arXiv subjects

Daniel Burbano

Publications and source records attributed to Daniel Burbano.

4 recordsLinked to original sources

arXiv2026

On Performance Guarantees for Federated Learning with Personalized Constraints

Federated learning (FL) has emerged as a communication-efficient algorithmic framework for distributed learning across multiple agents. While standard FL formulations capture unconstrained or globally constrained problems, many practical settings involve heterogeneous resource or model constraints, leading to optimization problems with agent-specific feasible sets. Here, we study a personalized constrained federated optimization problem in which each agent is associated with a convex local objective and a private constraint set. We propose PC-FedAvg, a method in which each agent maintains cross-estimates of the other agents' variables through a multi-block local decision vector. Each agent updates all blocks locally, penalizing infeasibility only in its own block. Moreover, the cross-estimate mechanism enables personalization without requiring consensus or sharing constraint information among agents. We establish communication-complexity rates of $\mathcal{O}(\epsilon^{-2})$ for suboptimality and $\mathcal{O}(\epsilon^{-1})$ for agent-wise infeasibility. Preliminary experiments on the MNIST and CIFAR-10 datasets validate our theoretical findings.

cs.LG↗

arXiv2025

On iteratively regularized first-order methods for simple bilevel optimization

We consider simple bilevel optimization (SBO) problems where the goal is to compute among the optimal solutions of a composite convex optimization problem, one that minimizes a secondary objective function. Our main contribution is threefold. (i) When the upper-level objective is composite and strongly convex, we propose IR-ISTAs, an iteratively regularized proximal gradient method with a prescribed update rule for the regularization parameter. We establish asymptotic convergence of the iterates to the unique optimal solution and simultaneous sublinear rates for suitably defined infeasibility and suboptimality error metrics. (ii) For the same setting, we propose IR-VFISTAs, an iteratively regularized accelerated proximal gradient method, establish its asymptotic convergence, and, under weak sharp minimality, derive faster simultaneous rates than IR-ISTAs. These appear to be the best-known convergence rate guarantees for SBO problems with a strongly convex upper-level objective and improve upon the rates previously established for methods requiring convexity of both levels. (iii) When the upper-level objective is smooth and nonconvex, we propose IPR-VFISTAnc, an inexactly projected iteratively regularized accelerated gradient method, and establish both asymptotic and nonasymptotic convergence guarantees. To the best of our knowledge, this is the first asymptotic stationarity result for this class of SBO problems that does not rely on the weak sharp minimality of the lower-level problem. Moreover, the total iteration complexity of IPR-VFISTAnc matches that of existing methods, while providing a sharper lower-level infeasibility guarantee. We present preliminary numerical experiments on three ill-posed linear inverse problems and an optimal classifier-selection problem.

math.OC↗

arXiv2023

Achieving optimal complexity guarantees for a class of bilevel convex optimization problems

We design and analyze a novel accelerated gradient-based algorithm for a class of bilevel optimization problems. These problems have various applications arising from machine learning and image processing, where optimal solutions of the two levels are interdependent. That is, achieving the optimal solution of an upper-level problem depends on the solution set of a lower-level optimization problem. We significantly improve existing iteration complexity to $\mathcal{O}(ε^{-0.5})$ for both suboptimality and infeasibility error metrics, where $ε>0$ denotes an arbitrary scalar. In addition, contrary to existing methods that require solving the optimization problem sequentially (initially solving an optimization problem to approximate the solution of the lower-level problem followed by a second algorithm), our algorithm concurrently solves the optimization problem. To the best of our knowledge, the proposed algorithm has the fastest known iteration complexity, which matches the optimal complexity for single-level optimization. We conduct numerical experiments on sparse linear regression problems to demonstrate the efficacy of our approach.

math.OC↗

arXiv2014

Distributed PID Control for Consensus of Homogeneous and Heterogeneous Networks

We investigate the use of distributed PID actions to achieve consensus in networks of homogeneous and heterogeneous linear systems. Convergence of the strategy is proved for both cases using appropriate state transformations and Lyapunov functions. The effectiveness of the theoretical results is illustrated via its application to a representative power grid model recently presented in the literature.

math.OC↗