Apostolos I. Rikos

Nicola Bastianello, Apostolos I. Rikos, Karl H. Johansson

In this paper we consider online distributed learning problems. Online distributed learning refers to the process of training learning models on distributed data sources. In our setting a set of agents need to cooperatively train a learning model from streaming data. Differently from federated learning, the proposed approach does not rely on a central server but only on peer-to-peer communications among the agents. This approach is often used in scenarios where data cannot be moved to a centralized location due to privacy, security, or cost reasons. In order to overcome the absence of a central server, we propose a distributed algorithm that relies on a quantized, finite-time coordination protocol to aggregate the locally trained models. Furthermore, our algorithm allows for the use of stochastic gradients during local training. Stochastic gradients are computed using a randomly sampled subset of the local training data, which makes the proposed algorithm more efficient and scalable than traditional gradient descent. In our paper, we analyze the performance of the proposed algorithm in terms of the mean distance from the online solution. Finally, we present numerical results for a logistic regression task.

Mahtab Talaei, Apostolos I. Rikos, Alex Olshevsky et al.

Motivated by the swift global transmission of infectious diseases, we present a comprehensive framework for network-based epidemic control. Our aim is to curb epidemics using two different approaches. In the first approach, we introduce an optimization strategy that optimally reduces travel rates. We analyze the convergence of this strategy and show that it hinges on the network structure to minimize infection spread. In the second approach, we expand the classic SIR model by incorporating and optimizing quarantined states to strategically contain the epidemic. We show that this problem reduces to the problem of matrix balancing. We establish a link between optimization constraints and the epidemic's reproduction number, highlighting the relationship between network structure and disease dynamics. We demonstrate that applying augmented primal-dual gradient dynamics to the optimal quarantine problem ensures exponential convergence to the KKT point. We conclude by validating our approaches using simulation studies that leverage public data from counties in the state of Massachusetts.

Xu Du, Boyu Han, Ivano Notarnicola et al.

This paper investigates distributed resource allocation optimization over directed graphs with limited communication bandwidth. We develop a novel distributed algorithm that integrates the centralized Proximal Jacobian Alternating Direction Method of Multipliers (PJ-ADMM) with a finite-level quantized consensus scheme, enabling nodes to cooperatively solve the optimization in a distributed fashion. Under the assumption of convex objective functions, we establish that the proposed algorithm achieves sublinear convergence to a neighborhood of the optimal solution, with the convergence accuracy explicitly bounded by the quantization level. Numerical experiments validate that the algorithm achieves competitive performance compared to existing approaches while exhibiting communication efficiency.

Ruochen Wu, Xu Du, Karl H. Johansson et al.

In modern large-scale networked systems, rapidly solving optimization problems while utilizing communication resources efficiently is critical for addressing complex tasks. In this paper, we consider an unconstrained distributed optimization problem in which information exchange among nodes is governed by a directed communication graph. In our setup we focus on two key challenges. The first is the zigzag phenomenon caused by the objective functions of individual nodes having significantly different curvature along different directions. The second is that the communication channels among nodes are subject to limited bandwidth, which motivates the use of compressed (quantized) messages. To address both challenges simultaneously, we propose QANM, a distributed optimization algorithm that combines Nesterov-accelerated gradient descent with a distributed finite-time quantized consensus protocol, enabling accelerated convergence. Under strong convexity and smoothness assumptions, we show that our proposed algorithm converges linearly to a neighborhood of the optimal solution. Finally, we validate our algorithm on a distributed sensor fusion application for multi-dimensional target parameter estimation, where simulations across two distinct scenarios confirm the convergence guarantees and demonstrate clear acceleration benefits over non-momentum baselines.

Xu Du, Jingzhe Wang, Karl H. Johansson et al.

Distributed optimization has found widespread applications in smart grids, optimal control, and machine learning. This paper studies distributed consensus optimization. We extend the Augmented Lagrangian-based Alternating Direction Inexact Newton (ALADIN) framework to propose Consensus ALADIN (C-ALADIN) with a central coordinator, which directly handles consensus constraints. Our C-ALADIN algorithm admits both a first-order variant and a second-order variant that employs a Hessian approximation, avoiding direct transmission of second-order information while preserving fast local convergence. We then develop a decentralized version of C-ALADIN that operates over directed graphs with quantized communication, using a finite-time coordination protocol. For both versions, we establish global convergence guarantees for convex problems and local convergence guarantees for non-convex problems. For the decentralized case, the iterates converge to a neighborhood of the optimum determined by the quantization level. Numerical results demonstrate that our methods retain fast convergence while substantially reducing communication and computational costs compared to existing decentralized approaches.

Boyu Han, Xu Du, Karl H. Johansson et al.

This paper addresses distributed consensus optimization problems with mixed-integer variables, with a specific focus on Boolean variables. We introduce a novel distributed algorithm that extends the Consensus Augmented Lagrangian Alternating Direction Inexact Newton (CALADIN) framework by incorporating specialized techniques for handling Boolean variables without relying on local mixed-integer solvers. Under the mild assumption of Lipschitz continuity of the objective functions, we establish rigorous convergence guarantees for both convex and nonconvex mixed-integer programming problems. Numerical experiments demonstrate that the proposed algorithm achieves competitive performance compared to existing approaches while providing rigorous convergence guarantees.