arXiv subjects

Muhammad Faraz Ul Abrar

Publications and source records attributed to Muhammad Faraz Ul Abrar.

8 recordsLinked to original sources

arXiv2026

Distributed Optimization with Streaming Data: A Temporal Weighting Perspective

Optimization theory is a widely used tool for intelligent decision-making. While classical optimization deals with fixed, time-invariant objective functions, many modern applications operate in dynamic environments where data arrive sequentially, and the learning objective evolves over time, often under decentralized data and communication constraints. Motivated by these trends, we study decentralized optimization from streaming data through a structured time-varying formulation in which the global objective is a temporally weighted average of losses observed across the network. We analyze multi-iteration decentralized first-order methods, including decentralized gradient descent. For strongly convex and smooth losses, we develop guarantees for the Euclidean-norm \emph{tracking error} through a contraction-mapping viewpoint. The resulting bounds decompose the tracking error into a fixed-point tracking component and a bias term induced by decentralization and data heterogeneity. We specialize our analysis to uniform and exponentially discounted weights, as well as their finite-memory \emph{windowed} counterparts. The bounds explicitly characterize the roles of the temporal weighting rule, per-step iteration budget, step size, and network connectivity. Uniform weighting yields a vanishing fixed-point tracking contribution of order $\mathcal O(1/t)$, whereas discounted and windowed strategies generally induce non-vanishing tracking floors governed by the discount factor and effective memory, respectively. In all cases, decentralization induces an additional non-zero bias floor under a constant step size. Numerical experiments illustrate the predicted trends.

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arXiv2026

Decentralized Time-Varying Optimization for Streaming Data via Temporal Weighting

Classical optimization theory largely focuses on fixed objective functions, whereas many modern learning systems operate in dynamic environments where data arrive sequentially and decisions must be updated continuously. In this work, we study optimization with streaming data over a distributed network of agents. We adopt a structured, weight-based formulation that explicitly captures the streaming-data origin of the time-varying objective: at each time step, every agent receives a new sample, and the network seeks to track the minimizer of a temporally weighted objective formed from all samples observed across the network so far. We focus on decentralized gradient descent (DGD) with a limited communication/computation budget, where at each time step, only a limited number of DGD iterations can be performed before the objective changes again. For strongly convex and smooth losses, we analyze the tracking error with respect to the time-varying minimizer through a fixed-point theory lens. Our analysis reveals that the tracking error decomposes into a fixed-point tracking term and a bias term induced by data heterogeneity across agents. We specialize the analysis to two natural weighting strategies: uniform weights, which treat all samples equally, and exponentially discounted weights, which geometrically decay the influence of older data. Under uniform weighting, DGD tracks the fixed-point at a rate $\mathcal{O}(1/t)$, whereas discounted weighting yields a non-vanishing fixed-point tracking floor controlled by the discount factor. In both cases, decentralization induces an additional non-zero bias floor under a constant step size. We validate our theoretical findings through numerical simulations.

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arXiv2026

Biased Federated Learning under Wireless Heterogeneity

Federated learning (FL) has emerged as a promising framework for distributed learning, enabling collaborative model training without sharing private data. Existing wireless FL works primarily adopt two communication strategies: (1) over-the-air (OTA) computation, which exploits wireless signal superposition for simultaneous gradient aggregation, and (2) digital communication, which allocates orthogonal resources for gradient uploads. Prior works on both schemes typically assume \emph{homogeneous} wireless conditions (equal path loss across devices) to enforce zero-bias updates or permit uncontrolled bias, resulting in suboptimal performance and high-variance model updates in \emph{heterogeneous} environments, where devices with poor channel conditions slow down convergence. This paper addresses FL over heterogeneous wireless networks by proposing novel OTA and digital FL updates that allow a structured, time-invariant model bias, thereby reducing variance in FL updates. We analyze their convergence under a unified framework and derive an upper bound on the model ``optimality error", which explicitly quantifies the effect of bias and variance in terms of design parameters. Next, to optimize this trade-off, we study a non-convex optimization problem and develop a successive convex approximation (SCA)-based framework to jointly optimize the design parameters. We perform extensive numerical evaluations with several related design variants and state-of-the-art OTA and digital FL schemes. Our results confirm that minimizing the bias-variance trade-off while allowing a structured bias provides better FL convergence performance than existing schemes.

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arXiv2026

Non-Convex Over-the-Air Heterogeneous Federated Learning: A Bias-Variance Trade-off

Over-the-air (OTA) federated learning (FL) has been well recognized as a scalable paradigm that exploits the waveform superposition of the wireless multiple-access channel to aggregate model updates in a single use. Existing OTA-FL designs largely enforce zero-bias model updates by either assuming \emph{homogeneous} wireless conditions (equal path loss across devices) or forcing zero-bias updates to guarantee convergence. Under \emph{heterogeneous} wireless scenarios, however, such designs are constrained by the weakest device and inflate the update variance. Moreover, prior analyses of biased OTA-FL largely address convex objectives, while most modern AI models are highly non-convex. Motivated by these gaps, we study OTA-FL with stochastic gradient descent (SGD) for general smooth non-convex objectives under wireless heterogeneity. We develop novel OTA-FL SGD updates that allow a structured, time-invariant model bias while facilitating reduced variance updates. We derive a finite-time stationarity bound (expected time average squared gradient norm) that explicitly reveals a bias-variance trade-off. To optimize this trade-off, we pose a non-convex joint OTA power-control design and develop an efficient successive convex approximation (SCA) algorithm that requires only statistical CSI at the base station. Experiments on a non-convex image classification task validate the approach: the SCA-based design accelerates convergence via an optimized bias and improves generalization over prior OTA-FL baselines.

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arXiv2025

Time-Varying Optimization for Streaming Data Via Temporal Weighting

Classical optimization theory deals with fixed, time-invariant objective functions. However, time-varying optimization has emerged as an important subject for decision-making in dynamic environments. In this work, we study the problem of learning from streaming data through a time-varying optimization lens. Unlike prior works that focus on generic formulations, we introduce a structured, \emph{weight-based} formulation that explicitly captures the streaming-data origin of the time-varying objective, where at each time step, an agent aims to minimize a weighted average loss over all the past data samples. We focus on two specific weighting strategies: (1) uniform weights, which treat all samples equally, and (2) discounted weights, which geometrically decay the influence of older data. For both schemes, we derive tight bounds on the ``tracking error'' (TE), defined as the deviation between the model parameter and the time-varying optimum at a given time step, under gradient descent (GD) updates. We show that under uniform weighting, the TE vanishes asymptotically with a $\mathcal{O}(1/t)$ decay rate, whereas discounted weighting incurs a nonzero error floor controlled by the discount factor and the number of gradient updates performed at each time step. Our theoretical findings are validated through numerical simulations.

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arXiv2024

Biased Over-the-Air Federated Learning under Wireless Heterogeneity

Recently, Over-the-Air (OTA) computation has emerged as a promising federated learning (FL) paradigm that leverages the waveform superposition properties of the wireless channel to realize fast model updates. Prior work focused on the OTA device ``pre-scaler" design under \emph{homogeneous} wireless conditions, in which devices experience the same average path loss, resulting in zero-bias solutions. Yet, zero-bias designs are limited by the device with the worst average path loss and hence may perform poorly in \emph{heterogeneous} wireless settings. In this scenario, there may be a benefit in designing \emph{biased} solutions, in exchange for a lower variance in the model updates. To optimize this trade-off, we study the design of OTA device pre-scalers by focusing on the OTA-FL convergence. We derive an upper bound on the model ``optimality error", which explicitly captures the effect of bias and variance in terms of the choice of the pre-scalers. Based on this bound, we identify two solutions of interest: minimum noise variance, and minimum noise variance zero-bias solutions. Numerical evaluations show that using OTA device pre-scalers that minimize the variance of FL updates, while allowing a small bias, can provide high gains over existing schemes.

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arXiv2024

Analog-digital Scheduling for Federated Learning: A Communication-Efficient Approach

Over-the-air (OTA) computation has recently emerged as a communication-efficient Federated Learning (FL) paradigm to train machine learning models over wireless networks. However, its performance is limited by the device with the worst SNR, resulting in fast yet noisy updates. On the other hand, allocating orthogonal resource blocks (RB) to individual devices via digital channels mitigates the noise problem, at the cost of increased communication latency. In this paper, we address this discrepancy and present ADFL, a novel Analog-Digital FL scheme: in each round, the parameter server (PS) schedules each device to either upload its gradient via the analog OTA scheme or transmit its quantized gradient over an orthogonal RB using the ``digital" scheme. Focusing on a single FL round, we cast the optimal scheduling problem as the minimization of the mean squared error (MSE) on the estimated global gradient at the PS, subject to a delay constraint, yielding the optimal device scheduling configuration and quantization bits for the digital devices. Our simulation results show that ADFL, by scheduling most of the devices in the OTA scheme while also occasionally employing the digital scheme for a few devices, consistently outperforms OTA-only and digital-only schemes, in both i.i.d. and non-i.i.d. settings.

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arXiv2022

STAR-RIS-Assisted Hybrid NOMA mmWave Communication: Optimization and Performance Analysis

Simultaneously reflecting and transmitting reconfigurable intelligent surfaces (STAR-RIS) has recently emerged as prominent technology that exploits the transmissive property of RIS to mitigate the half-space coverage limitation of conventional RIS operating on millimeter-wave (mmWave). In this paper, we study a downlink STAR-RIS-based multi-user multiple-input single-output (MU-MISO) mmWave hybrid non-orthogonal multiple access (H-NOMA) wireless network, where a sum-rate maximization problem has been formulated. The design of active and passive beamforming vectors, time and power allocation for H-NOMA is a highly coupled non-convex problem. To handle the problem, we propose an optimization framework based on alternating optimization (AO) that iteratively solves active and passive beamforming sub-problems. Channel correlations and channel strength-based techniques have been proposed for a specific case of two-user optimal clustering and decoding order assignment, respectively, for which analytical solutions to joint power and time allocation for H-NOMA have also been derived. Simulation results show that: 1) the proposed framework leveraging H-NOMA outperforms conventional OMA and NOMA to maximize the achievable sum-rate; 2) using the proposed framework, the supported number of clusters for the given design constraints can be increased considerably; 3) through STAR-RIS, the number of elements can be significantly reduced as compared to conventional RIS to ensure a similar quality-of-service (QoS).

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