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Federated learning (FL) has emerged as a widely adopted training paradigm for privacy-preserving machine learning. While the SGD-based FL algorithms have demonstrated considerable success in the past, there is a growing trend towards adopting adaptive federated optimization methods, particularly for training large-scale models. However, the conventional synchronous aggregation design poses a significant challenge to the practical deployment of those adaptive federated optimization methods, particularly in the presence of straggler clients. To fill this research gap, this paper introduces federated adaptive asynchronous optimization, named FADAS, a novel method that incorporates asynchronous updates into adaptive federated optimization with provable guarantees. To further enhance the efficiency and resilience of our proposed method in scenarios with significant asynchronous delays, we also extend FADAS with a delay-adaptive learning adjustment strategy. We rigorously establish the convergence rate of the proposed algorithms and empirical results demonstrate the superior performance of FADAS over other asynchronous FL baselines., Comment: Accepted by ICML 2024

In federated learning (FL), data heterogeneity is the main reason that existing theoretical analyses are pessimistic about the convergence rate. In particular, for many FL algorithms, the convergence rate grows dramatically when the number of local updates becomes large, especially when the product of the gradient divergence and local Lipschitz constant is large. However, empirical studies can show that more local updates can improve the convergence rate even when these two parameters are large, which is inconsistent with the theoretical findings. This paper aims to bridge this gap between theoretical understanding and practical performance by providing a theoretical analysis from a new perspective on data heterogeneity. In particular, we propose a new and weaker assumption compared to the local Lipschitz gradient assumption, named the heterogeneity-driven pseudo-Lipschitz assumption. We show that this and the gradient divergence assumptions can jointly characterize the effect of data heterogeneity. By deriving a convergence upper bound for FedAvg and its extensions, we show that, compared to the existing works, local Lipschitz constant is replaced by the much smaller heterogeneity-driven pseudo-Lipschitz constant and the corresponding convergence upper bound can be significantly reduced for the same number of local updates, although its order stays the same. In addition, when the local objective function is quadratic, more insights on the impact of data heterogeneity can be obtained using the heterogeneity-driven pseudo-Lipschitz constant. For example, we can identify a region where FedAvg can outperform mini-batch SGD even when the gradient divergence can be arbitrarily large. Our findings are validated using experiments., Comment: ICML 2024

Decentralized learning has emerged as an alternative method to the popular parameter-server framework which suffers from high communication burden, single-point failure and scalability issues due to the need of a central server. However, most existing works focus on a single shared model for all workers regardless of the data heterogeneity problem, rendering the resulting model performing poorly on individual workers. In this work, we propose a novel personalized decentralized learning algorithm named DePRL via shared representations. Our algorithm relies on ideas from representation learning theory to learn a low-dimensional global representation collaboratively among all workers in a fully decentralized manner, and a user-specific low-dimensional local head leading to a personalized solution for each worker. We show that DePRL achieves, for the first time, a provable linear speedup for convergence with general non-linear representations (i.e., the convergence rate is improved linearly with respect to the number of workers). Experimental results support our theoretical findings showing the superiority of our method in data heterogeneous environments., Comment: AAAI 2024

In federated learning (FL), clients usually have diverse participation statistics that are unknown a priori, which can significantly harm the performance of FL if not handled properly. Existing works aiming at addressing this problem are usually based on global variance reduction, which requires a substantial amount of additional memory in a multiplicative factor equal to the total number of clients. An important open problem is to find a lightweight method for FL in the presence of clients with unknown participation rates. In this paper, we address this problem by adapting the aggregation weights in federated averaging (FedAvg) based on the participation history of each client. We first show that, with heterogeneous participation statistics, FedAvg with non-optimal aggregation weights can diverge from the optimal solution of the original FL objective, indicating the need of finding optimal aggregation weights. However, it is difficult to compute the optimal weights when the participation statistics are unknown. To address this problem, we present a new algorithm called FedAU, which improves FedAvg by adaptively weighting the client updates based on online estimates of the optimal weights without knowing the statistics of client participation. We provide a theoretical convergence analysis of FedAU using a novel methodology to connect the estimation error and convergence. Our theoretical results reveal important and interesting insights, while showing that FedAU converges to an optimal solution of the original objective and has desirable properties such as linear speedup. Our experimental results also verify the advantage of FedAU over baseline methods with various participation patterns., Comment: Accepted to ICLR 2024

Federated learning (FL) enables distributed model training from local data collected by users. In distributed systems with constrained resources and potentially high dynamics, e.g., mobile edge networks, the efficiency of FL is an important problem. Existing works have separately considered different configurations to make FL more efficient, such as infrequent transmission of model updates, client subsampling, and compression of update vectors. However, an important open problem is how to jointly apply and tune these control knobs in a single FL algorithm, to achieve the best performance by allowing a high degree of freedom in control decisions. In this paper, we address this problem and propose FlexFL - an FL algorithm with multiple options that can be adjusted flexibly. Our FlexFL algorithm allows both arbitrary rates of local computation at clients and arbitrary amounts of communication between clients and the server, making both the computation and communication resource consumption adjustable. We prove a convergence upper bound of this algorithm. Based on this result, we further propose a stochastic optimization formulation and algorithm to determine the control decisions that (approximately) minimize the convergence bound, while conforming to constraints related to resource consumption. The advantage of our approach is also verified using experiments., Comment: Accepted to IEEE INFOCOM 2023

This paper presents a sufficient condition for stochastic gradients not to slow down the convergence of Nesterov's accelerated gradient method. The new condition has the strong-growth condition by Schmidt \& Roux as a special case, and it also allows us to (i) model problems with constraints and (ii) design new types of oracles (e.g., oracles for finite-sum problems such as SAGA). Our results are obtained by revisiting Nesterov's accelerated algorithm and are useful for designing stochastic oracles without changing the underlying first-order method.

Federated learning (FL) faces challenges of intermittent client availability and computation/communication efficiency. As a result, only a small subset of clients can participate in FL at a given time. It is important to understand how partial client participation affects convergence, but most existing works have either considered idealized participation patterns or obtained results with non-zero optimality error for generic patterns. In this paper, we provide a unified convergence analysis for FL with arbitrary client participation. We first introduce a generalized version of federated averaging (FedAvg) that amplifies parameter updates at an interval of multiple FL rounds. Then, we present a novel analysis that captures the effect of client participation in a single term. By analyzing this term, we obtain convergence upper bounds for a wide range of participation patterns, including both non-stochastic and stochastic cases, which match either the lower bound of stochastic gradient descent (SGD) or the state-of-the-art results in specific settings. We also discuss various insights, recommendations, and experimental results., Comment: Accepted to NeurIPS 2022

Federated learning (FL) algorithms usually sample a fraction of clients in each round (partial participation) when the number of participants is large and the server's communication bandwidth is limited. Recent works on the convergence analysis of FL have focused on unbiased client sampling, e.g., sampling uniformly at random, which suffers from slow wall-clock time for convergence due to high degrees of system heterogeneity and statistical heterogeneity. This paper aims to design an adaptive client sampling algorithm that tackles both system and statistical heterogeneity to minimize the wall-clock convergence time. We obtain a new tractable convergence bound for FL algorithms with arbitrary client sampling probabilities. Based on the bound, we analytically establish the relationship between the total learning time and sampling probabilities, which results in a non-convex optimization problem for training time minimization. We design an efficient algorithm for learning the unknown parameters in the convergence bound and develop a low-complexity algorithm to approximately solve the non-convex problem. Experimental results from both hardware prototype and simulation demonstrate that our proposed sampling scheme significantly reduces the convergence time compared to several baseline sampling schemes. Notably, our scheme in hardware prototype spends 73% less time than the uniform sampling baseline for reaching the same target loss., Comment: Accepted in IEEE INFOCOM 2022

Federated learning (FL) is a distributed learning paradigm that enables a large number of mobile devices to collaboratively learn a model under the coordination of a central server without sharing their raw data. Despite its practical efficiency and effectiveness, the iterative on-device learning process (e.g., local computations and global communications with the server) incurs a considerable cost in terms of learning time and energy consumption, which depends crucially on the number of selected clients and the number of local iterations in each training round. In this paper, we analyze how to design adaptive FL in mobile edge networks that optimally chooses these essential control variables to minimize the total cost while ensuring convergence. We establish the analytical relationship between the total cost and the control variables with the convergence upper bound. To efficiently solve the cost minimization problem, we develop a low-cost sampling-based algorithm to learn the convergence related unknown parameters. We derive important solution properties that effectively identify the design principles for different optimization metrics. Practically, we evaluate our theoretical results both in a simulated environment and on a hardware prototype. Experimental evidence verifies our derived properties and demonstrates that our proposed solution achieves near-optimal performance for different optimization metrics for various datasets and heterogeneous system and statistical settings., Comment: Accepted in IEEE JSAC Special Issue on Distributed Learning over Wireless Edge Networks. arXiv admin note: substantial text overlap with arXiv:2012.08336

Federated learning (FL) is a distributed learning paradigm that enables a large number of devices to collaboratively learn a model without sharing their raw data. Despite its practical efficiency and effectiveness, the iterative on-device learning process incurs a considerable cost in terms of learning time and energy consumption, which depends crucially on the number of selected clients and the number of local iterations in each training round. In this paper, we analyze how to design adaptive FL that optimally chooses these essential control variables to minimize the total cost while ensuring convergence. Theoretically, we analytically establish the relationship between the total cost and the control variables with the convergence upper bound. To efficiently solve the cost minimization problem, we develop a low-cost sampling-based algorithm to learn the convergence related unknown parameters. We derive important solution properties that effectively identify the design principles for different metric preferences. Practically, we evaluate our theoretical results both in a simulated environment and on a hardware prototype. Experimental evidence verifies our derived properties and demonstrates that our proposed solution achieves near-optimal performance for various datasets, different machine learning models, and heterogeneous system settings., Comment: Accepted in IEEE INFOCOM 2021

Hierarchical SGD (H-SGD) has emerged as a new distributed SGD algorithm for multi-level communication networks. In H-SGD, before each global aggregation, workers send their updated local models to local servers for aggregations. Despite recent research efforts, the effect of local aggregation on global convergence still lacks theoretical understanding. In this work, we first introduce a new notion of "upward" and "downward" divergences. We then use it to conduct a novel analysis to obtain a worst-case convergence upper bound for two-level H-SGD with non-IID data, non-convex objective function, and stochastic gradient. By extending this result to the case with random grouping, we observe that this convergence upper bound of H-SGD is between the upper bounds of two single-level local SGD settings, with the number of local iterations equal to the local and global update periods in H-SGD, respectively. We refer to this as the "sandwich behavior". Furthermore, we extend our analytical approach based on "upward" and "downward" divergences to study the convergence for the general case of H-SGD with more than two levels, where the "sandwich behavior" still holds. Our theoretical results provide key insights of why local aggregation can be beneficial in improving the convergence of H-SGD., Comment: 36 pages, in AAAI 2022

Federated learning (FL) is an emerging technique for training machine learning models using geographically dispersed data collected by local entities. It includes local computation and synchronization steps. To reduce the communication overhead and improve the overall efficiency of FL, gradient sparsification (GS) can be applied, where instead of the full gradient, only a small subset of important elements of the gradient is communicated. Existing work on GS uses a fixed degree of gradient sparsity for i.i.d.-distributed data within a datacenter. In this paper, we consider adaptive degree of sparsity and non-i.i.d. local datasets. We first present a fairness-aware GS method which ensures that different clients provide a similar amount of updates. Then, with the goal of minimizing the overall training time, we propose a novel online learning formulation and algorithm for automatically determining the near-optimal communication and computation trade-off that is controlled by the degree of gradient sparsity. The online learning algorithm uses an estimated sign of the derivative of the objective function, which gives a regret bound that is asymptotically equal to the case where exact derivative is available. Experiments with real datasets confirm the benefits of our proposed approaches, showing up to $40\%$ improvement in model accuracy for a finite training time., Comment: Accepted at IEEE ICDCS 2020

Mobile edge computing (MEC) is a promising technique for providing low-latency access to services at the network edge. The services are hosted at various types of edge nodes with both computation and communication capabilities. Due to the heterogeneity of edge node characteristics and user locations, the performance of MEC varies depending on where the service is hosted. In this paper, we consider such a heterogeneous MEC system, and focus on the problem of placing multiple services in the system to maximize the total reward. We show that the problem is NP-hard via reduction from the set cover problem, and propose a deterministic approximation algorithm to solve the problem, which has an approximation ratio that is not worse than $\left(1-e^{-1}\right)/4$. The proposed algorithm is based on two sub-routines that are suitable for small and arbitrarily sized services, respectively. The algorithm is designed using a novel way of partitioning each edge node into multiple slots, where each slot contains one service. The approximation guarantee is obtained via a specialization of the method of conditional expectations, which uses a randomized procedure as an intermediate step. In addition to theoretical guarantees, simulation results also show that the proposed algorithm outperforms other state-of-the-art approaches., Comment: Extended version of paper presented at IEEE INFOCOM 2019

Emerging technologies and applications including Internet of Things (IoT), social networking, and crowd-sourcing generate large amounts of data at the network edge. Machine learning models are often built from the collected data, to enable the detection, classification, and prediction of future events. Due to bandwidth, storage, and privacy concerns, it is often impractical to send all the data to a centralized location. In this paper, we consider the problem of learning model parameters from data distributed across multiple edge nodes, without sending raw data to a centralized place. Our focus is on a generic class of machine learning models that are trained using gradient-descent based approaches. We analyze the convergence bound of distributed gradient descent from a theoretical point of view, based on which we propose a control algorithm that determines the best trade-off between local update and global parameter aggregation to minimize the loss function under a given resource budget. The performance of the proposed algorithm is evaluated via extensive experiments with real datasets, both on a networked prototype system and in a larger-scale simulated environment. The experimentation results show that our proposed approach performs near to the optimum with various machine learning models and different data distributions., Comment: This version (excluding appendices) has been accepted for publication in the IEEE Journal on Selected Areas in Communications

Mobile edge computing is a new cloud computing paradigm which makes use of small-sized edge-clouds to provide real-time services to users. These mobile edge-clouds (MECs) are located in close proximity to users, thus enabling users to seamlessly access applications running on MECs. Due to the co-existence of the core (centralized) cloud, users, and one or multiple layers of MECs, an important problem is to decide where (on which computational entity) to place different components of an application. This problem, known as the application or workload placement problem, is notoriously hard, and therefore, heuristic algorithms without performance guarantees are generally employed in common practice, which may unknowingly suffer from poor performance as compared to the optimal solution. In this paper, we address the application placement problem and focus on developing algorithms with provable performance bounds. We model the user application as an application graph and the physical computing system as a physical graph, with resource demands/availabilities annotated on these graphs. We first consider the placement of a linear application graph and propose an algorithm for finding its optimal solution. Using this result, we then generalize the formulation and obtain online approximation algorithms with polynomial-logarithmic (poly-log) competitive ratio for tree application graph placement. We jointly consider node and link assignment, and incorporate multiple types of computational resources at nodes., Comment: This is the author's version of the paper accepted for publication in IEEE Access

In mobile edge computing, local edge servers can host cloud-based services, which reduces network overhead and latency but requires service migrations as users move to new locations. It is challenging to make migration decisions optimally because of the uncertainty in such a dynamic cloud environment. In this paper, we formulate the service migration problem as a Markov Decision Process (MDP). Our formulation captures general cost models and provides a mathematical framework to design optimal service migration policies. In order to overcome the complexity associated with computing the optimal policy, we approximate the underlying state space by the distance between the user and service locations. We show that the resulting MDP is exact for uniform one-dimensional user mobility while it provides a close approximation for uniform two-dimensional mobility with a constant additive error. We also propose a new algorithm and a numerical technique for computing the optimal solution which is significantly faster than traditional methods based on standard value or policy iteration. We illustrate the application of our solution in practical scenarios where many theoretical assumptions are relaxed. Our evaluations based on real-world mobility traces of San Francisco taxis show superior performance of the proposed solution compared to baseline solutions., Comment: Journal version

Mobile micro-cloud is an emerging technology in distributed computing, which is aimed at providing seamless computing/data access to the edge of the network when a centralized service may suffer from poor connectivity and long latency. Different from the traditional cloud, a mobile micro-cloud is smaller and deployed closer to users, typically attached to a cellular basestation or wireless network access point. Due to the relatively small coverage area of each basestation or access point, when a user moves across areas covered by different basestations or access points which are attached to different micro-clouds, issues of service performance and service migration become important. In this paper, we consider such migration issues. We model the general problem as a Markov decision process (MDP), and show that, in the special case where the mobile user follows a one-dimensional asymmetric random walk mobility model, the optimal policy for service migration is a threshold policy. We obtain the analytical solution for the cost resulting from arbitrary thresholds, and then propose an algorithm for finding the optimal thresholds. The proposed algorithm is more efficient than standard mechanisms for solving MDPs., Comment: in Proc. of IEEE MILCOM 2014, Oct. 2014

Mobile micro-clouds are promising for enabling performance-critical cloud applications. However, one challenge therein is the dynamics at the network edge. In this paper, we study how to place service instances to cope with these dynamics, where multiple users and service instances coexist in the system. Our goal is to find the optimal placement (configuration) of instances to minimize the average cost over time, leveraging the ability of predicting future cost parameters with known accuracy. We first propose an offline algorithm that solves for the optimal configuration in a specific look-ahead time-window. Then, we propose an online approximation algorithm with polynomial time-complexity to find the placement in real-time whenever an instance arrives. We analytically show that the online algorithm is $O(1)$-competitive for a broad family of cost functions. Afterwards, the impact of prediction errors is considered and a method for finding the optimal look-ahead window size is proposed, which minimizes an upper bound of the average actual cost. The effectiveness of the proposed approach is evaluated by simulations with both synthetic and real-world (San Francisco taxi) user-mobility traces. The theoretical methodology used in this paper can potentially be applied to a larger class of dynamic resource allocation problems., Comment: This is the author's version of the paper accepted for publication in the IEEE Transactions on Parallel and Distributed Systems