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Register a new userAccelerated Zeroth-order Algorithm for Stochastic Distributed Nonconvex Optimization
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This paper investigates how to accelerate the convergence of distributed optimization algorithms on nonconvex problems with zeroth-order information available only. We propose a zeroth-order (ZO) distributed primal-dual stochastic coordinates algorithm equipped with powerball method to accelerate. We prove that the proposed algorithm has a convergence rate of $mathcal{O}(sqrt{p}/sqrt{nT})$ for general nonconvex cost functions. We consider solving the generation of adversarial examples from black-box DNNs problem to compare with the existing state-of-the-art centralized and distributed ZO algorithms. The numerical results demonstrate the faster convergence rate of the proposed algorithm and match the theoretical analysis.
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In this paper, we consider a stochastic distributed nonconvex optimization problem with the cost function being distributed over $n$ agents having access only to zeroth-order (ZO) information of the cost. This problem has various machine learning applications. As a solution, we propose two distributed ZO algorithms, in which at each iteration each agent samples the local stochastic ZO oracle at two points with an adaptive smoothing parameter. We show that the proposed algorithms achieve the linear speedup convergence rate $mathcal{O}(sqrt{p/(nT)})$ for smooth cost functions and $mathcal{O}(p/(nT))$ convergence rate when the global cost function additionally satisfies the Polyak--Lojasiewicz (P--L) condition, where $p$ and $T$ are the dimension of the decision variable and the total number of iterations, respectively. To the best of our knowledge, this is the first linear speedup result for distributed ZO algorithms, which enables systematic processing performance improvements by adding more agents. We also show that the proposed algorithms converge linearly when considering deterministic centralized optimization problems under the P--L condition. We demonstrate through numerical experiments the efficiency of our algorithms on generating adversarial examples from deep neural networks in comparison with baseline and recently proposed centralized and distributed ZO algorithms.
This paper investigates the stochastic distributed nonconvex optimization problem of minimizing a global cost function formed by the summation of $n$ local cost functions. We solve such a problem by involving zeroth-order (ZO) information exchange. In this paper, we propose a ZO distributed primal-dual coordinate method (ZODIAC) to solve the stochastic optimization problem. Agents approximate their own local stochastic ZO oracle along with coordinates with an adaptive smoothing parameter. We show that the proposed algorithm achieves the convergence rate of $mathcal{O}(sqrt{p}/sqrt{T})$ for general nonconvex cost functions. We demonstrate the efficiency of proposed algorithms through a numerical example in comparison with the existing state-of-the-art centralized and distributed ZO algorithms.
As application demands for zeroth-order (gradient-free) optimization accelerate, the need for variance reduced and faster converging approaches is also intensifying. This paper addresses these challenges by presenting: a) a comprehensive theoretical analysis of variance reduced zeroth-order (ZO) optimization, b) a novel variance reduced ZO algorithm, called ZO-SVRG, and c) an experimental evaluation of our approach in the context of two compelling applications, black-box chemical material classification and generation of adversarial examples from black-box deep neural network models. Our theoretical analysis uncovers an essential difficulty in the analysis of ZO-SVRG: the unbiased assumption on gradient estimates no longer holds. We prove that compared to its first-order counterpart, ZO-SVRG with a two-point random gradient estimator could suffer an additional error of order $O(1/b)$, where $b$ is the mini-batch size. To mitigate this error, we propose two accelerate
Stochastic gradient descent (SGD) is one of the most widely used optimization methods for parallel and distributed processing of large datasets. One of the key limitations of distributed SGD is the need to regularly communicate the gradients between different computation nodes. To reduce this communication bottleneck, recent work has considered a one-bit variant of SGD, where only the sign of each gradient element is used in optimization. In this paper, we extend this idea by proposing a stochastic variant of the proximal-gradient method that also uses one-bit per update element. We prove the theoretical convergence of the method for non-convex optimization under a set of explicit assumptions. Our results indicate that the compressed method can match the convergence rate of the uncompressed one, making the proposed method potentially appealing for distributed processing of large datasets.
While many distributed optimization algorithms have been proposed for solving smooth or convex problems over the networks, few of them can handle non-convex and non-smooth problems. Based on a proximal primal-dual approach, this paper presents a new (stochastic) distributed algorithm with Nesterov momentum for accelerated optimization of non-convex and non-smooth problems. Theoretically, we show that the proposed algorithm can achieve an $epsilon$-stationary solution under a constant step size with $mathcal{O}(1/epsilon^2)$ computation complexity and $mathcal{O}(1/epsilon)$ communication complexity. When compared to the existing gradient tracking based methods, the proposed algorithm has the same order of computation complexity but lower order of communication complexity. To the best of our knowledge, the presented result is the first stochastic algorithm with the $mathcal{O}(1/epsilon)$ communication complexity for non-convex and non-smooth problems. Numerical experiments for a distributed non-convex regression problem and a deep neural network based classification problem are presented to illustrate the effectiveness of the proposed algorithms.
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