The alternating direction method of multipliers (ADMM) is a powerful optimization solver in machine learning. Recently, stochastic ADMM has been integrated with variance reduction methods for stochastic gradient, leading to SAG-ADMM and SDCA-ADMM that have fast convergence rates and low iteration complexities. However,…
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Recently, many variance reduced stochastic alternating direction method of multipliers (ADMM) methods (e.g.\ SAG-ADMM, SDCA-ADMM and SVRG-ADMM) have made exciting progress such as linear convergence rates for strongly convex problems. However, the best known convergence rate for general convex problems is O(1/T) as opp…
A faster ADMM method for nonconvex optimization with improved complexity.
problem Nonconvex optimization problems in machine learning.
method SPIDER-ADMM, a stochastic ADMM method using a new differential estimator.
result Achieves optimal IFO complexity of for finding an -approximate stationary point.
In the paper, we study the stochastic alternating direction method of multipliers (ADMM) for the nonconvex optimizations, and propose three classes of the nonconvex stochastic ADMM with variance reduction, based on different reduced variance stochastic gradients. Specifically, the first class called the nonconvex stoch…
Two-block ADMM outperformed multi-block ADMM in multi-task learning experiments.
problem Comparing two-block vs. multi-block ADMM in optimization performance.
method Compared two-block and multi-block ADMM on multi-task learning problems.
result Multi-block ADMM consistently outperformed two-block ADMM in optimization and prediction performance.
Unified view connects CoCoA and ADMM for distributed ERM.
problem Connection between CoCoA and ADMM for distributed ERM.
method Unified primal-dual perspective reformulation.
result Unified ADMM variants perform at least as good as CoCoA in ridge-regularized ERM.
We consider the problem of maximum a posteriori (MAP) inference in discrete graphical models. We present a parallel MAP inference algorithm called Bethe-ADMM based on two ideas: tree-decomposition of the graph and the alternating direction method of multipliers (ADMM). However, unlike the standard ADMM, we use an inexa…
The mirror descent algorithm (MDA) generalizes gradient descent by using a Bregman divergence to replace squared Euclidean distance. In this paper, we similarly generalize the alternating direction method of multipliers (ADMM) to Bregman ADMM (BADMM), which allows the choice of different Bregman divergences to exploit …
Bayesian approach generalizes ADMM for federated learning.
problem Improving federated learning efficiency and accuracy.
method Integrates Bayesian duality with ADMM for optimization.
result New extensions of ADMM for various distributions.
New method solves nonconvex optimization problems without explicit gradients.
problem Solving nonconvex optimization problems with multiple nonsmooth penalties.
method Zeroth-order stochastic ADMM methods (ZO-SVRG-ADMM and ZO-SAGA-ADMM).
result Convergence rate of for nonconvex optimization.
We present ADMM-Softmax, an alternating direction method of multipliers (ADMM) for solving multinomial logistic regression (MLR) problems. Our method is geared toward supervised classification tasks with many examples and features. It decouples the nonlinear optimization problem in MLR into three steps that can be solv…
New methods solve complex optimization problems with fewer function queries.
problem Solving nonconvex optimization problems with multiple penalties and constraints.
method ZO-SPIDER-ADMM and ZOO-ADMM+ methods for nonconvex finite-sum and online problems.
result Achieved lower function query complexity for finding ε-stationary points.
Unified analysis of stochastic ADMM variants via SME.
problem Analyzing and optimizing stochastic ADMM variants for machine learning.
method Unified mathematical framework of SME for continuous-time analysis.
result Dynamics of stochastic ADMM approximated by SDEs with small noise.
Due to massive amounts of data distributed across multiple locations, distributed machine learning has attracted a lot of research interests. Alternating Direction Method of Multipliers (ADMM) is a powerful method of designing distributed machine learning algorithm, whereby each agent computes over local datasets and e…
This paper converts ADMM to proximal gradient for efficient sparse estimation.
problem Sparse estimation problems like fused lasso and convex clustering.
method General method converting ADMM to proximal gradient, assuming Lipschitz continuity of derivative.
result Significant improvement in efficiency for sparse estimation problems.
Alternating Direction Method of Multipliers (ADMM) is a widely used tool for machine learning in distributed settings, where a machine learning model is trained over distributed data sources through an interactive process of local computation and message passing. Such an iterative process could cause privacy concerns o…
Alternating direction method of multiplier (ADMM) is a popular method used to design distributed versions of a machine learning algorithm, whereby local computations are performed on local data with the output exchanged among neighbors in an iterative fashion. During this iterative process the leakage of data privacy a…
Novel PP-ADMM and IPP-ADMM algorithms improve differential privacy in distributed machine learning.
problem Privacy concerns in ADMM-based distributed machine learning.
method Proposes PP-ADMM and IPP-ADMM algorithms to provide differential privacy while improving model accuracy and convergence.
result The proposed algorithms achieve better model accuracy and convergence under the same privacy guarantee.
We address the problem of solving convex optimization problems with many convex constraints in a distributed setting. Our approach is based on an extension of the alternating direction method of multipliers (ADMM) that recently gained a lot of attention in the Big Data context. Although it has been invented decades ago…
This work improves DNN weight quantization with ADMM, achieving lossless binarization and reduced search space.
problem Improving DNN model compression and accuracy with low bit quantization.
method Extending ADMM framework for DNN weight quantization with progressive multi-step approach.
result Achieved lossless and fully binarized DNNs with reduced accuracy loss.
The alternating direction method of multipliers (ADMM) has been successfully applied to solve structured convex optimization problems due to its superior practical performance. The convergence properties of the 2-block ADMM have been studied extensively in the literature. Specifically, it has been proven that the 2-blo…
In this paper, we design and analyze a new zeroth-order online algorithm, namely, the zeroth-order online alternating direction method of multipliers (ZOO-ADMM), which enjoys dual advantages of being gradient-free operation and employing the ADMM to accommodate complex structured regularizers. Compared to the first-ord…
Paper tackles privacy-preserving distributed learning with ADMM.
problem Privacy-preserving distributed learning with vertically partitioned features.
method Proposes ADMM sharing framework to minimize risk over distributed features.
result Demonstrates efficient convergence and privacy guarantees for ADMM algorithms.
With the large rising of complex data, the nonconvex models such as nonconvex loss function and nonconvex regularizer are widely used in machine learning and pattern recognition. In this paper, we propose a class of mini-batch stochastic ADMMs (alternating direction method of multipliers) for solving large-scale noncon…
This paper solves parameter estimation with ordered regularization using ADMM.
problem Scaling up ordered regularization for large-scale data.
method Alternating Direction Method of Multipliers (ADMM) for ordered regularization.
result ADMM-O outperforms or matches state-of-the-art methods in parameter estimation.
Deep learning aids ADMM-based decoding for binary linear codes.
problem Improving decoding efficiency for binary linear codes.
method Designing a decoding network based on ADMM and deep learning.
result Numerical results show improved performance compared to original ADMM.
Paper proposes a novel unsupervised feature selection method using K-means and ADMM.
problem Finding a subset of features for high-dimensional unsupervised learning problems.
method Developed K-means Derived Unsupervised Feature Selection (K-means UFS) using ADMM to solve NP-hard optimization.
result K-means UFS outperforms baselines in feature selection for clustering.
Develops ADMM for deep neural networks with sigmoid activations to avoid saturation and improve approximation.
problem Gradient saturation in deep neural networks with sigmoid activations.
method Introduces sigmoid-ADMM pair for training deep sigmoid nets and proves its convergence.
result ADMM avoids saturation and improves approximation of deep sigmoid nets compared to ReLU nets.
New ADMM method for PARAFAC2 tensor decomposition with flexible regularization.
problem Challenges in applying regularisation to the evolving mode of PARAFAC2.
method Alternating Direction Method of Multipliers (AO-ADMM) for PARAFAC2 tensor fitting.
result The proposed ADMM-based approach accurately recovers underlying components from simulated data.
Co-Clustering, the problem of simultaneously identifying clusters across multiple aspects of a data set, is a natural generalization of clustering to higher-order structured data. Recent convex formulations of bi-clustering and tensor co-clustering, which shrink estimated centroids together using a convex fusion penalt…
Combines ADMM and VB for federated learning.
problem Improving federated learning performance.
method Derives ADMM variants from VB with flexible covariances and functional regularisation.
result Improves federated learning performance through new ADMM variants.
ADMM solves constrained CASH problems by breaking them into smaller, manageable pieces.
problem Handling black-box constraints in CASH problems.
method Leverages ADMM optimization framework to decompose CASH problems.
result ADMM facilitates incorporation of black-box constraints.
Improved ADMM for convex distributed learning with differential privacy.
problem Privacy concerns in distributed learning with sensitive data.
method Approximate multi-step ADMM with calibrated noise.
result Higher utility and error bounds asymptotic to state-of-the-art.
The Alternating Direction Method of Multipliers (ADMM) has been studied for years. The traditional ADMM algorithm needs to compute, at each iteration, an (empirical) expected loss function on all training examples, resulting in a computational complexity proportional to the number of training examples. To reduce the ti…
In this paper, we develop a variant of the well-known Gauss-Newton (GN) method to solve a class of nonconvex optimization problems involving low-rank matrix variables. As opposed to the standard GN method, our algorithm allows one to handle general smooth convex objective function. We show, under mild conditions, that …
This paper examines ADMM for network averaging, revealing its convergence rates and network topology impacts.
problem Efficiently averaging local information over a network using ADMM.
method Comparative analysis of ADMM and other algorithms on a canonical distributed averaging problem.
result Characterization of ADMM convergence and optimal parameter tuning based on network spectral properties.
Paper presents an ADMM-based approach to efficiently integrate quadratic programming layers into neural networks.
problem Integrating quadratic programs into neural networks for optimization.
method An ADMM-based network layer architecture for solving quadratic programs efficiently.
result The ADMM layer is approximately an order of magnitude faster than existing methods for medium scaled problems.
We consider the stochastic composition optimization problem proposed in \cite{wang2017stochastic}, which has applications ranging from estimation to statistical and machine learning. We propose the first ADMM-based algorithm named com-SVR-ADMM, and show that com-SVR-ADMM converges linearly for strongly convex and Lipsc…
New algorithm solves maximal monotone inclusion problems.
problem Solving maximal monotone inclusion problems.
method Bregman Douglas-Rachford splitting method and variants.
result Convergence of algorithms under certain assumptions.
Paper proposes ADMM algorithms for non-smooth optimization under RDP.
problem Optimizing composite functions with non-smooth penalties under privacy constraints.
method Developed ssADMM and mpADMM algorithms for non-smooth optimization problems with RDP guarantees.
result Both ssADMM and mpADMM outperform baseline methods in high privacy settings.
Paper proposes a privacy-preserving DML framework using local randomization and ADMM perturbation.
problem Privacy concerns in distributed machine learning with sensitive user data.
method Local randomization and ADMM perturbation to provide differential privacy and heterogeneous privacy levels.
result The framework minimizes privacy losses and maintains model generalization.
New ADMM algorithm tackles nonconvex constraints from GANs for faster learning.
problem Learning with nonconvex constraints from neural network outputs.
method Linearized ADMM algorithm for convex objective with nonconvex constraint.
result Efficient algorithm with provable convergence rates for specific neural network architectures.
Decentralized Gaussian processes for multi-agent learning.
problem Training and prediction in multi-agent systems.
method Decentralized ADMM for GP hyper-parameter training and iterative consensus for prediction.
result Subset of agents can perform predictions using covariance-based nearest neighbor selection.
FPC tackles big data challenges with polynomial kernels and ADMM.
problem Efficiently classify massive data with scalability and storage challenges.
method Polynomial feature mapping and ADMM for non-smooth convex optimization.
result FPC significantly reduces computational burden and storage memory without sacrificing generalization ability.
New method speeds up solving machine learning problems by splitting variables randomly.
problem Solving large-scale machine learning and signal processing problems efficiently.
method Randomized Multi-Block ADMM (RAC-MBADMM) for convex and nonconvex quadratic optimization.
result RAC-MBADMM converges linearly and outperforms other algorithms in solution time and quality.
Improved neural network training with ADMM for hardware compatibility.
problem Training scalable and parallelizable neural networks.
method Alternating Direction Method of Multipliers (ADMM) combined with iterative least-square methods.
result Achieved significant accuracy improvements over SGD and Adam.
Paper proposes efficient GP hyper-parameter optimization methods.
problem Efficient hyper-parameter optimization for Gaussian process regression.
method Cross-validation and ADMM for complexity.
result Proposed methods outperform traditional ML-based routines.
Flexible ADMM-based algorithm for non-convex problems with convergence guarantees.
problem Solving non-convex problems with smooth and convex components.
method Incorporates ADMM, SCA, distributed, asynchronous, and inexact gradient methods.
result Establishes first-order convergence rate guarantees under mild assumptions.