Federated learning with differential privacy suffers from two major costs: each client must transmit $d$-dimensional gradients every round, and the magnitude of DP noise grows with $d$. Yet empirical studies show that gradient updates exhibit strong temporal correlations and lie in a $k$-dimensional subspace with $k \ll d$. Motivated by this, we introduce DOME, a decentralized DP optimization framework in which each client maintains a compact sketch to project gradients into $\mathbb{R}^k$ before privatization and Secure Aggregation. This reduces per-round communication from order $d$ to order $k$ and moves towards a gradient approximation mean-squared error of $\sigma^2 k$. To allow the sketch to span new directions and prevent it from collapsing onto historical gradients, we augment it with random probes orthogonal to historical directions. We prove that our overall protocol satisfies $(\epsilon,\delta)$-Differential Privacy.
We propose two first-order methods for convex, non-smooth, distributed optimization problems, hereafter called Multi-Timescale Gradient Sliding (MT-GS) and its accelerated variant (AMT-GS). Our MT-GS and AMT-GS can take advantage of similarities between (local) objectives to reduce the communication rounds, are flexible so that different subsets (of agents) can communicate at different, user-picked rates, and are fully deterministic. These three desirable features are achieved through a block-decomposable primal-dual formulation, and a multi-timescale variant of the sliding method introduced in Lan et al. (2020), Lan (2016), where different dual blocks are updated at potentially different rates. To find an $\epsilon$-suboptimal solution, the complexities of our algorithms achieve optimal dependency on $\epsilon$: MT-GS needs $O(\overline{r}A/\epsilon)$ communication rounds and $O(\overline{r}/\epsilon^2)$ subgradient steps for Lipchitz objectives, and AMT-GS needs $O(\overline{r}A/\sqrt{\epsilon\mu})$ communication rounds and $O(\overline{r}/(\epsilon\mu))$ subgradient steps if the objectives are also $\mu$-strongly convex. Here, $\overline{r}$ measures the ``average rate of updates'' for dual blocks, and $A$ measures similarities between (subgradients of) local functions. In addition, the linear dependency of communication rounds on $A$ is optimal (Arjevani and Shamir 2015), thereby providing a positive answer to the open question whether such dependency is achievable for non-smooth objectives (Arjevani and Shamir 2015).
\textit{DPLib} is an open-source MATLAB-based benchmark library created to support research and development in distributed and decentralized power system analysis and optimization. Distributed and decentralized methods offer scalability, privacy preservation, and resilience to single points of failure, making them increasingly important for modern power systems. However, unlike centralized tools such as MATPOWER, no general-purpose, reproducible data library package currently exists for distributed power system studies. DPLib fills this gap by providing a standard power system library featuring over 20 multi-region benchmark test cases of varying sizes, along with a graph-based partitioning toolkit that decomposes any MATPOWER test system into multiple electrically coherent regions. The partitioning toolkit, an easy-to-use MATLAB code, generates standardized \texttt{.mat} and \texttt{.m} files, along with region visualizations for intuitive understanding. We also provide modular, easy-to-use distributed optimal power flow (OPF) solvers: an alternating direction method of multipliers(ADMM)-based DC-OPF solver implemented in YALMIP, and an ADMM-based AC-OPF solver leveraging IPOPT. These solvers validate the generated test systems for distributed optimization applications. Numerical results validate the generated test cases, establishing DPLib as a foundation for reproducible distributed power system research.
This paper considers the problem of decentralized optimization on compact submanifolds, where a finite sum of smooth (possibly non-convex) local functions is minimized by $n$ agents forming an undirected and connected graph. However, the efficiency of distributed optimization is often hindered by communication bottlenecks. To mitigate this, we propose the Quantized Riemannian Gradient Tracking (Q-RGT) algorithm, where agents update their local variables using quantized gradients. The introduction of quantization noise allows our algorithm to bypass the constraints of the accurate Riemannian projection operator (such as retraction), further improving iterative efficiency. To the best of our knowledge, this is the first algorithm to achieve an $\mathcal{O}(1/K)$ convergence rate in the presence of quantization, matching the convergence rate of methods without quantization. Additionally, we explicitly derive lower bounds on decentralized consensus associated with a function of quantization levels. Numerical experiments demonstrate that Q-RGT performs comparably to non-quantized methods while reducing communication bottlenecks and computational overhead.
Distributed optimization has become the default training paradigm in modern machine learning due to the growing scale of models and datasets. To mitigate communication overhead, local updates are often applied before global aggregation, resulting in a nested optimization approach with inner and outer steps. However, heavy-tailed stochastic gradient noise remains a significant challenge, particularly in attention-based models, hindering effective training. In this work, we propose TailOPT, an efficient framework designed to address heavy-tailed noise by leveraging adaptive optimization or clipping techniques. We establish convergence guarantees for the TailOPT framework under heavy-tailed noise with potentially unbounded gradient variance and local updates. Among its variants, we highlight a memory and communication efficient instantiation which we call $Bi^2Clip$, which performs coordinate-wise clipping at both the inner and outer optimizers, achieving adaptive-like performance (e.g., Adam) without the cost of maintaining or transmitting additional gradient statistics. Empirically, TailOPT, including $Bi^2Clip$, demonstrates superior performance on several language tasks and models, outperforming state-of-the-art methods.
We consider a standard distributed optimization problem in which networked nodes collaboratively minimize the sum of their locally known convex costs. For this setting, we address for the first time the fundamental problem of design and analysis of distributed methods to solve the above problem when inter-node communication is subject to \emph{heavy-tailed} noise. Heavy-tailed noise is highly relevant and frequently arises in densely deployed wireless sensor and Internet of Things (IoT) networks. Specifically, we design a distributed gradient-type method that features a carefully balanced mixed time-scale time-varying consensus and gradient contribution step sizes and a bounded nonlinear operator on the consensus update to limit the effect of heavy-tailed noise. Assuming heterogeneous strongly convex local costs with mutually different minimizers that are arbitrarily far apart, we show that the proposed method converges to a neighborhood of the network-wide problem solution in the mean squared error (MSE) sense, and we also characterize the corresponding convergence rate. We further show that the asymptotic MSE can be made arbitrarily small through consensus step-size tuning, possibly at the cost of slowing down the transient error decay. Numerical experiments corroborate our findings and demonstrate the resilience of the proposed method to heavy-tailed (and infinite variance) communication noise. They also show that existing distributed methods, designed for finite-communication-noise-variance settings, fail in the presence of infinite variance noise.
The massive integration of uncertain distributed renewable energy resources into power systems raises power imbalance concerns. Peer-to-peer (P2P) energy trading provides a promising way to balance the prosumers' volatile energy power generation and demands locally. Particularly, to protect the privacy of prosumers, distributed P2P energy trading is broadly advocated. However, severe privacy leakage issues can emerge in the realistic fully distributed P2P energy trading paradigm. Meanwhile, in this paradigm, two-party and multi-party computations coexist, challenging the naive privacy-preserving techniques. To tackle privacy leakage issues arising from the fully distributed P2P energy trading, this paper proposes a privacy-preserving approach via hybrid secure computations. A secure multi-party computation mechanism consisting of offline and online phases is developed to ensure the security of shared data by leveraging the tailored secret sharing method. In addition, the Paillier encryption method based on the Chinese Remainder Theorem is proposed for both the secure two-party computation and the offline phase of the multi-party computation. The random encryption coefficient is designed to enhance the security of the two-party computation and simultaneously guarantee the convergence of the distributed optimization. The feasible range for the encryption coefficient is derived with a strict mathematical proof. Numerical simulations demonstrate the exactness, effectiveness, and scalability of the proposed privacy-preserving approach.
The proliferation of distributed renewable energy triggers the peer-to-peer (P2P) energy market formations. To make profits, prosumers equipped with photovoltaic (PV) panels and even the energy storage system (ESS) can actively participate in the real-time P2P energy market and trade energy. However, in real situations, system states such as energy demands and renewable energy power generation are highly uncertain, making it difficult for prosumers to make optimal real-time decisions. Moreover, severe problems with the physical network can arise from the real-time P2P energy trading, such as bus voltage violations and line overload. To handle these problems, this work first formulates the real-time P2P energy trading problem as a spatio-temporally constrained stochastic optimization problem by considering ESS and the spatial physical network constraints. To deal with the uncertainties online, a modified Lyapunov optimization method is innovatively proposed to approximately reformulate the stochastic optimization problem into an online one by relaxing the time-coupling constraints. Compared with the state-of-the-art online methods, the proposed one renders more flexibility and better performance for the real-time P2P energy market operation. Additionally, to protect the prosumers' privacy, an online distributed algorithm based on the consensus alternating direction method of multipliers (ADMM) is developed to solve the reformulated online problem by decoupling the spatial constraints. The theoretical near-optimal performance guarantee of the proposed online distributed algorithm is derived, and its performance can be further improved by minimizing the performance gap. Simulation results demonstrate that the proposed online distributed algorithm can guarantee the fast, stable, and safe long-term operation of the real-time P2P energy market.
This book offers a hands-on introduction to building and understanding federated learning (FL) systems. FL enables multiple devices -- such as smartphones, sensors, or local computers -- to collaboratively train machine learning (ML) models, while keeping their data private and local. It is a powerful solution when data cannot or should not be centralized due to privacy, regulatory, or technical reasons. The book is designed for students, engineers, and researchers who want to learn how to design scalable, privacy preserving FL systems. Our main focus is on personalization: enabling each device to train its own model while still benefiting from collaboration with relevant devices. This is achieved by leveraging similarities between (the learning tasks associated with) devices that are encoded by the weighted edges (or links) of a federated learning network (FL network). The key idea is to represent real-world FL systems as networks of devices, where nodes correspond to device and edges represent communication links and data similarities between them. The training of personalized models for these devices can be naturally framed as a distributed optimization problem. This optimization problem is referred to as generalized total variation minimization (GTVMin) and ensures that devices with similar learning tasks learn similar model parameters. Our approach is both mathematically principled and practically motivated. While we introduce some advanced ideas from optimization theory and graph-based learning, we aim to keep the book accessible. Readers are guided through the core ideas step by step, with intuitive explanations.
We propose a history-driven target (HDT) framework in Markov Chain Monte Carlo (MCMC) to improve any random walk algorithm on discrete state spaces, such as general undirected graphs, for efficient sampling from target distribution $\boldsymbol{\mu}$. With broad applications in network science and distributed optimization, recent innovations like the self-repellent random walk (SRRW) achieve near-zero variance by prioritizing under-sampled states through transition kernel modifications based on past visit frequencies. However, SRRW's reliance on explicit computation of transition probabilities for all neighbors at each step introduces substantial computational overhead, while its strict dependence on time-reversible Markov chains excludes advanced non-reversible MCMC methods. To overcome these limitations, instead of direct modification of transition kernel, HDT introduces a history-dependent target distribution $\boldsymbol{\pi}[\mathbf{x}]$ to replace the original target $\boldsymbol{\mu}$ in any graph sampler, where $\mathbf{x}$ represents the empirical measure of past visits. This design preserves lightweight implementation by requiring only local information between the current and proposed states and achieves compatibility with both reversible and non-reversible MCMC samplers, while retaining unbiased samples with target distribution $\boldsymbol{\mu}$ and near-zero variance performance. Extensive experiments in graph sampling demonstrate consistent performance gains, and a memory-efficient Least Recently Used (LRU) cache ensures scalability to large general graphs.
We propose LAGO - Language Similarity-Aware Graph Optimization - a novel approach for few-shot cross-lingual embedding inversion attacks, addressing critical privacy vulnerabilities in multilingual NLP systems. Unlike prior work in embedding inversion attacks that treat languages independently, LAGO explicitly models linguistic relationships through a graph-based constrained distributed optimization framework. By integrating syntactic and lexical similarity as edge constraints, our method enables collaborative parameter learning across related languages. Theoretically, we show this formulation generalizes prior approaches, such as ALGEN, which emerges as a special case when similarity constraints are relaxed. Our framework uniquely combines Frobenius-norm regularization with linear inequality or total variation constraints, ensuring robust alignment of cross-lingual embedding spaces even with extremely limited data (as few as 10 samples per language). Extensive experiments across multiple languages and embedding models demonstrate that LAGO substantially improves the transferability of attacks with 10-20% increase in Rouge-L score over baselines. This work establishes language similarity as a critical factor in inversion attack transferability, urging renewed focus on language-aware privacy-preserving multilingual embeddings.
In modern large-scale systems with sensor networks and IoT devices it is essential to collaboratively solve complex problems while utilizing network resources efficiently. In our paper we present three distributed optimization algorithms that exhibit efficient communication among nodes. Our first algorithm presents a simple quantized averaged gradient procedure for distributed optimization, which is shown to converge to a neighborhood of the optimal solution. Our second algorithm incorporates a novel event-triggered refinement mechanism, which refines the utilized quantization level to enhance the precision of the estimated optimal solution. It enables nodes to terminate their operation according to predefined performance guarantees. Our third algorithm is tailored to operate in environments where each message consists of only a few bits. It incorporates a novel event-triggered mechanism for adjusting the quantizer basis and quantization level, allowing nodes to collaboratively decide operation termination based on predefined performance criteria. We analyze the three algorithms and establish their linear convergence. Finally, an application on distributed sensor fusion for target localization is used to demonstrate their favorable performance compared to existing algorithms in the literature.
This paper presents a novel distributed model predictive control (MPC) formulation without terminal cost and a corresponding distributed synthesis approach for distributed linear discrete-time systems with coupled constraints. The proposed control scheme introduces an explicit stability condition as an additional constraint based on relaxed dynamic programming. As a result, contrary to other related approaches, system stability with the developed controller does not rely on designing a terminal cost. A distributed synthesis approach is then introduced to handle the stability constraint locally within each local agent. To solve the underlying optimization problem for distributed MPC, a violation-free distributed optimization approach is developed, using constraint tightening to ensure feasibility throughout iterations. A numerical example demonstrates that the proposed distributed MPC approach ensures closed-loop stability for each feasible control sequence, with each agent computing its control input in parallel.
In this paper, we address the problem of optimizing flows on generalized graphs that feature multiple entry points and multiple populations, each with varying cost structures. We tackle this problem by considering the multi-population Wardrop equilibrium, defined through variational inequalities. We rigorously analyze the existence and uniqueness of the Wardrop equilibrium. Furthermore, we introduce an efficient numerical method to find the solution. In particular, we reformulate the equilibrium problem as a distributed optimization problem over subgraphs and introduce a novel Hessian Riemannian flow method, a Riemannian-manifold-projected Hessian flow, to efficiently compute a solution. Finally, we demonstrate the effectiveness of our approach through examples in urban traffic management, including routing for diverse vehicle types and strategies for minimizing emissions in congested environments.
This paper presents two attack strategies designed to evade detection in ADMM-based systems by preventing significant changes to the residual during the attacked iteration. While many detection algorithms focus on identifying false data injection through residual changes, we show that our attacks remain undetected by keeping the residual largely unchanged. The first strategy uses a random starting point combined with Gram-Schmidt orthogonalization to ensure stealth, with potential for refinement by enhancing the orthogonal component to increase system disruption. The second strategy builds on the first, targeting financial gains by manipulating reactive power and pushing the system to its upper voltage limit, exploiting operational constraints. The effectiveness of the proposed attack-resilient mechanism is demonstrated through case studies on the IEEE 14-bus system. A comparison of the two strategies, along with commonly used naive attacks, reveals trade-offs between simplicity, detectability, and effectiveness, providing insights into ADMM system vulnerabilities. These findings underscore the need for more robust monitoring algorithms to protect against advanced attack strategies.
In this paper, we address the distributed optimization problem over unidirectional networks with possibly time-invariant heterogeneous bounded transmission delays. In particular, we propose a modified version of the Accelerated Distributed Directed OPTimization (ADD-OPT) algorithm, herein called Robustified ADD-OPT (R-ADD-OPT), which is able to solve the distributed optimization problem, even when the communication links suffer from heterogeneous but bounded transmission delays. We show that if the gradient step-size of the R-ADD-OPT algorithm is within a certain range, which also depends on the maximum time delay in the network, then the nodes are guaranteed to converge to the optimal solution of the distributed optimization problem. The range of the gradient step-size that guarantees convergence can be computed a priori based on the maximum time delay in the network.
In this paper, we consider the distributed optimal control problem for linear networked systems. In particular, we are interested in learning distributed optimal controllers using graph recurrent neural networks (GRNNs). Most of the existing approaches result in centralized optimal controllers with offline training processes. However, as the increasing demand of network resilience, the optimal controllers are further expected to be distributed, and are desirable to be trained in an online distributed fashion, which are also the main contributions of our work. To solve this problem, we first propose a GRNN-based distributed optimal control method, and we cast the problem as a self-supervised learning problem. Then, the distributed online training is achieved via distributed gradient computation, and inspired by the (consensus-based) distributed optimization idea, a distributed online training optimizer is designed. Furthermore, the local closed-loop stability of the linear networked system under our proposed GRNN-based controller is provided by assuming that the nonlinear activation function of the GRNN-based controller is both local sector-bounded and slope-restricted. The effectiveness of our proposed method is illustrated by numerical simulations using a specifically developed simulator.
Communication remains a key factor limiting the applicability of distributed model predictive control (DMPC) in realistic settings, despite advances in wireless communication. DMPC schemes can require an overwhelming amount of information exchange between agents as the amount of data depends on the length of the predication horizon, for which some applications require a significant length to formally guarantee nominal asymptotic stability. This work aims to provide an approach to reduce the communication effort of DMPC by reducing the size of the communicated data between agents. Using an autoencoder, the communicated data is reduced by the encoder part of the autoencoder prior to communication and reconstructed by the decoder part upon reception within the distributed optimization algorithm that constitutes the DMPC scheme. The choice of a learning-based reduction method is motivated by structure inherent to the data, which results from the data's connection to solutions of optimal control problems. The approach is implemented and tested at the example of formation control of differential-drive robots, which is challenging for optimization-based control due to the robots' nonholonomic constraints, and which is interesting due to the practical importance of mobile robotics. The applicability of the proposed approach is presented first in form of a simulative analysis showing that the resulting control performance yields a satisfactory accuracy. In particular, the proposed approach outperforms the canonical naive way to reduce communication by reducing the length of the prediction horizon. Moreover, it is shown that numerical experiments conducted on embedded computation hardware, with real distributed computation and wireless communication, work well with the proposed way of reducing communication even in practical scenarios in which full communication fails.
This paper presents an enhanced electric vehicle demand response system based on large language models, aimed at optimizing the application of vehicle-to-grid technology. By leveraging an large language models-driven multi-agent framework to construct user digital twins integrated with multidimensional user profile features, it enables deep simulation and precise prediction of users' charging and discharging decision-making patterns. Additionally, a data- and knowledge-driven dynamic incentive mechanism is proposed, combining a distributed optimization model under network constraints to optimize the grid-user interaction while ensuring both economic viability and security. Simulation results demonstrate that the approach significantly improves load peak-valley regulation and charging/discharging strategies. Experimental validation highlights the system's substantial advantages in load balancing, user satisfaction and grid stability, providing decision-makers with a scalable V2G management tool that promotes the sustainable, synergistic development of vehicle-grid integration.
In this paper, we develop a fast mixed-integer convex programming (MICP) framework for multi-robot navigation by combining graph attention networks and distributed optimization. We formulate a mixed-integer optimization problem for receding horizon motion planning of a multi-robot system, taking into account the surrounding obstacles. To address the resulting multi-agent MICP problem in real time, we propose a framework that utilizes heterogeneous graph attention networks to learn the latent mapping from problem parameters to optimal binary solutions. Furthermore, we apply a distributed proximal alternating direction method of multipliers algorithm for solving the convex continuous optimization problem. We demonstrate the effectiveness of our proposed framework through experiments conducted on a robotic testbed.