arXiv subjects

Stefan Vlaski

Publications and source records attributed to Stefan Vlaski.

At least 19 recordsLinked to original sources

arXiv2026

Decentralized Multitask Learning over Learned Task Graphs

This paper investigates decentralized multitask learning over networks when the underlying task relationships are unknown. While existing graph-regularized multitask frameworks typically assume a known structure, practical settings often require learning inter-task dependencies directly from distributed data. We propose a decentralized two-phase strategy that first estimates a generalized graph Laplacian from noisy non-cooperative stochastic gradient iterates, and subsequently exploits the learned graph to enable cooperative multitask diffusion learning. This framework is motivated by a Gaussian Markov random field prior, which gives rise to a decentralized maximum likelihood estimator for the graph Laplacian. The analysis quantifies the Laplacian estimation error and its propagation to the steady-state performance of the multitask diffusion recursion, and introduces a topology sensitivity index to capture the effect of network heterogeneity. Simulation results corroborate the theoretical findings and demonstrate that cooperation enabled by the learned task graph significantly improves performance over non-cooperative learning, while approaching the true-graph baseline when the estimation stepsize is sufficiently small.

cs.LG↗

arXiv2026

Quantitative Error Feedback for Quantization Noise Reduction of Filtering over Graphs

This paper introduces an innovative error feedback framework designed to mitigate quantization noise in distributed graph filtering, where communications are constrained to quantized messages. It comes from error spectrum shaping techniques from state-space digital filters, and therefore establishes connections between quantized filtering processes over different domains. In contrast to existing error compensation methods, our framework quantitatively feeds back the quantization noise for exact compensation. We examine the framework under three key scenarios: (i) deterministic graph filtering, (ii) graph filtering over random graphs, and (iii) graph filtering with random node-asynchronous updates. Rigorous theoretical analysis demonstrates that the proposed framework significantly reduces the effect of quantization noise, and we provide closed-form solutions for the optimal error feedback coefficients. Moreover, this quantitative error feedback mechanism can be seamlessly integrated into communication-efficient decentralized optimization frameworks, enabling lower error floors. Numerical experiments validate the theoretical results, consistently showing that our method outperforms conventional quantization strategies in terms of both accuracy and robustness.

cs.LG↗

arXiv2026

On the Convergence of Decentralized Stochastic Gradient-Tracking with Finite-Time Consensus

Algorithms for decentralized optimization and learning rely on local optimization steps coupled with combination steps over a graph. Recent works have demonstrated that using a time-varying sequence of matrices that achieves finite-time consensus can improve the communication and iteration complexity of decentralized optimization algorithms based on gradient tracking. In practice, a sequence of matrices satisfying the exact finite-time consensus property may not be available due to imperfect knowledge of the network topology, a limit on the length of the sequence, or numerical instabilities. In this work, we quantify the impact of approximate finite-time consensus sequences on the convergence of a gradient-tracking based decentralized optimization algorithm. Our results hold for any periodic sequence of combination matrices. We clarify the interplay between approximation error of the finite-time consensus sequence and the length of the sequence as well as typical problem parameters such as smoothness and gradient noise.

math.OC↗

arXiv2026

Graph-Aware Learning Rates for Decentralized Optimization

We propose an adaptive step-size rule for decentralized optimization. Choosing a step-size that balances convergence and stability is challenging. This is amplified in the decentralized setting as agents observe only local (possibly stochastic) gradients and global information (like smoothness) is unavailable. We derive a step-size rule from first principles. The resulting formulation reduces to the well-known Polyak's rule in the single-agent setting, and is suitable for use with stochastic gradients. The method is parameter free, apart from requiring the optimal objective value, which is readily available in many applications. Numerical simulations demonstrate that the performance is comparable to the optimally fine-tuned step-size.

math.OC↗

arXiv2026

Topology-Independent Robustness of the Weighted Mean under Label Poisoning Attacks in Heterogeneous Decentralized Learning

Robustness to malicious attacks is crucial for practical decentralized signal processing and machine learning systems. A typical example of such attacks is label poisoning, meaning that some agents possess corrupted local labels and share models trained on these poisoned data. To defend against malicious attacks, existing works often focus on designing robust aggregators; meanwhile, the weighted mean aggregator is typically considered a simple, vulnerable baseline. This paper analyzes the robustness of decentralized gradient descent under label poisoning attacks, considering both robust and weighted mean aggregators. Theoretical results reveal that the learning errors of robust aggregators depend on the network topology, whereas the performance of weighted mean aggregator is topology-independent. Remarkably, the weighted mean aggregator, although often considered vulnerable, can outperform robust aggregators under sufficient heterogeneity, particularly when: (i) the global contamination rate (i.e., the fraction of poisoned agents for the entire network) is smaller than the local contamination rate (i.e., the maximal fraction of poisoned neighbors for the regular agents); (ii) the network of regular agents is disconnected; or (iii) the network of regular agents is sparse and the local contamination rate is high. Empirical results support our theoretical findings, highlighting the important role of network topology in the robustness to label poisoning attacks.

cs.LG↗

arXiv2025

Decentralized AI Service Placement, Selection and Routing in Mobile Networks

The rapid development and usage of large-scale AI models by mobile users will dominate the traffic load in future communication networks. The advent of AI technology also facilitates a decentralized AI ecosystem where small organizations or even individuals can host AI services. In such scenarios, AI service (models) placement, selection, and request routing decisions are tightly coupled, posing a challenging yet fundamental trade-off between service quality and service latency, especially when considering user mobility. Existing solutions for related problems in mobile edge computing (MEC) and data-intensive networks fall short due to restrictive assumptions about network structure or user mobility. To bridge this gap, we propose a decentralized framework that jointly optimizes AI service placement, selection, and request routing. In the proposed framework, we use traffic tunneling to support user mobility without costly AI service migrations. To account for nonlinear queuing delays, we formulate a nonconvex problem to optimize the trade-off between service quality and end-to-end latency. We derive the node-level KKT conditions and develop a decentralized Frank--Wolfe algorithm with a novel messaging protocol. Numerical evaluations validate the proposed approach and show substantial performance improvements over existing methods.

cs.NI↗

arXiv2025

Multitask Learning with Learned Task Relationships

Classical consensus-based strategies for federated and decentralized learning are statistically suboptimal in the presence of heterogeneous local data or task distributions. As a result, in recent years, there has been growing interest in multitask or personalized strategies, which allow individual agents to benefit from one another in pursuing locally optimal models without enforcing consensus. Existing strategies require either precise prior knowledge of the underlying task relationships or are fully non-parametric and instead rely on meta-learning or proximal constructions. In this work, we introduce an algorithmic framework that strikes a balance between these extremes. By modeling task relationships through a Gaussian Markov Random Field with an unknown precision matrix, we develop a strategy that jointly learns both the task relationships and the local models, allowing agents to self-organize in a way consistent with their individual data distributions. Our theoretical analysis quantifies the quality of the learned relationship, and our numerical experiments demonstrate its practical effectiveness.

cs.LG↗

arXiv2025

Decentralized Adversarial Training over Graphs

The vulnerability of machine learning models to adversarial attacks has been attracting considerable attention in recent years. Most existing studies focus on the behavior of stand-alone single-agent learners. In comparison, this work studies adversarial training over graphs, where individual agents are subjected to perturbations of varied strength levels across space. It is expected that interactions by linked agents, and the heterogeneity of the attack models that are possible over the graph, can help enhance robustness in view of the coordination power of the group. Using a min-max formulation of distributed learning, we develop a decentralized adversarial training framework for multi-agent systems. Specifically, we devise two decentralized adversarial training algorithms by relying on two popular decentralized learning strategies--diffusion and consensus. We analyze the convergence properties of the proposed framework for strongly-convex, convex, and non-convex environments, and illustrate the enhanced robustness to adversarial attacks.

cs.LG↗

arXiv2025

Alpha-Beta HMM: Interpretable Low-Parameter Hidden Markov Filtering in Dynamic Environments

Practical online inference in dynamic environments requires a lightweight filtering mechanism that remains adaptive to state changes while retaining reliable information from past noisy observations. To address this challenge, we propose the $\alpha\beta$-HMM, an interpretable low-parameter hidden Markov filtering framework that replaces the full transition matrix with an equal-exit surrogate governed by an exit-probability parameter $\alpha$, and introduces a step-size parameter $\beta$ through a generalized measurement update to regulate the influence of observational evidence. A central feature of the proposed method is that it preserves the nonlinear log-belief-ratio dynamics of HMM-type filtering, which turn out to be critical for strong performance. To analyze this nonlinear recursion, we develop a dynamical-systems framework and a deterministic reference system, through which we characterize adaptation capability, learning performance, and practical guidance for selecting the two proposed parameters. In parallel, we study the approximation error induced by the equal-exit surrogate and show that the resulting low-parameter filter remains competitive with the oracle HMM across a broad range of environments. These results reveal an explicit learning-adaptation trade-off induced by the two proposed parameters, provide principled guidance for parameter tuning, and show that strong filtering performance can be achieved within a tractable and interpretable low-parameter framework.

eess.SY↗

arXiv2025

Convergence Analysis of alpha-SVRG under Strong Convexity

Stochastic first-order methods for empirical risk minimization employ gradient approximations based on sampled data in lieu of exact gradients. Such constructions introduce noise into the learning dynamics, which can be corrected through variance-reduction techniques. There is increasing evidence in the literature that in many modern learning applications noise can have a beneficial effect on optimization and generalization. To this end, the recently proposed variance-reduction technique, alpha-SVRG [Yin et al., 2023] allows for fine-grained control of the level of residual noise in the learning dynamics, and has been reported to empirically outperform both SGD and SVRG in modern deep learning scenarios. By focusing on strongly convex environments, we first provide a unified convergence rate expression for alpha-SVRG under fixed learning rate, which reduces to that of either SGD or SVRG by setting alpha=0 or alpha=1, respectively. We show that alpha-SVRG has faster convergence rate compared to SGD and SVRG under suitable choice of alpha. Simulation results on linear regression validate our theory.

cs.LG↗

arXiv2025

Scalable Min-Max Optimization via Primal-Dual Exact Pareto Optimization

In multi-objective optimization, minimizing the worst objective can be preferable to minimizing the average objective, as this ensures improved fairness across objectives. Due to the non-smooth nature of the resultant min-max optimization problem, classical subgradient-based approaches typically exhibit slow convergence. Motivated by primal-dual consensus techniques in multi-agent optimization and learning, we formulate a smooth variant of the min-max problem based on the augmented Lagrangian. The resultant Exact Pareto Optimization via Augmented Lagrangian (EPO-AL) algorithm scales better with the number of objectives than subgradient-based strategies, while exhibiting lower per-iteration complexity than recent smoothing-based counterparts. We establish that every fixed-point of the proposed algorithm is both Pareto and min-max optimal under mild assumptions and demonstrate its effectiveness in numerical simulations.

math.OC↗

arXiv2025

Decentralized Hidden Markov Modeling with Equal Exit Probabilities

Social learning strategies enable agents to infer the underlying true state of nature in a distributed manner by receiving private environmental signals and exchanging beliefs with their neighbors. Previous studies have extensively focused on static environments, where the underlying true state remains unchanged over time. In this paper, we consider a dynamic setting where the true state evolves according to a Markov chain with equal exit probabilities. Based on this assumption, we present a social learning strategy for dynamic environments, termed Diffusion $α$-HMM. By leveraging a simplified parameterization, we derive a nonlinear dynamical system that governs the evolution of the log-belief ratio over time. This formulation further reveals the relationship between the linearized form of Diffusion $α$-HMM and Adaptive Social Learning, a well-established social learning strategy for dynamic environments. Furthermore, we analyze the convergence and fixed-point properties of a reference system, providing theoretical guarantees on the learning performance of the proposed algorithm in dynamic settings. Numerical experiments compare various distributed social learning strategies across different dynamic environments, demonstrating the impact of nonlinearity and parameterization on learning performance in a range of dynamic scenarios.

cs.MA↗

arXiv2025

Deep-Relative-Trust-Based Diffusion for Decentralized Deep Learning

Decentralized learning strategies allow a collection of agents to learn efficiently from local data sets without the need for central aggregation or orchestration. Current decentralized learning paradigms typically rely on an averaging mechanism to encourage agreement in the parameter space. We argue that in the context of deep neural networks, which are often over-parameterized, encouraging consensus of the neural network outputs, as opposed to their parameters can be more appropriate. This motivates the development of a new decentralized learning algorithm, termed DRT diffusion, based on deep relative trust (DRT), a recently introduced similarity measure for neural networks. We provide convergence analysis for the proposed strategy, and numerically establish its benefit to generalization, especially with sparse topologies, in an image classification task.

cs.LG↗

arXiv2025

Decentralized Learning with Approximate Finite-Time Consensus

The performance of algorithms for decentralized optimization is affected by both the optimization error and the consensus error, the latter of which arises from the variation between agents' local models. Classically, algorithms employ averaging and gradient-tracking mechanisms with constant combination matrices to drive the collection of agents to consensus. Recent works have demonstrated that using sequences of combination matrices that achieve finite-time consensus (FTC) can result in improved communication efficiency or iteration complexity for decentralized optimization. Notably, these studies apply to highly structured networks, where exact finite-time consensus sequences are known exactly and in closed form. In this work we investigate the impact of utilizing approximate FTC matrices in decentralized learning algorithms, and quantify the impact of the approximation error on convergence rate and steady-state performance. Approximate FTC matrices can be inferred for general graphs and do not rely on a particular graph structure or prior knowledge, making the proposed scheme applicable to a broad range of decentralized learning settings.

eess.SP↗

arXiv2024

Mean Aggregator is More Robust than Robust Aggregators under Label Poisoning Attacks on Distributed Heterogeneous Data

Robustness to malicious attacks is of paramount importance for distributed learning. Existing works usually consider the classical Byzantine attacks model, which assumes that some workers can send arbitrarily malicious messages to the server and disturb the aggregation steps of the distributed learning process. To defend against such worst-case Byzantine attacks, various robust aggregators have been proposed. They are proven to be effective and much superior to the often-used mean aggregator. In this paper, however, we demonstrate that the robust aggregators are too conservative for a class of weak but practical malicious attacks, as known as label poisoning attacks, where the sample labels of some workers are poisoned. Surprisingly, we are able to show that the mean aggregator is more robust than the state-of-the-art robust aggregators in theory, given that the distributed data are sufficiently heterogeneous. In fact, the learning error of the mean aggregator is proven to be order-optimal in this case. Experimental results corroborate our theoretical findings, showing the superiority of the mean aggregator under label poisoning attacks.

cs.LG↗

arXiv2024

Sensitivity Curve Maximization: Attacking Robust Aggregators in Distributed Learning

In distributed learning agents aim at collaboratively solving a global learning problem. It becomes more and more likely that individual agents are malicious or faulty with an increasing size of the network. This leads to a degeneration or complete breakdown of the learning process. Classical aggregation schemes are prone to breakdown at small contamination rates, therefore robust aggregation schemes are sought for. While robust aggregation schemes can generally tolerate larger contamination rates, many have been shown to be susceptible to carefully crafted malicious attacks. In this work, we show how the sensitivity curve (SC), a classical tool from robust statistics, can be used to systematically derive optimal attack patterns against arbitrary robust aggregators, in most cases rendering them ineffective. We show the effectiveness of the proposed attack in multiple simulations.

cs.LG↗

arXiv2024

Non-Bayesian Social Learning with Multiview Observations

Non-Bayesian social learning enables multiple agents to conduct networked signal and information processing through observing environmental signals and information aggregating. Traditional non-Bayesian social learning models only consider single signals, limiting their applications in scenarios where multiple viewpoints of information are available. In this work, we exploit, in the information aggregation step, the independently learned results from observations taken from multiple viewpoints and propose a novel non-Bayesian social learning model for scenarios with multiview observations. We prove the convergence of the model under traditional assumptions and provide convergence conditions for the algorithm in the presence of misleading signals. Through theoretical analyses and numerical experiments, we validate the strong reliability and robustness of the proposed algorithm, showcasing its potential for real-world applications.

cs.SI↗

arXiv2024

Differential error feedback for communication-efficient decentralized learning

Communication-constrained algorithms for decentralized learning and optimization rely on local updates coupled with the exchange of compressed signals. In this context, differential quantization is an effective technique to mitigate the negative impact of compression by leveraging correlations between successive iterates. In addition, the use of error feedback, which consists of incorporating the compression error into subsequent steps, is a powerful mechanism to compensate for the bias caused by the compression. Under error feedback, performance guarantees in the literature have so far focused on algorithms employing a fusion center or a special class of contractive compressors that cannot be implemented with a finite number of bits. In this work, we propose a new decentralized communication-efficient learning approach that blends differential quantization with error feedback. The approach is specifically tailored for decentralized learning problems where agents have individual risk functions to minimize subject to subspace constraints that require the minimizers across the network to lie in low-dimensional subspaces. This constrained formulation includes consensus or single-task optimization as special cases, and allows for more general task relatedness models such as multitask smoothness and coupled optimization. We show that, under some general conditions on the compression noise, and for sufficiently small step-sizes $μ$, the resulting communication-efficient strategy is stable both in terms of mean-square error and average bit rate: by reducing $μ$, it is possible to keep the estimation errors small (on the order of $μ$) without increasing indefinitely the bit rate as $μ\rightarrow 0$. The results establish that, in the small step-size regime and with a finite number of bits, it is possible to attain the performance achievable in the absence of compression.

cs.MA↗