With the proliferation of training data, distributed machine learning (DML) is becoming more competent for large-scale learning tasks. However, privacy concerns have to be given priority in DML, since training data may contain sensitive information of users. In this paper, we propose a privacy-preserving ADMM-based DML framework with two novel features: First, we remove the assumption commonly made in the literature that the users trust the server collecting their data. Second, the framework provides heterogeneous privacy for users depending on data's sensitive levels and servers' trust degrees. The challenging issue is to keep the accumulation of privacy losses over ADMM iterations minimal. In the proposed framework, a local randomization approach, which is differentially private, is adopted to provide users with self-controlled privacy guarantee for the most sensitive information. Further, the ADMM algorithm is perturbed through a combined noise-adding method, which simultaneously preserves privacy for users' less sensitive information and strengthens the privacy protection of the most sensitive information. We provide detailed analyses on the performance of the trained model according to its generalization error. Finally, we conduct extensive experiments using real-world datasets to validate the theoretical results and evaluate the classification performance of the proposed framework.
As one of the important applications of distributed optimization, DML has received widespread attentions from researchers. Besides the ADMM scheme, many distributed approaches have been proposed in the existing literature, e.g., subgradient descent methods @cite_15 , local message-passing algorithms @cite_20 , adaptive diffusion mechanisms @cite_16 , and dual averaging approaches @cite_27 . Compared with these approaches, ADMM schemes achieve faster empirical convergence @cite_4 , making it more suitable for large-scale DML tasks.
@cite_4 @cite_27 @cite_15 @cite_16 @cite_20
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Distributed optimization algorithms are highly attractive for solving big data problems. In particular, many machine learning problems can be formulated as the global consensus optimization problem, which can then be solved in a distributed manner by the alternating direction method of multipliers (ADMM) algorithm. However, this suffers from the straggler problem as its updates have to be synchronized. In this paper, we propose an asynchronous ADMM algorithm by using two conditions to control the asynchrony: partial barrier and bounded delay. The proposed algorithm has a simple structure and good convergence guarantees (its convergence rate can be reduced to that of its synchronous counterpart). Experiments on different distributed ADMM applications show that asynchrony reduces the time on network waiting, and achieves faster convergence than its synchronous counterpart in terms of the wall clock time. Aiming at solving large-scale optimization problems, this paper studies distributed optimization methods based on the alternating direction method of multipliers (ADMM). By formulating the optimization problem as a consensus problem, the ADMM can be used to solve the consensus problem in a fully parallel fashion over a computer network with a star topology. However, traditional synchronized computation does not scale well with the problem size, as the speed of the algorithm is limited by the slowest workers. This is particularly true in a heterogeneous network where the computing nodes experience different computation and communication delays. In this paper, we propose an asynchronous distributed ADMM (AD-ADMM), which can effectively improve the time efficiency of distributed optimization. Our main interest lies in analyzing the convergence conditions of the AD-ADMM, under the popular partially asynchronous model, which is defined based on a maximum tolerable delay of the network. Specifically, by considering general and possibly non-convex cost functions, we show that the AD-ADMM is guaranteed to converge to the set of Karush–Kuhn–Tucker (KKT) points as long as the algorithm parameters are chosen appropriately according to the network delay. We further illustrate that the asynchrony of the ADMM has to be handled with care, as slightly modifying the implementation of the AD-ADMM can jeopardize the algorithm convergence, even under the standard convex setting. We consider a distributed total transmit power minimization in a multi-hop single-sink data gathering wireless sensor network by jointly optimizing the resource allocation and the routing with given source rates. An inherent coupling in optimal routing and resource allocation is taken into account via cross-layer optimization to increase the energy efficiency of the network. Instead of distributing the solution process horizontally by commonly used dual decomposition, we apply consensus optimization in conjunction with the alternating direction method of multipliers (ADMM). By duplicating flow variables, the problem decomposes into node specific subproblems with local variables. These variables are iteratively driven into consensus via the ADMM. Numerical examples show that the proposed algorithm converges significantly faster as compared to the state of the art methods based on the dual decomposition. Additionally, the algorithm is appealing for practical implementation due to its low local communication overhead, robust operation in slightly changing channel conditions and scalability to large networks. Distributed optimization has gained popularity in many areas because it can to cope with the increasing volume of data, and the corresponding demand for computational resources. A popular distributed solver is the alternating direction method of multipliers (ADMM). Fully decentralized (D) ADMM arises when node-to-node communications have to abide by the underlying network connectivity. DADMM’s convergence however, slows down as the network diameter grows large. To deal with this challenge, the recently proposed hybrid (H) ADMM provides considerable performance boost over DADMM by exploiting local topology information. But HADMM only applies to unweighted graphs. The present contribution develops a weighted hybrid (WH) consensus-based ADMM approach that can deal with weighted graphs. The resultant scheme further improves the performance of HADMM through graph-aware weight tuning. Theoretical analysis offers convergence guarantees and establishes linear convergence rate, while numerical tests on various graphs demonstrate the WHADMM merits.