Related papers: A Fully First-Order Layer for Differentiable Optim…
Differentiable simulators promise faster computation time for reinforcement learning by replacing zeroth-order gradient estimates of a stochastic objective with an estimate based on first-order gradients. However, it is yet unclear what…
In modern decentralized applications, ensuring communication efficiency and privacy for the users are the key challenges. In order to train machine-learning models, the algorithm has to communicate to the data center and sample data for its…
First-order methods for solving convex optimization problems have been at the forefront of mathematical optimization in the last 20 years. The rapid development of this important class of algorithms is motivated by the success stories…
Second-order methods, which utilize gradients as well as Hessians to optimize a given function, are of major importance in mathematical optimization. In this work, we prove tight bounds on the oracle complexity of such methods for smooth…
We establish new lower-bounds for the information complexity of mixed-integer convex optimization under two "bit-wise" oracles. The first oracle provides bits of first-order information in the standard coordinate model, and the second…
First-order algorithms have been popular for solving convex and non-convex optimization problems. A key assumption for the majority of these algorithms is that the gradient of the objective function is globally Lipschitz continuous, but…
Bilevel reinforcement learning (RL), which features intertwined two-level problems, has attracted growing interest recently. The inherent non-convexity of the lower-level RL problem is, however, to be an impediment to developing bilevel…
In this paper, we study a class of bilevel optimization program (BP), where the feasible set of the lower level program is independent of the upper level variable. For bilevel programs it is known that the first order approach requires the…
We propose first order algorithms for convex optimization problems where the feasible set is described by a large number of convex inequalities that is to be explored by subgradient projections. The first algorithm is an adaptation of a…
Bilevel optimization provides a powerful framework for modelling hierarchical decision-making systems. This work presents a sensitivity-based algorithm that addresses the bilevel structure directly by treating the lower-level optimal…
This paper considers distributed optimization problems, where each agent cooperatively minimizes the sum of local objective functions through the communication with its neighbors. The widely adopted distributed gradient method in solving…
Second-order optimization uses curvature information about the objective function, which can help in faster convergence. However, such methods typically require expensive computation of the Hessian matrix, preventing their usage in a…
Simple bilevel problems are optimization problems in which we want to find an optimal solution to an inner problem that minimizes an outer objective function. Such problems appear in many machine learning and signal processing applications…
Bilevel optimization is a powerful tool for many machine learning problems, such as hyperparameter optimization and meta-learning. Estimating hypergradients (also known as implicit gradients) is crucial for developing gradient-based methods…
We develop and analyze several different second-order algorithms for computing a near-optimal solution path of a convex parametric optimization problem with smooth Hessian. Our algorithms are inspired by a differential equation perspective…
We study a class of algorithms for solving bilevel optimization problems in both stochastic and deterministic settings when the inner-level objective is strongly convex. Specifically, we consider algorithms based on inexact implicit…
Federated learning (FL) has emerged as a powerful paradigm for collaborative model training across distributed clients while preserving data privacy. However, existing FL algorithms predominantly focus on unconstrained optimization problems…
The complexity in large-scale optimization can lie in both handling the objective function and handling the constraint set. In this respect, stochastic Frank-Wolfe algorithms occupy a unique position as they alleviate both computational…
We derive several numerical methods for designing optimized first-order algorithms in unconstrained convex optimization settings. Our methods are based on the Performance Estimation Problem (PEP) framework, which casts the worst-case…
Hierarchical decision making problems, such as bilevel programs and Stackelberg games, are attracting increasing interest in both the engineering and machine learning communities. Yet, existing solution methods lack either convergence…