Nicolò Michelusi

Nicolò Michelusi, Petar Popovski, Osvaldo Simeone et al.

This paper introduces a novel technique for access by a cognitive Secondary User (SU) using best-effort transmission to a spectrum with an incumbent Primary User (PU), which uses Type-I Hybrid ARQ. The technique leverages the primary ARQ protocol to perform Interference Cancellation (IC) at the SU receiver (SUrx). Two IC mechanisms that work in concert are introduced: Forward IC, where SUrx, after decoding the PU message, cancels its interference in the (possible) following PU retransmissions of the same message, to improve the SU throughput; Backward IC, where SUrx performs IC on previous SU transmissions, whose decoding failed due to severe PU interference. Secondary access policies are designed that determine the secondary access probability in each state of the network so as to maximize the average long-term SU throughput by opportunistically leveraging IC, while causing bounded average long-term PU throughput degradation and SU power expenditure. It is proved that the optimal policy prescribes that the SU prioritizes its access in the states where SUrx knows the PU message, thus enabling IC. An algorithm is provided to optimally allocate additional secondary access opportunities in the states where the PU message is unknown. Numerical results are shown to assess the throughput gain provided by the proposed techniques.

Frank Po-Chen Lin, Seyyedali Hosseinalipour, Nicolò Michelusi et al.

Federated learning has gained popularity as a means of training models distributed across the wireless edge. The paper introduces delay-aware hierarchical federated learning (DFL) to improve the efficiency of distributed machine learning (ML) model training by accounting for communication delays between edge and cloud. Different from traditional federated learning, DFL leverages multiple stochastic gradient descent iterations on local datasets within each global aggregation period and intermittently aggregates model parameters through edge servers in local subnetworks. During global synchronization, the cloud server consolidates local models with the outdated global model using a local-global combiner, thus preserving crucial elements of both, enhancing learning efficiency under the presence of delay. A set of conditions is obtained to achieve the sub-linear convergence rate of O(1/k) for strongly convex and smooth loss functions. Based on these findings, an adaptive control algorithm is developed for DFL, implementing policies to mitigate energy consumption and communication latency while aiming for sublinear convergence. Numerical evaluations show DFL's superior performance in terms of faster global model convergence, reduced resource consumption, and robustness against communication delays compared to existing FL algorithms. In summary, this proposed method offers improved efficiency and results when dealing with both convex and non-convex loss functions.

Nicolò Michelusi

Non-coherent over-the-air (NCOTA) computation enables low-latency and bandwidth-efficient decentralized optimization by exploiting the average energy superposition property of wireless channels. It has recently been proposed as a powerful tool for executing consensus-based optimization algorithms in fully decentralized systems. A key advantage of NCOTA is that it enables unbiased consensus estimation without channel state information at either transmitters or receivers, requires no transmission scheduling, and scales efficiently to dense network deployments. However, NCOTA is inherently susceptible to external interference, which can bias the consensus estimate and deteriorate the convergence of the underlying decentralized optimization algorithm. In this paper, we propose a novel interference-robust (IR-)NCOTA scheme. The core idea is to apply a coordinated random rotation of the frame of reference across all nodes, and transmit a pseudo-random pilot signal, allowing to transform external interference into a circularly symmetric distribution with zero mean relative to the rotated frame. This ensures that the consensus estimates remain unbiased, preserving the convergence guarantees of the underlying optimization algorithm. Through numerical results on a classification task, it is demonstrated that IR-NCOTA exhibits superior performance over the baseline NCOTA algorithm in the presence of external interference.

Muhammad Faraz Ul Abrar, Nicolò Michelusi

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.

Muhammad Faraz Ul Abrar, Nicolò Michelusi, Erik G. Larsson

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.

Muhammad Faraz Ul Abrar, Nicolò Michelusi

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.

Muhammad Faraz Ul Abrar, Nicolò Michelusi

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.

Muhammad Faraz Ul Abrar, Nicolò Michelusi

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.

Muhammad Faraz Ul Abrar, Nicolò Michelusi, Erik G. Larsson

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.

Manish Kumar, Tzu-Hsuan Chou, Byunghyun Lee et al.

Low-latency localization is critical in cellular networks to support real-time applications requiring precise positioning. In this paper, we propose a distributed machine learning (ML) framework for fingerprint-based localization tailored to cell-free massive multiple-input multiple-output (MIMO) systems, an emerging architecture for 6G networks. The proposed framework enables each access point (AP) to independently train a Gaussian process regression model using local angle-of-arrival and received signal strength fingerprints. These models provide probabilistic position estimates for the user equipment (UE), which are then fused by the UE with minimal computational overhead to derive a final location estimate. This decentralized approach eliminates the need for fronthaul communication between the APs and the central processing unit (CPU), thereby reducing latency. Additionally, distributing computational tasks across the APs alleviates the processing burden on the CPU compared to traditional centralized localization schemes. Simulation results demonstrate that the proposed distributed framework achieves localization accuracy comparable to centralized methods, despite lacking the benefits of centralized data aggregation. Moreover, it effectively reduces uncertainty of the location estimates, as evidenced by the 95\% covariance ellipse. The results highlight the potential of distributed ML for enabling low-latency, high-accuracy localization in future 6G networks.

Haifeng Wen, Nicolò Michelusi, Osvaldo Simeone et al.

Over-the-air federated learning (FL), i.e., AirFL, leverages computing primitively over multiple access channels. A long-standing challenge in AirFL is to achieve coherent signal alignment without relying on expensive channel estimation and feedback. This paper proposes NCAirFL, a CSI-free AirFL scheme based on unbiased non-coherent detection at the edge server. By exploiting binary dithering and a long-term memory based error-compensation mechanism, NCAirFL achieves a convergence rate of order $\mathcal{O}(1/\sqrt{T})$ in terms of the average square norm of the gradient for general non-convex and smooth objectives, where $T$ is the number of communication rounds. Experiments demonstrate the competitive performance of NCAirFL compared to vanilla FL with ideal communications and to coherent transmission-based benchmarks.

Frank Po-Chen Lin, Seyyedali Hosseinalipour, Sheikh Shams Azam et al.

Federated learning has emerged as a popular technique for distributing model training across the network edge. Its learning architecture is conventionally a star topology between the devices and a central server. In this paper, we propose two timescale hybrid federated learning (TT-HF), which migrates to a more distributed topology via device-to-device (D2D) communications. In TT-HF, local model training occurs at devices via successive gradient iterations, and the synchronization process occurs at two timescales: (i) macro-scale, where global aggregations are carried out via device-server interactions, and (ii) micro-scale, where local aggregations are carried out via D2D cooperative consensus formation in different device clusters. Our theoretical analysis reveals how device, cluster, and network-level parameters affect the convergence of TT-HF, and leads to a set of conditions under which a convergence rate of O(1/t) is guaranteed. Experimental results demonstrate the improvements in convergence and utilization that can be obtained by TT-HF over state-of-the-art federated learning baselines.

Nicolò Michelusi, Gesualdo Scutari, Chang-Shen Lee

This paper studies distributed algorithms for (strongly convex) composite optimization problems over mesh networks, subject to quantized communications. Instead of focusing on a specific algorithmic design, a black-box model is proposed, casting linearly convergent distributed algorithms in the form of fixed-point iterates. The algorithmic model is equipped with a novel random or deterministic Biased Compression (BC) rule on the quantizer design, and a new Adaptive encoding Nonuniform Quantizer (ANQ) coupled with a communication-efficient encoding scheme, which implements the BC-rule using a finite number of bits (below machine precision). This fills a gap existing in most state-of-the-art quantization schemes, such as those based on the popular compression rule, which rely on communication of some scalar signals with negligible quantization error (in practice quantized at the machine precision). A unified communication complexity analysis is developed for the black-box model, determining the average number of bits required to reach a solution of the optimization problem within a target accuracy. It is shown that the proposed BC-rule preserves linear convergence of the unquantized algorithms, and a trade-off between convergence rate and communication cost under ANQ-based quantization is characterized. Numerical results validate our theoretical findings and show that distributed algorithms equipped with the proposed ANQ have more favorable communication cost than algorithms using state-of-the-art quantization rules.

Frank Po-Chen Lin, Christopher G. Brinton, Nicolò Michelusi

Federated learning has received significant attention as a potential solution for distributing machine learning (ML) model training through edge networks. This work addresses an important consideration of federated learning at the network edge: communication delays between the edge nodes and the aggregator. A technique called FedDelAvg (federated delayed averaging) is developed, which generalizes the standard federated averaging algorithm to incorporate a weighting between the current local model and the delayed global model received at each device during the synchronization step. Through theoretical analysis, an upper bound is derived on the global model loss achieved by FedDelAvg, which reveals a strong dependency of learning performance on the values of the weighting and learning rate. Experimental results on a popular ML task indicate significant improvements in terms of convergence speed when optimizing the weighting scheme to account for delays.