Stefan Werner

Reza Arablouei, Kutluyıl Doğançay, Stefan Werner

The so-called constrained least mean-square algorithm is one of the most commonly used linear-equality-constrained adaptive filtering algorithms. Its main advantages are adaptability and relative simplicity. In order to gain analytical insights into the performance of this algorithm, we examine its mean-square performance and derive theoretical expressions for its transient and steady-state mean-square deviation. Our methodology is inspired by the principle of energy conservation in adaptive filters. Simulation results corroborate the accuracy of the derived formula.

Francois Gauthier, Vinay Chakravarthi Gogineni, Stefan Werner et al.

This paper presents a personalized graph federated learning (PGFL) framework in which distributedly connected servers and their respective edge devices collaboratively learn device or cluster-specific models while maintaining the privacy of every individual device. The proposed approach exploits similarities among different models to provide a more relevant experience for each device, even in situations with diverse data distributions and disproportionate datasets. Furthermore, to ensure a secure and efficient approach to collaborative personalized learning, we study a variant of the PGFL implementation that utilizes differential privacy, specifically zero-concentrated differential privacy, where a noise sequence perturbs model exchanges. Our mathematical analysis shows that the proposed privacy-preserving PGFL algorithm converges to the optimal cluster-specific solution for each cluster in linear time. It also shows that exploiting similarities among clusters leads to an alternative output whose distance to the original solution is bounded, and that this bound can be adjusted by modifying the algorithm's hyperparameters. Further, our analysis shows that the algorithm ensures local differential privacy for all clients in terms of zero-concentrated differential privacy. Finally, the performance of the proposed PGFL algorithm is examined by performing numerical experiments in the context of regression and classification using synthetic data and the MNIST dataset.

Francois Gauthier, Vinay Chakravarthi Gogineni, Stefan Werner et al.

Online federated learning (FL) enables geographically distributed devices to learn a global shared model from locally available streaming data. Most online FL literature considers a best-case scenario regarding the participating clients and the communication channels. However, these assumptions are often not met in real-world applications. Asynchronous settings can reflect a more realistic environment, such as heterogeneous client participation due to available computational power and battery constraints, as well as delays caused by communication channels or straggler devices. Further, in most applications, energy efficiency must be taken into consideration. Using the principles of partial-sharing-based communications, we propose a communication-efficient asynchronous online federated learning (PAO-Fed) strategy. By reducing the communication overhead of the participants, the proposed method renders participation in the learning task more accessible and efficient. In addition, the proposed aggregation mechanism accounts for random participation, handles delayed updates and mitigates their effect on accuracy. We prove the first and second-order convergence of the proposed PAO-Fed method and obtain an expression for its steady-state mean square deviation. Finally, we conduct comprehensive simulations to study the performance of the proposed method on both synthetic and real-life datasets. The simulations reveal that in asynchronous settings, the proposed PAO-Fed is able to achieve the same convergence properties as that of the online federated stochastic gradient while reducing the communication overhead by 98 percent.

Reza Arablouei, Kutluyıl Doğançay, Stefan Werner et al.

We revisit the asymptotic bias analysis of the distributed Pareto optimization algorithm developed based on the diffusion strategies. We propose an alternative way to analyze the asymptotic bias of this algorithm at small step-sizes and show that the asymptotic bias descends to zero with a linear dependence on the largest step-size parameter when this parameter is sufficiently small. In addition, through the proposed analytic approach, we provide an expression for the small-step-size asymptotic bias when a condition assumed jointly on the combination matrices and the step-sizes does not strictly hold. This is a likely scenario in practice, which has not been considered in the original paper that introduced the algorithm. Our methodology provides new insights into the inner workings of the diffusion Pareto optimization algorithm while being considerably less involved than the small-step-size asymptotic bias analysis presented in the original work. This is because we take advantage of the special eigenstructure of the composite combination matrix used in the algorithm without calling for any eigenspace decomposition or matrix inversion.

Stefan Werner, Sebastian Peitz

The goal of this paper is to make a strong point for the usage of dynamical models when using reinforcement learning (RL) for feedback control of dynamical systems governed by partial differential equations (PDEs). To breach the gap between the immense promises we see in RL and the applicability in complex engineering systems, the main challenges are the massive requirements in terms of the training data, as well as the lack of performance guarantees. We present a solution for the first issue using a data-driven surrogate model in the form of a convolutional LSTM with actuation. We demonstrate that learning an actuated model in parallel to training the RL agent significantly reduces the total amount of required data sampled from the real system. Furthermore, we show that iteratively updating the model is of major importance to avoid biases in the RL training. Detailed ablation studies reveal the most important ingredients of the modeling process. We use the chaotic Kuramoto-Sivashinsky equation do demonstarte our findings.

Reza Mirzaeifard, Naveen K. D. Venkategowda, Vinay Chakravarthi Gogineni et al.

This paper investigates quantile regression in the presence of non-convex and non-smooth sparse penalties, such as the minimax concave penalty (MCP) and smoothly clipped absolute deviation (SCAD). The non-smooth and non-convex nature of these problems often leads to convergence difficulties for many algorithms. While iterative techniques like coordinate descent and local linear approximation can facilitate convergence, the process is often slow. This sluggish pace is primarily due to the need to run these approximation techniques until full convergence at each step, a requirement we term as a \emph{secondary convergence iteration}. To accelerate the convergence speed, we employ the alternating direction method of multipliers (ADMM) and introduce a novel single-loop smoothing ADMM algorithm with an increasing penalty parameter, named SIAD, specifically tailored for sparse-penalized quantile regression. We first delve into the convergence properties of the proposed SIAD algorithm and establish the necessary conditions for convergence. Theoretically, we confirm a convergence rate of $o\big({k^{-\frac{1}{4}}}\big)$ for the sub-gradient bound of augmented Lagrangian. Subsequently, we provide numerical results to showcase the effectiveness of the SIAD algorithm. Our findings highlight that the SIAD method outperforms existing approaches, providing a faster and more stable solution for sparse-penalized quantile regression.

Ehsan Lari, Reza Arablouei, Vinay Chakravarthi Gogineni et al.

Federated learning (FL) leverages client-server communications to train global models on decentralized data. However, communication noise or errors can impair model accuracy. To address this problem, we propose a novel FL algorithm that enhances robustness against communication noise while also reducing communication load. We derive the proposed algorithm through solving the weighted least-squares (WLS) regression problem as an illustrative example. We first frame WLS regression as a distributed convex optimization problem over a federated network employing random scheduling for improved communication efficiency. We then apply the alternating direction method of multipliers (ADMM) to iteratively solve this problem. To counteract the detrimental effects of cumulative communication noise, we introduce a key modification by eliminating the dual variable and implementing a new local model update at each participating client. This subtle yet effective change results in using a single noisy global model update at each client instead of two, improving robustness against additive communication noise. Furthermore, we incorporate another modification enabling clients to continue local updates even when not selected by the server, leading to substantial performance improvements. Our theoretical analysis confirms the convergence of our algorithm in both mean and the mean-square senses, even when the server communicates with a random subset of clients over noisy links at each iteration. Numerical results validate the effectiveness of our proposed algorithm and corroborate our theoretical findings.

Dawit Kiros Redie, Reza Arablouei, Stefan Werner

Biased gradient compression with error feedback (EF) reduces communication in federated learning (FL), but under non-IID data, the residual error can decay slowly, causing gradient mismatch and stalled progress in the early rounds. We propose step-ahead partial error feedback (SA-PEF), which integrates step-ahead (SA) correction with partial error feedback (PEF). SA-PEF recovers EF when the step-ahead coefficient $α=0$ and step-ahead EF (SAEF) when $α=1$. For non-convex objectives and $δ$-contractive compressors, we establish a second-moment bound and a residual recursion that guarantee convergence to stationarity under heterogeneous data and partial client participation. The resulting rates match standard non-convex Fed-SGD guarantees up to constant factors, achieving $O((η,η_0TR)^{-1})$ convergence to a variance/heterogeneity floor with a fixed inner step size. Our analysis reveals a step-ahead-controlled residual contraction $ρ_r$ that explains the observed acceleration in the early training phase. To balance SAEF's rapid warm-up with EF's long-term stability, we select $α$ near its theory-predicted optimum. Experiments across diverse architectures and datasets show that SA-PEF consistently reaches target accuracy faster than EF.

Reza Mirzaeifard, Naveen K. D. Venkategowda, Alexander Jung et al.

This paper proposes a proximal variant of the alternating direction method of multipliers (ADMM) for distributed optimization. Although the current versions of ADMM algorithm provide promising numerical results in producing solutions that are close to optimal for many convex and non-convex optimization problems, it remains unclear if they can converge to a stationary point for weakly convex and locally non-smooth functions. Through our analysis using the Moreau envelope function, we demonstrate that MADM can indeed converge to a stationary point under mild conditions. Our analysis also includes computing the bounds on the amount of change in the dual variable update step by relating the gradient of the Moreau envelope function to the proximal function. Furthermore, the results of our numerical experiments indicate that our method is faster and more robust than widely-used approaches.

Reza Mirzaeifard, Naveen K. D. Venkategowda, Stefan Werner

This paper addresses the problem of localization, which is inherently non-convex and non-smooth in a federated setting where the data is distributed across a multitude of devices. Due to the decentralized nature of federated environments, distributed learning becomes essential for scalability and adaptability. Moreover, these environments are often plagued by outlier data, which presents substantial challenges to conventional methods, particularly in maintaining estimation accuracy and ensuring algorithm convergence. To mitigate these challenges, we propose a method that adopts an $L_1$-norm robust formulation within a distributed sub-gradient framework, explicitly designed to handle these obstacles. Our approach addresses the problem in its original form, without resorting to iterative simplifications or approximations, resulting in enhanced computational efficiency and improved estimation accuracy. We demonstrate that our method converges to a stationary point, highlighting its effectiveness and reliability. Through numerical simulations, we confirm the superior performance of our approach, notably in outlier-rich environments, which surpasses existing state-of-the-art localization methods.

Reza Mirzaeifard, Diyako Ghaderyan, Stefan Werner

In the rapidly evolving internet-of-things (IoT) ecosystem, effective data analysis techniques are crucial for handling distributed data generated by sensors. Addressing the limitations of existing methods, such as the sub-gradient approach, which fails to distinguish between active and non-active coefficients effectively, this paper introduces the decentralized smoothing alternating direction method of multipliers (DSAD) for penalized quantile regression. Our method leverages non-convex sparse penalties like the minimax concave penalty (MCP) and smoothly clipped absolute deviation (SCAD), improving the identification and retention of significant predictors. DSAD incorporates a total variation norm within a smoothing ADMM framework, achieving consensus among distributed nodes and ensuring uniform model performance across disparate data sources. This approach overcomes traditional convergence challenges associated with non-convex penalties in decentralized settings. We present theoretical proofs and extensive simulation results to validate the effectiveness of the DSAD, demonstrating its superiority in achieving reliable convergence and enhancing estimation accuracy compared with prior methods.

Reza Mirzaeifard, Diyako Ghaderyan, Stefan Werner

Distributed sensors in the internet-of-things (IoT) generate vast amounts of sparse data. Analyzing this high-dimensional data and identifying relevant predictors pose substantial challenges, especially when data is preferred to remain on the device where it was collected for reasons such as data integrity, communication bandwidth, and privacy. This paper introduces a federated quantile regression algorithm to address these challenges. Quantile regression provides a more comprehensive view of the relationship between variables than mean regression models. However, traditional approaches face difficulties when dealing with nonconvex sparse penalties and the inherent non-smoothness of the loss function. For this purpose, we propose a federated smoothing proximal gradient (FSPG) algorithm that integrates a smoothing mechanism with the proximal gradient framework, thereby enhancing both precision and computational speed. This integration adeptly handles optimization over a network of devices, each holding local data samples, making it particularly effective in federated learning scenarios. The FSPG algorithm ensures steady progress and reliable convergence in each iteration by maintaining or reducing the value of the objective function. By leveraging nonconvex penalties, such as the minimax concave penalty (MCP) and smoothly clipped absolute deviation (SCAD), the proposed method can identify and preserve key predictors within sparse models. Comprehensive simulations validate the robust theoretical foundations of the proposed algorithm and demonstrate improved estimation precision and reliable convergence.

Ehsan Lari, Reza Arablouei, Stefan Werner

We propose a Byzantine-resilient federated conformal prediction (FCP) method that leverages partial model sharing, where only a subset of model parameters is exchanged each round. Unlike existing robust FCP approaches that primarily harden the calibration stage, our method protects both the federated training and conformal calibration phases. During training, partial sharing inherently restricts the attack surface and attenuates poisoned updates while reducing communication. During calibration, clients compress their non-conformity scores into histogram-based characterization vectors, enabling the server to detect Byzantine clients via distance-based maliciousness scores and to estimate the conformal quantile using only benign contributors. Experiments across diverse Byzantine attack scenarios show that the proposed method achieves closer-to-nominal coverage with substantially tighter prediction intervals than standard FCP, establishing a robust and communication-efficient approach to federated uncertainty quantification.

Ehsan Lari, Reza Arablouei, Naveen K. D. Venkategowda et al.

We introduce a distributed algorithm, termed noise-robust distributed maximum consensus (RD-MC), for estimating the maximum value within a multi-agent network in the presence of noisy communication links. Our approach entails redefining the maximum consensus problem as a distributed optimization problem, allowing a solution using the alternating direction method of multipliers. Unlike existing algorithms that rely on multiple sets of noise-corrupted estimates, RD-MC employs a single set, enhancing both robustness and efficiency. To further mitigate the effects of link noise and improve robustness, we apply moving averaging to the local estimates. Through extensive simulations, we demonstrate that RD-MC is significantly more robust to communication link noise compared to existing maximum-consensus algorithms.

Ehsan Lari, Reza Arablouei, Stefan Werner

Nonnegative matrix factorization (NMF) is an effective data representation tool with numerous applications in signal processing and machine learning. However, deploying NMF in a decentralized manner over ad-hoc networks introduces privacy concerns due to the conventional approach of sharing raw data among network agents. To address this, we propose a privacy-preserving algorithm for fully-distributed NMF that decomposes a distributed large data matrix into left and right matrix factors while safeguarding each agent's local data privacy. It facilitates collaborative estimation of the left matrix factor among agents and enables them to estimate their respective right factors without exposing raw data. To ensure data privacy, we secure information exchanges between neighboring agents utilizing the Paillier cryptosystem, a probabilistic asymmetric algorithm for public-key cryptography that allows computations on encrypted data without decryption. Simulation results conducted on synthetic and real-world datasets demonstrate the effectiveness of the proposed algorithm in achieving privacy-preserving distributed NMF over ad-hoc networks.

Ehsan Lari, Reza Arablouei, Stefan Werner

We propose PRISM-FCP (Partial shaRing and robust calIbration with Statistical Margins for Federated Conformal Prediction), a Byzantine-resilient federated conformal prediction framework that utilizes partial model sharing to improve robustness against Byzantine attacks during both model training and conformal calibration. Existing approaches address adversarial behavior only in the calibration stage, leaving the learned model susceptible to poisoned updates. In contrast, PRISM-FCP mitigates attacks end-to-end. During training, clients partially share updates by transmitting only $M$ of $D$ parameters per round. This attenuates the expected energy of an adversary's perturbation in the aggregated update by a factor of $M/D$, yielding lower mean-square error (MSE) and tighter prediction intervals. During calibration, clients convert nonconformity scores into characterization vectors, compute distance-based maliciousness scores, and downweight or filter suspected Byzantine contributions before estimating the conformal quantile. Extensive experiments on both synthetic data and the UCI Superconductivity dataset demonstrate that PRISM-FCP maintains nominal coverage guarantees under Byzantine attacks while avoiding the interval inflation observed in standard FCP with reduced communication, providing a robust and communication-efficient approach to federated uncertainty quantification.

Reza Mirzaeifard, Ashkan Moradi, Masahiro Yukawa et al.

This paper addresses the challenge of localization in federated settings, which are characterized by distributed data, non-convexity, and non-smoothness. To tackle the scalability and outlier issues inherent in such environments, we propose a robust algorithm that employs an $\ell_1$-norm formulation within a novel federated ADMM framework. This approach addresses the problem by integrating an iterative smooth approximation for the total variation consensus term and employing a Moreau envelope approximation for the convex function that appears in a subtracted form. This transformation ensures that the problem is smooth and weakly convex in each iteration, which results in enhanced computational efficiency and improved estimation accuracy. The proposed algorithm supports asynchronous updates and multiple client updates per iteration, which ensures its adaptability to real-world federated systems. To validate the reliability of the proposed algorithm, we show that the method converges to a stationary point, and numerical simulations highlight its superior performance in convergence speed and outlier resilience compared to existing state-of-the-art localization methods.

Reza Mirzaeifard, Stefan Werner

This paper presents a hierarchical federated learning (FL) framework that extends the alternating direction method of multipliers (ADMM) with smoothing techniques, tailored for non-convex and non-smooth objectives. Unlike traditional hierarchical FL methods, our approach supports asynchronous updates and multiple updates per iteration, enhancing adaptability to heterogeneous data and system settings. Additionally, we introduce a flexible mechanism to leverage diverse regularization functions at each layer, allowing customization to the specific prior information within each cluster and accommodating (possibly) non-smooth penalty objectives. Depending on the learning goal, the framework supports both consensus and personalization: the total variation norm can be used to enforce consensus across layers, while non-convex penalties such as minimax concave penalty (MCP) or smoothly clipped absolute deviation (SCAD) enable personalized learning. Experimental results demonstrate the superior convergence rates and accuracy of our method compared to conventional approaches, underscoring its robustness and versatility for a wide range of FL scenarios.

Ehsan Lari, Reza Arablouei, Vinay Chakravarthi Gogineni et al.

Federated learning (FL) allows training machine learning models on distributed data without compromising privacy. However, FL is vulnerable to model-poisoning attacks where malicious clients tamper with their local models to manipulate the global model. In this work, we investigate the resilience of the partial-sharing online FL (PSO-Fed) algorithm against such attacks. PSO-Fed reduces communication overhead by allowing clients to share only a fraction of their model updates with the server. We demonstrate that this partial sharing mechanism has the added advantage of enhancing PSO-Fed's robustness to model-poisoning attacks. Through theoretical analysis, we show that PSO-Fed maintains convergence even under Byzantine attacks, where malicious clients inject noise into their updates. Furthermore, we derive a formula for PSO-Fed's mean square error, considering factors like stepsize, attack probability, and the number of malicious clients. Interestingly, we find a non-trivial optimal stepsize that maximizes PSO-Fed's resistance to these attacks. Extensive numerical experiments confirm our theoretical findings and showcase PSO-Fed's superior performance against model-poisoning attacks compared to other leading FL algorithms.

Francois Gauthier, Vinay Chakravarthi Gogineni, Stefan Werner et al.

Many assumptions in the federated learning literature present a best-case scenario that can not be satisfied in most real-world applications. An asynchronous setting reflects the realistic environment in which federated learning methods must be able to operate reliably. Besides varying amounts of non-IID data at participants, the asynchronous setting models heterogeneous client participation due to available computational power and battery constraints and also accounts for delayed communications between clients and the server. To reduce the communication overhead associated with asynchronous online federated learning (ASO-Fed), we use the principles of partial-sharing-based communication. In this manner, we reduce the communication load of the participants and, therefore, render participation in the learning task more accessible. We prove the convergence of the proposed ASO-Fed and provide simulations to analyze its behavior further. The simulations reveal that, in the asynchronous setting, it is possible to achieve the same convergence as the federated stochastic gradient (Online-FedSGD) while reducing the communication tenfold.

Vinay Chakravarthi Gogineni, Stefan Werner, Yih-Fang Huang et al.

Federated learning (FL) literature typically assumes that each client has a fixed amount of data, which is unrealistic in many practical applications. Some recent works introduced a framework for online FL (Online-Fed) wherein clients perform model learning on streaming data and communicate the model to the server; however, they do not address the associated communication overhead. As a solution, this paper presents a partial-sharing-based online federated learning framework (PSO-Fed) that enables clients to update their local models using continuous streaming data and share only portions of those updated models with the server. During a global iteration of PSO-Fed, non-participant clients have the privilege to update their local models with new data. Here, we consider a global task of kernel regression, where clients use a random Fourier features-based kernel LMS on their data for local learning. We examine the mean convergence of the PSO-Fed for kernel regression. Experimental results show that PSO-Fed can achieve competitive performance with a significantly lower communication overhead than Online-Fed.

Alexander Tornede, Marcel Wever, Stefan Werner et al.

Algorithm selection (AS) deals with the automatic selection of an algorithm from a fixed set of candidate algorithms most suitable for a specific instance of an algorithmic problem class, where "suitability" often refers to an algorithm's runtime. Due to possibly extremely long runtimes of candidate algorithms, training data for algorithm selection models is usually generated under time constraints in the sense that not all algorithms are run to completion on all instances. Thus, training data usually comprises censored information, as the true runtime of algorithms timed out remains unknown. However, many standard AS approaches are not able to handle such information in a proper way. On the other side, survival analysis (SA) naturally supports censored data and offers appropriate ways to use such data for learning distributional models of algorithm runtime, as we demonstrate in this work. We leverage such models as a basis of a sophisticated decision-theoretic approach to algorithm selection, which we dub Run2Survive. Moreover, taking advantage of a framework of this kind, we advocate a risk-averse approach to algorithm selection, in which the avoidance of a timeout is given high priority. In an extensive experimental study with the standard benchmark ASlib, our approach is shown to be highly competitive and in many cases even superior to state-of-the-art AS approaches.

Franz-Josef Streit, Florian Fritz, Andreas Becher et al.

In modern embedded systems, the trust in comprehensive security standards all along the product life cycle has become an increasingly important access-to-market requirement. However, these security standards rely on mandatory immunity assumptions such as the integrity and authenticity of an initial system configuration typically loaded from Non-Volatile Memory (NVM). This applies especially to FPGA-based Programmable System-on-Chip (PSoC) architectures, since object codes as well as configuration data easily exceed the capacity of a secure bootROM. In this context, an attacker could try to alter the content of the NVM device in order to manipulate the system. The PSoC therefore relies on the integrity of the NVM particularly at boot-time. In this paper, we propose a methodology for securely booting from an NVM in a potentially unsecure environment by exploiting the reconfigurable logic of the FPGA. Here, the FPGA serves as a secure anchor point by performing required integrity and authenticity verifications prior to the configuration and execution of any user application loaded from the NVM on the PSoC. The proposed secure boot process is based on the following assumptions and steps: 1) The boot configurationis stored on a fully encrypted Secure Digital memory card (SD card) or alternatively Flash acting as NVM. 2) At boot time, a hardware design called Trusted Memory-Interface Unit (TMIU) is loaded to verify first the authenticity of the deployed NVM and then after decryption the integrity of its content. To demonstrate the practicability of our approach, we integrated the methodology into the vendor-specific secure boot process of a Xilinx Zynq PSoC and evaluated the design objectives performance, power and resource costs.

Reza Arablouei, Stefan Werner, Kutluyıl Doğançay et al.

In diffusion-based algorithms for adaptive distributed estimation, each node of an adaptive network estimates a target parameter vector by creating an intermediate estimate and then combining the intermediate estimates available within its closed neighborhood. We analyze the performance of a reduced-communication diffusion least mean-square (RC-DLMS) algorithm, which allows each node to receive the intermediate estimates of only a subset of its neighbors at each iteration. This algorithm eases the usage of network communication resources and delivers a trade-off between estimation performance and communication cost. We show analytically that the RC-DLMS algorithm is stable and convergent in both mean and mean-square senses. We also calculate its theoretical steady-state mean-square deviation. Simulation results demonstrate a good match between theory and experiment.

Reza Arablouei, Kutluyıl Doğançay, Stefan Werner

We develop a recursive total least-squares (RTLS) algorithm for errors-in-variables system identification utilizing the inverse power method and the dichotomous coordinate-descent (DCD) iterations. The proposed algorithm, called DCD-RTLS, outperforms the previously-proposed RTLS algorithms, which are based on the line-search method, with reduced computational complexity. We perform a comprehensive analysis of the DCD-RTLS algorithm and show that it is asymptotically unbiased as well as being stable in the mean. We also find a lower bound for the forgetting factor that ensures mean-square stability of the algorithm and calculate the theoretical steady-state mean-square deviation (MSD). We verify the effectiveness of the proposed algorithm and the accuracy of the predicted steady-state MSD via simulations.