arXiv subjects

Marina Costantini

Publications and source records attributed to Marina Costantini.

3 recordsLinked to original sources

arXiv2025

Setwise Coordinate Descent for Dual Asynchronous Decentralized Optimization

In decentralized optimization over networks, synchronizing the updates of all nodes incurs significant communication overhead. For this reason, much of the recent literature has focused on the analysis and design of asynchronous optimization algorithms where nodes can activate anytime and contact a single neighbor to complete an iteration together. However, most works assume that the neighbor selection is done at random based on a fixed probability distribution (e.g., uniform), a choice that ignores the optimization landscape at the moment of activation. Instead, in this work we introduce an optimization-aware selection rule that chooses the neighbor providing the highest dual cost improvement (a quantity related to a dualization of the problem based on consensus). This scheme is related to the coordinate descent (CD) method with the Gauss-Southwell (GS) rule for coordinate updates; in our setting however, only a subset of coordinates is accessible at each iteration (because each node can communicate only with its neighbors), so the existing literature on GS methods does not apply. To overcome this difficulty, we develop a new analytical framework for smooth and strongly convex functions that covers our new class of setwise CD algorithms -- a class that applies to both decentralized and parallel distributed computing scenarios -- and we show that the proposed setwise GS rule can speed up the convergence in terms of iterations by a factor equal to the size of the largest coordinate set. We analyze extensions of these algorithms that exploit the knowledge of the smoothness constants when available and otherwise propose an algorithm to estimate these constants. Finally, we validate our theoretical results through extensive simulations.

math.OC↗

arXiv2023

FedDec: Peer-to-peer Aided Federated Learning

Federated learning (FL) has enabled training machine learning models exploiting the data of multiple agents without compromising privacy. However, FL is known to be vulnerable to data heterogeneity, partial device participation, and infrequent communication with the server, which are nonetheless three distinctive characteristics of this framework. While much of the recent literature has tackled these weaknesses using different tools, only a few works have explored the possibility of exploiting inter-agent communication to improve FL's performance. In this work, we present FedDec, an algorithm that interleaves peer-to-peer communication and parameter averaging (similar to decentralized learning in networks) between the local gradient updates of FL. We analyze the convergence of FedDec under the assumptions of non-iid data distribution, partial device participation, and smooth and strongly convex costs, and show that inter-agent communication alleviates the negative impact of infrequent communication rounds with the server by reducing the dependence on the number of local updates $H$ from $O(H^2)$ to $O(H)$. Furthermore, our analysis reveals that the term improved in the bound is multiplied by a constant that depends on the spectrum of the inter-agent communication graph, and that vanishes quickly the more connected the network is. We confirm the predictions of our theory in numerical simulations, where we show that FedDec converges faster than FedAvg, and that the gains are greater as either $H$ or the connectivity of the network increase.

cs.LG↗

arXiv2022

Pick your Neighbor: Local Gauss-Southwell Rule for Fast Asynchronous Decentralized Optimization

In decentralized optimization environments, each agent $i$ in a network of $n$ nodes has its own private function $f_i$, and nodes communicate with their neighbors to cooperatively minimize the aggregate objective $\sum_{i=1}^n f_i$. In this setting, synchronizing the nodes' updates incurs significant communication overhead and computational costs, so much of the recent literature has focused on the analysis and design of asynchronous optimization algorithms, where agents activate and communicate at arbitrary times without needing a global synchronization enforcer. However, most works assume that when a node activates, it selects the neighbor to contact based on a fixed probability (e.g., uniformly at random), a choice that ignores the optimization landscape at the moment of activation. Instead, in this work we introduce an optimization-aware selection rule that chooses the neighbor providing the highest dual cost improvement (a quantity related to a dualization of the problem based on consensus). This scheme is related to the coordinate descent (CD) method with the Gauss-Southwell (GS) rule for coordinate updates; in our setting however, only a subset of coordinates is accessible at each iteration (because each node can communicate only with its neighbors), so the existing literature on GS methods does not apply. To overcome this difficulty, we develop a new analytical framework for smooth and strongly convex $f_i$ that covers the class of set-wise CD algorithms -- a class that directly applies to decentralized scenarios, but is not limited to them -- and we show that the proposed set-wise GS rule achieves a speedup factor of up to the maximum degree in the network (which is in the order of $Θ(n)$ for highly connected graphs). The speedup predicted by our analysis is validated in numerical experiments with synthetic data.

math.OC↗