We consider non-differentiable dynamic optimization problems such as those arising in robotics and subspace tracking. Given the computational constraints and the time-varying nature of the problem, a low-complexity algorithm is desirable, while the accuracy of the solution may only increase slowly over time. We put forth the proximal online gradient descent (OGD) algorithm for tracking the optimum of a composite objective function comprising of a differentiable loss function and a non-differentiable regularizer. An online learning framework is considered and the gradient of the loss function is allowed to be erroneous. Both, the gradient error as well as the dynamics of the function optimum or target are adversarial and the performance of the inexact proximal OGD is characterized in terms of its dynamic regret, expressed in terms of the cumulative error and path length of the target. The proposed inexact proximal OGD is generalized for application to large-scale problems where the loss function has a finite sum structure. In such cases, evaluation of the full gradient may not be viable and a variance reduced version is proposed that allows the component functions to be sub-sampled. The efficacy of the proposed algorithms is tested on the problem of formation control in robotics and on the dynamic foreground-background separation problem in video.
In this paper, we propose a fast, privacy-aware, and communication-efficient decentralized framework to solve the distributed machine learning (DML) problem. The proposed algorithm is based on the Alternating Direction Method of Multipliers (ADMM) algorithm. The key novelty in the proposed algorithm is that it solves the problem in a decentralized topology where at most half of the workers are competing the limited communication resources at any given time. Moreover, each worker exchanges the locally trained model only with two neighboring workers, thereby training a global model with a lower amount of communication overhead in each exchange. We prove that GADMM converges faster than the centralized batch gradient descent for convex loss functions, and numerically show that it converges faster and more communication-efficient than the state-of-the-art communication-efficient algorithms such as the Lazily Aggregated Gradient (LAG) and dual averaging, in linear and logistic regression tasks on synthetic and real datasets.
In this paper, we propose a communication-efficient decentralized machine learning (ML) algorithm, coined quantized group ADMM (Q-GADMM). Every worker in Q-GADMM communicates only with two neighbors, and updates its model via the group alternating direct method of multiplier (GADMM), thereby ensuring fast convergence while reducing the number of communication rounds. Furthermore, each worker quantizes its model updates before transmissions, thereby decreasing the communication payload sizes. We prove that Q-GADMM converges to the optimal solution for convex loss functions, and numerically show that Q-GADMM yields 7x less communication cost while achieving almost the same accuracy and convergence speed compared to GADMM without quantization.
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