Related papers: Scalable Min-Max Optimization via Primal-Dual Exac…
Hyperparameter tuning is an active area of research in machine learning, where the aim is to identify the optimal hyperparameters that provide the best performance on the validation set. Hyperparameter tuning is often achieved using naive…
We introduce the primal-dual quasi-Newton (PD-QN) method as an approximated second order method for solving decentralized optimization problems. The PD-QN method performs quasi-Newton updates on both the primal and dual variables of the…
This work aims to minimize a continuously differentiable convex function with Lipschitz continuous gradient under linear equality constraints. The proposed inertial algorithm results from the discretization of the second-order primal-dual…
This paper proposes and establishes the iteration-complexity of an inexact proximal accelerated augmented Lagrangian (IPAAL) method for solving linearly constrained smooth nonconvex composite optimization problems. Each IPAAL iteration…
Motivated by energy management for micro-grids, we study convex optimization problems with uncertainty in the objective function and sequential decision making. To solve these problems, we propose a new framework called ``Online…
We address the problem of minimizing a smooth function under smooth equality constraints. Under regularity assumptions on these constraints, we propose a notion of approximate first- and second-order critical point which relies on the…
This paper addresses the problem of safe optimization under a single smooth constraint, a scenario that arises in diverse real-world applications such as robotics and autonomous navigation. The objective of safe optimization is to solve a…
Recent results in Compressive Sensing have shown that, under certain conditions, the solution to an underdetermined system of linear equations with sparsity-based regularization can be accurately recovered by solving convex relaxations of…
In this paper, we consider optimizing a smooth, convex, lower semicontinuous function in Riemannian space with constraints. To solve the problem, we first convert it to a dual problem and then propose a general primal-dual algorithm to…
AI inference scaling is often tuned through 1D heuristics (a fixed reasoning pass) or 2D bivariate trade-offs (e.g., accuracy vs. compute), which fail to consider cost and latency constraints. We introduce a 3D optimization framework that…
Prediction+optimization is a common real-world paradigm where we have to predict problem parameters before solving the optimization problem. However, the criteria by which the prediction model is trained are often inconsistent with the goal…
We consider the problem of minimizing a high-dimensional objective function, which may include a regularization term, using (possibly noisy) evaluations of the function. Such optimization is also called derivative-free, zeroth-order, or…
We study a class of convex-concave saddle-point problems of the form $\min_x\max_y \langle Kx,y\rangle+f_{\cal{P}}(x)-h^\ast(y)$ where $K$ is a linear operator, $f_{\cal{P}}$ is the sum of a convex function $f$ with a Lipschitz-continuous…
In a multiobjective optimization problem a solution is called Pareto-optimal if no criterion can be improved without deteriorating at least one of the other criteria. Computing the set of all Pareto-optimal solutions is a common task in…
Multiobjective optimization plays an increasingly important role in modern applications, where several objectives are often of equal importance. The task in multiobjective optimization and multiobjective optimal control is therefore to…
We prove a general result demonstrating the power of Lagrangian relaxation in solving constrained maximization problems with arbitrary objective functions. This yields a unified approach for solving a wide class of {\em subset selection}…
Despite the success of single-agent reinforcement learning, multi-agent reinforcement learning (MARL) remains challenging due to complex interactions between agents. Motivated by decentralized applications such as sensor networks, swarm…
Classification, recommendation, and ranking problems often involve competing goals with additional constraints (e.g., to satisfy fairness or diversity criteria). Such optimization problems are quite challenging, often involving non-convex…
During the past two decades, multi-agent optimization problems have drawn increased attention from the research community. When multiple objective functions are present among agents, many works optimize the sum of these objective functions.…
Gradient-based minimax optimal algorithms have greatly promoted the development of continuous optimization and machine learning. One seminal work due to Yurii Nesterov [Nes83a] established $\tilde{\mathcal{O}}(\sqrt{L/\mu})$ gradient…