Federated Learning (FL) has opened the opportunity for collaboratively training machine learning models on heterogeneous mobile or Edge devices while keeping local data private.With an increase in its adoption, a growing concern is related to its economic and environmental cost (as is also the case for other machine learning techniques).Unfortunately, little work has been done to optimize its energy consumption or emissions of carbon dioxide or equivalents, as energy minimization is usually left as a secondary objective.In this paper, we investigate the problem of minimizing the energy consumption of FL training on heterogeneous devices by controlling the workload distribution.We model this as the Minimal Cost FL Schedule problem, a total cost minimization problem with identical, independent, and atomic tasks that have to be assigned to heterogeneous resources with arbitrary cost functions.We propose a pseudo-polynomial optimal solution to the problem based on the previously unexplored Multiple-Choice Minimum-Cost Maximal Knapsack Packing Problem.We also provide four algorithms for scenarios where cost functions are monotonically increasing and follow the same behavior.These solutions are likewise applicable on the minimization of other kinds of costs, and in other one-dimensional data partition problems.
相關內容
The interplay between Machine Learning (ML) and Constrained Optimization (CO) has recently been the subject of increasing interest, leading to a new and prolific research area covering (e.g.) Decision Focused Learning and Constrained Reinforcement Learning. Such approaches strive to tackle complex decision problems under uncertainty over multiple stages, involving both explicit (cost function, constraints) and implicit knowledge (from data), and possibly subject to execution time restrictions. While a good degree of success has been achieved, the existing methods still have limitations in terms of both applicability and effectiveness. For problems in this class, we propose UNIFY, a unified framework to design a solution policy for complex decision-making problems. Our approach relies on a clever decomposition of the policy in two stages, namely an unconstrained ML model and a CO problem, to take advantage of the strength of each approach while compensating for its weaknesses. With a little design effort, UNIFY can generalize several existing approaches, thus extending their applicability. We demonstrate the method effectiveness on two practical problems, namely an Energy Management System and the Set Multi-cover with stochastic coverage requirements. Finally, we highlight some current challenges of our method and future research directions that can benefit from the cross-fertilization of the two fields.
Recently introduced distributed zeroth-order optimization (ZOO) algorithms have shown their utility in distributed reinforcement learning (RL). Unfortunately, in the gradient estimation process, almost all of them require random samples with the same dimension as the global variable and/or require evaluation of the global cost function, which may induce high estimation variance for large-scale networks. In this paper, we propose a novel distributed zeroth-order algorithm by leveraging the network structure inherent in the optimization objective, which allows each agent to estimate its local gradient by local cost evaluation independently, without use of any consensus protocol. The proposed algorithm exhibits an asynchronous update scheme, and is designed for stochastic non-convex optimization with a possibly non-convex feasible domain based on the block coordinate descent method. The algorithm is later employed as a distributed model-free RL algorithm for distributed linear quadratic regulator design, where a learning graph is designed to describe the required interaction relationship among agents in distributed learning. We provide an empirical validation of the proposed algorithm to benchmark its performance on convergence rate and variance against a centralized ZOO algorithm.
Sampling from a target measure whose density is only known up to a normalization constant is a fundamental problem in computational statistics and machine learning. In this paper, we present a new optimization-based method for sampling called mollified interaction energy descent (MIED). MIED minimizes a new class of energies on probability measures called mollified interaction energies (MIEs). These energies rely on mollifier functions -- smooth approximations of the Dirac delta originated from PDE theory. We show that as the mollifier approaches the Dirac delta, the MIE converges to the chi-square divergence with respect to the target measure and the gradient flow of the MIE agrees with that of the chi-square divergence. Optimizing this energy with proper discretization yields a practical first-order particle-based algorithm for sampling in both unconstrained and constrained domains. We show experimentally that for unconstrained sampling problems our algorithm performs on par with existing particle-based algorithms like SVGD, while for constrained sampling problems our method readily incorporates constrained optimization techniques to handle more flexible constraints with strong performance compared to alternatives.
We propose a novel and efficient lifting approach for the optimal control of rigid-body systems with contacts to improve the convergence properties of Newton-type methods. To relax the high nonlinearity, we consider the state, acceleration, contact forces, and control input torques, as optimization variables and the inverse dynamics and acceleration constraints on the contact frames as equality constraints. We eliminate the update of the acceleration, contact forces, and their dual variables from the linear equation to be solved in each Newton-type iteration in an efficient manner. As a result, the computational cost per Newton-type iteration is almost identical to that of the conventional non-lifted Newton-type iteration that embeds contact dynamics in the state equation. We conducted numerical experiments on the whole-body optimal control of various quadrupedal gaits subject to the friction cone constraints considered in interior-point methods and demonstrated that the proposed method can significantly increase the convergence speed to more than twice that of the conventional non-lifted approach.
We propose cooperative edge-assisted dynamic federated learning (CE-FL). CE-FL introduces a distributed machine learning (ML) architecture, where data collection is carried out at the end devices, while the model training is conducted cooperatively at the end devices and the edge servers, enabled via data offloading from the end devices to the edge servers through base stations. CE-FL also introduces floating aggregation point, where the local models generated at the devices and the servers are aggregated at an edge server, which varies from one model training round to another to cope with the network evolution in terms of data distribution and users' mobility. CE-FL considers the heterogeneity of network elements in terms of communication/computation models and the proximity to one another. CE-FL further presumes a dynamic environment with online variation of data at the network devices which causes a drift at the ML model performance. We model the processes taken during CE-FL, and conduct analytical convergence analysis of its ML model training. We then formulate network-aware CE-FL which aims to adaptively optimize all the network elements via tuning their contribution to the learning process, which turns out to be a non-convex mixed integer problem. Motivated by the large scale of the system, we propose a distributed optimization solver to break down the computation of the solution across the network elements. We finally demonstrate the effectiveness of our framework with the data collected from a real-world testbed.
One common approach to detecting change-points is minimizing a cost function over possible numbers and locations of change-points. The framework includes several well-established procedures, such as the penalized likelihood and minimum description length. Such an approach requires finding the cost value repeatedly over different segments of the data set, which can be time-consuming when (i) the data sequence is long and (ii) obtaining the cost value involves solving a non-trivial optimization problem. This paper introduces a new sequential method (SE) that can be coupled with gradient descent (SeGD) and quasi-Newton's method (SeN) to find the cost value effectively. The core idea is to update the cost value using the information from previous steps without re-optimizing the objective function. The new method is applied to change-point detection in generalized linear models and penalized regression. Numerical studies show that the new approach can be orders of magnitude faster than the Pruned Exact Linear Time (PELT) method without sacrificing estimation accuracy.
Heterogeneous graph neural networks (GNNs) achieve strong performance on node classification tasks in a semi-supervised learning setting. However, as in the simpler homogeneous GNN case, message-passing-based heterogeneous GNNs may struggle to balance between resisting the oversmoothing that may occur in deep models, and capturing long-range dependencies of graph structured data. Moreover, the complexity of this trade-off is compounded in the heterogeneous graph case due to the disparate heterophily relationships between nodes of different types. To address these issues, we propose a novel heterogeneous GNN architecture in which layers are derived from optimization steps that descend a novel relation-aware energy function. The corresponding minimizer is fully differentiable with respect to the energy function parameters, such that bilevel optimization can be applied to effectively learn a functional form whose minimum provides optimal node representations for subsequent classification tasks. In particular, this methodology allows us to model diverse heterophily relationships between different node types while avoiding oversmoothing effects. Experimental results on 8 heterogeneous graph benchmarks demonstrates that our proposed method can achieve competitive node classification accuracy
In this paper, we address the dichotomy between heterogeneous models and simultaneous training in Federated Learning (FL) via a clustering framework. We define a new clustering model for FL based on the (optimal) local models of the users: two users belong to the same cluster if their local models are close; otherwise they belong to different clusters. A standard algorithm for clustered FL is proposed in \cite{ghosh_efficient_2021}, called \texttt{IFCA}, which requires \emph{suitable} initialization and the knowledge of hyper-parameters like the number of clusters (which is often quite difficult to obtain in practical applications) to converge. We propose an improved algorithm, \emph{Successive Refine Federated Clustering Algorithm} (\texttt{SR-FCA}), which removes such restrictive assumptions. \texttt{SR-FCA} treats each user as a singleton cluster as an initialization, and then successively refine the cluster estimation via exploiting similar users belonging to the same cluster. In any intermediate step, \texttt{SR-FCA} uses a robust federated learning algorithm within each cluster to exploit simultaneous training and to correct clustering errors. Furthermore, \texttt{SR-FCA} does not require any \emph{good} initialization (warm start), both in theory and practice. We show that with proper choice of learning rate, \texttt{SR-FCA} incurs arbitrarily small clustering error. Additionally, we validate the performance of our algorithm on standard FL datasets in non-convex problems like neural nets, and we show the benefits of \texttt{SR-FCA} over baselines.
Federated Learning (FL) is a decentralized machine-learning paradigm, in which a global server iteratively averages the model parameters of local users without accessing their data. User heterogeneity has imposed significant challenges to FL, which can incur drifted global models that are slow to converge. Knowledge Distillation has recently emerged to tackle this issue, by refining the server model using aggregated knowledge from heterogeneous users, other than directly averaging their model parameters. This approach, however, depends on a proxy dataset, making it impractical unless such a prerequisite is satisfied. Moreover, the ensemble knowledge is not fully utilized to guide local model learning, which may in turn affect the quality of the aggregated model. Inspired by the prior art, we propose a data-free knowledge distillation} approach to address heterogeneous FL, where the server learns a lightweight generator to ensemble user information in a data-free manner, which is then broadcasted to users, regulating local training using the learned knowledge as an inductive bias. Empirical studies powered by theoretical implications show that, our approach facilitates FL with better generalization performance using fewer communication rounds, compared with the state-of-the-art.
In recent years, mobile devices have gained increasingly development with stronger computation capability and larger storage. Some of the computation-intensive machine learning and deep learning tasks can now be run on mobile devices. To take advantage of the resources available on mobile devices and preserve users' privacy, the idea of mobile distributed machine learning is proposed. It uses local hardware resources and local data to solve machine learning sub-problems on mobile devices, and only uploads computation results instead of original data to contribute to the optimization of the global model. This architecture can not only relieve computation and storage burden on servers, but also protect the users' sensitive information. Another benefit is the bandwidth reduction, as various kinds of local data can now participate in the training process without being uploaded to the server. In this paper, we provide a comprehensive survey on recent studies of mobile distributed machine learning. We survey a number of widely-used mobile distributed machine learning methods. We also present an in-depth discussion on the challenges and future directions in this area. We believe that this survey can demonstrate a clear overview of mobile distributed machine learning and provide guidelines on applying mobile distributed machine learning to real applications.
小貼士
登錄享
相關主題
注冊地址： 北京市海淀區羊坊店路18號2幢3層301-191