for the minimization of objectives that are augmented with large quadratic penalties of overdetermined inconsistent equality constraints. Such objectives arise from quadratic integral penalty methods for the…
The use of momentum in stochastic optimization algorithms has shown empirical success across a range of machine learning tasks. Recently, a new class of stochastic momentum algorithms has emerged within the Linear Minimization Oracle (LMO)…
This paper presents a novel approach to enhance Model Predictive Control (MPC) for legged robots through Distributed Optimization. Our method focuses on decomposing the robot dynamics into smaller, parallelizable subsystems, and utilizing…
Within the framework of the augmented Lagrangian (AL), we propose a novel distributed optimization method, termed Distributed Augmented Lagrangian Decomposition (DALD), and provide a rigorous convergence proof for its standard version. To…
This work presents an adaptive superfast proximal augmented Lagrangian (AS-PAL) method for solving linearly-constrained smooth nonconvex composite optimization problems. Each iteration of AS-PAL inexactly solves a possibly nonconvex…
First-order methods (FOMs) have been widely used for solving large-scale problems. A majority of existing works focus on problems without constraint or with simple constraints. Several recent works have studied FOMs for problems with…
Constrained reinforcement learning has achieved promising progress in safety-critical fields where both rewards and constraints are considered. However, constrained reinforcement learning methods face challenges in striking the right…
We propose a new self-adaptive, double-loop smoothing algorithm to solve composite, nonsmooth, and constrained convex optimization problems. Our algorithm is based on Nesterov's smoothing technique via general Bregman distance functions. It…
This paper presents a majorized alternating direction method of multipliers (ADMM) with indefinite proximal terms for solving linearly constrained $2$-block convex composite optimization problems with each block in the objective being the…
Applications abound in which optimization problems must be repeatedly solved, each time with new (but similar) data. Analytic optimization algorithms can be hand-designed to provably solve these problems in an iterative fashion. On one…
The remarkable performance of Large Language Models (LLMs) highly relies on crafted prompts. However, manual prompt engineering is a laborious process, creating a core bottleneck for practical application of LLMs. This phenomenon has led to…
Efficient estimation of high-dimensional matrices-including covariance and precision matrices-is a cornerstone of modern multivariate statistics. Most existing studies have focused primarily on the theoretical properties of the estimators…
The nonconvex and nonsmooth finite-sum optimization problem with linear constraint has attracted much attention in the fields of artificial intelligence, computer, and mathematics, due to its wide applications in machine learning and the…
Alternating Direction Method of Multipliers (ADMM) algorithm has been widely adopted for solving the distributed optimization problem (DOP). In this paper, a new distributed parallel ADMM algorithm is proposed, which allows the agents to…
The alternating direction method of multipliers (ADMM) is one of the most widely used first-order optimisation methods in the literature owing to its simplicity, flexibility and efficiency. Over the years, numerous efforts are made to…
Multi-objective combinatorial optimization seeks Pareto-optimal solutions over exponentially large discrete spaces, yet existing methods sacrifice generality, scalability, or theoretical guarantees. We reformulate it as an online learning…