Joint Probability Selection and Power Allocation for Federated Learning

In this paper, we study the performance of federated learning over wireless networks, where devices with a limited energy budget train a machine learning model. The federated learning performance depends on the selection of the clients participating in the learning at each round. Most existing studies suggest deterministic approaches for the client selection, resulting in challenging optimization problems that are usually solved using heuristics, and therefore without guarantees on the quality of the final solution. We formulate a new probabilistic approach to jointly select clients and allocate power optimally so that the expected number of participating clients is maximized. To solve the problem, a new alternating algorithm is proposed, where at each step, the closed-form solutions for user selection probabilities and power allocations are obtained. Our numerical results show that the proposed approach achieves a significant performance in terms of energy consumption, completion time and accuracy as compared to the studied benchmarks.

Demystifying the Myths and Legends of Nonconvex Convergence of SGD

Stochastic gradient descent (SGD) and its variants are the main workhorses for solving large-scale optimization problems with nonconvex objective functions. Although the convergence of SGDs in the (strongly) convex case is well-understood, their convergence for nonconvex functions stands on weak mathematical foundations. Most existing studies on the nonconvex convergence of SGD show the complexity results based on either the minimum of the expected gradient norm or the functional sub-optimality gap (for functions with extra structural property) by searching the entire range of iterates. Hence the last iterations of SGDs do not necessarily maintain the same complexity guarantee. This paper shows that an $\epsilon$-stationary point exists in the final iterates of SGDs, given a large enough total iteration budget, $T$, not just anywhere in the entire range of iterates -- a much stronger result than the existing one. Additionally, our analyses allow us to measure the density of the $\epsilon$-stationary points in the final iterates of SGD, and we recover the classical $O(\frac{1}{\sqrt{T}})$ asymptotic rate under various existing assumptions on the objective function and the bounds on the stochastic gradient. As a result of our analyses, we addressed certain myths and legends related to the nonconvex convergence of SGD and posed some thought-provoking questions that could set new directions for research.

Ensemble DNN for Age-of-Information Minimization in UAV-assisted Networks

This paper addresses the problem of Age-of-Information (AoI) in UAV-assisted networks. Our objective is to minimize the expected AoI across devices by optimizing UAVs' stopping locations and device selection probabilities. To tackle this problem, we first derive a closed-form expression of the expected AoI that involves the probabilities of selection of devices. Then, we formulate the problem as a non-convex minimization subject to quality of service constraints. Since the problem is challenging to solve, we propose an Ensemble Deep Neural Network (EDNN) based approach which takes advantage of the dual formulation of the studied problem. Specifically, the Deep Neural Networks (DNNs) in the ensemble are trained in an unsupervised manner using the Lagrangian function of the studied problem. Our experiments show that the proposed EDNN method outperforms traditional DNNs in reducing the expected AoI, achieving a remarkable reduction of $29.5\%$.

A Note on Randomized Kaczmarz Algorithm for Solving Doubly-Noisy Linear Systems

Large-scale linear systems, $Ax=b$, frequently arise in practice and demand effective iterative solvers. Often, these systems are noisy due to operational errors or faulty data-collection processes. In the past decade, the randomized Kaczmarz (RK) algorithm has been studied extensively as an efficient iterative solver for such systems. However, the convergence study of RK in the noisy regime is limited and considers measurement noise in the right-hand side vector, $b$. Unfortunately, in practice, that is not always the case; the coefficient matrix $A$ can also be noisy. In this paper, we analyze the convergence of RK for noisy linear systems when the coefficient matrix, $A$, is corrupted with both additive and multiplicative noise, along with the noisy vector, $b$. In our analyses, the quantity $\tilde R=\| \tilde A^{\dagger} \|_2^2 \|\tilde A \|_F^2$ influences the convergence of RK, where $\tilde A$ represents a noisy version of $A$. We claim that our analysis is robust and realistically applicable, as we do not require information about the noiseless coefficient matrix, $A$, and considering different conditions on noise, we can control the convergence of RK. We substantiate our theoretical findings by performing comprehensive numerical experiments.

Muti-Agent Proximal Policy Optimization For Data Freshness in UAV-assisted Networks

Unmanned aerial vehicles (UAVs) are seen as a promising technology to perform a wide range of tasks in wireless communication networks. In this work, we consider the deployment of a group of UAVs to collect the data generated by IoT devices. Specifically, we focus on the case where the collected data is time-sensitive, and it is critical to maintain its timeliness. Our objective is to optimally design the UAVs' trajectories and the subsets of visited IoT devices such as the global Age-of-Updates (AoU) is minimized. To this end, we formulate the studied problem as a mixed-integer nonlinear programming (MINLP) under time and quality of service constraints. To efficiently solve the resulting optimization problem, we investigate the cooperative Multi-Agent Reinforcement Learning (MARL) framework and propose an RL approach based on the popular on-policy Reinforcement Learning (RL) algorithm: Policy Proximal Optimization (PPO). Our approach leverages the centralized training decentralized execution (CTDE) framework where the UAVs learn their optimal policies while training a centralized value function. Our simulation results show that the proposed MAPPO approach reduces the global AoU by at least a factor of 1/2 compared to conventional off-policy reinforcement learning approaches.

Linear Scalarization for Byzantine-robust learning on non-IID data

In this work we study the problem of Byzantine-robust learning when data among clients is heterogeneous. We focus on poisoning attacks targeting the convergence of SGD. Although this problem has received great attention; the main Byzantine defenses rely on the IID assumption causing them to fail when data distribution is non-IID even with no attack. We propose the use of Linear Scalarization (LS) as an enhancing method to enable current defenses to circumvent Byzantine attacks in the non-IID setting. The LS method is based on the incorporation of a trade-off vector that penalizes the suspected malicious clients. Empirical analysis corroborates that the proposed LS variants are viable in the IID setting. For mild to strong non-IID data splits, LS is either comparable or outperforming current approaches under state-of-the-art Byzantine attack scenarios.

Personalized Federated Learning with Communication Compression

In contrast to training traditional machine learning (ML) models in data centers, federated learning (FL) trains ML models over local datasets contained on resource-constrained heterogeneous edge devices. Existing FL algorithms aim to learn a single global model for all participating devices, which may not be helpful to all devices participating in the training due to the heterogeneity of the data across the devices. Recently, Hanzely and Richt\'{a}rik (2020) proposed a new formulation for training personalized FL models aimed at balancing the trade-off between the traditional global model and the local models that could be trained by individual devices using their private data only. They derived a new algorithm, called Loopless Gradient Descent (L2GD), to solve it and showed that this algorithms leads to improved communication complexity guarantees in regimes when more personalization is required. In this paper, we equip their L2GD algorithm with a bidirectional compression mechanism to further reduce the communication bottleneck between the local devices and the server. Unlike other compression-based algorithms used in the FL-setting, our compressed L2GD algorithm operates on a probabilistic communication protocol, where communication does not happen on a fixed schedule. Moreover, our compressed L2GD algorithm maintains a similar convergence rate as vanilla SGD without compression. To empirically validate the efficiency of our algorithm, we perform diverse numerical experiments on both convex and non-convex problems and using various compression techniques.

Client Selection in Federated Learning based on Gradients Importance

Federated learning (FL) enables multiple devices to collaboratively learn a global model without sharing their personal data. In real-world applications, the different parties are likely to have heterogeneous data distribution and limited communication bandwidth. In this paper, we are interested in improving the communication efficiency of FL systems. We investigate and design a device selection strategy based on the importance of the gradient norms. In particular, our approach consists of selecting devices with the highest norms of gradient values at each communication round. We study the convergence and the performance of such a selection technique and compare it to existing ones. We perform several experiments with non-iid set-up. The results show the convergence of our method with a considerable increase of test accuracy comparing to the random selection.

On the Discrepancy between the Theoretical Analysis and Practical Implementations of Compressed Communication for Distributed Deep Learning

Compressed communication, in the form of sparsification or quantization of stochastic gradients, is employed to reduce communication costs in distributed data-parallel training of deep neural networks. However, there exists a discrepancy between theory and practice: while theoretical analysis of most existing compression methods assumes compression is applied to the gradients of the entire model, many practical implementations operate individually on the gradients of each layer of the model. In this paper, we prove that layer-wise compression is, in theory, better, because the convergence rate is upper bounded by that of entire-model compression for a wide range of biased and unbiased compression methods. However, despite the theoretical bound, our experimental study of six well-known methods shows that convergence, in practice, may or may not be better, depending on the actual trained model and compression ratio. Our findings suggest that it would be advantageous for deep learning frameworks to include support for both layer-wise and entire-model compression.

Direct Nonlinear Acceleration

Optimization acceleration techniques such as momentum play a key role in state-of-the-art machine learning algorithms. Recently, generic vector sequence extrapolation techniques, such as regularized nonlinear acceleration (RNA) of Scieur et al., were proposed and shown to accelerate fixed point iterations. In contrast to RNA which computes extrapolation coefficients by (approximately) setting the gradient of the objective function to zero at the extrapolated point, we propose a more direct approach, which we call direct nonlinear acceleration (DNA). In DNA, we aim to minimize (an approximation of) the function value at the extrapolated point instead. We adopt a regularized approach with regularizers designed to prevent the model from entering a region in which the functional approximation is less precise. While the computational cost of DNA is comparable to that of RNA, our direct approach significantly outperforms RNA on both synthetic and real-world datasets. While the focus of this paper is on convex problems, we obtain very encouraging results in accelerating the training of neural networks.