Distributed Randomized Gradient-Free Mirror Descent Algorithm for Constrained Optimization

Yu, Zhan; Ho, Daniel W. C.; Yuan, Deming

doi:10.48550/arxiv.1903.04157

Cited by 8 publications

(15 citation statements)

References 25 publications

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“…Aforementioned ZO optimization algorithms are all centralized and thus not suitable to solve distributed optimization problems. Recently distributed ZO algorithms have being proposed, e.g., distributed ZO gradient descent algorithms [53]- [57], distributed ZO push-sum algorithm [58], distributed ZO mirror descent algorithm [59], distributed ZO gradient tracking algorithm [57], distributed ZO primal-dual algorithms [60], [61], distributed ZO sliding algorithm [62].…”

Section: A Literature Reviewmentioning

confidence: 99%

“…Among these algorithms, the algorithms in [53], [54], [57]- [59], [61] are suitable to solve the deterministic form of (1), while the algorithm in [60] can be directly applied to solve the stochastic optimization problem (1). However, the algorithm in [60] requires each agent to have an O(T ) sampling size per iteration, which is not favorable in practice, although it was shown that first-order stationary points can be found at an O(p 2 n/T ) convergence rate.…”

Section: A Literature Reviewmentioning

confidence: 99%

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Zeroth-Order Algorithms for Stochastic Distributed Nonconvex Optimization

Yi¹,

Zhang²,

Yang³

et al. 2021

Preprint

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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 O( p/(nT )) for smooth cost functions and O(p/(nT )) convergence rate when the global cost function additionally satisfies the Polyak-Łojasiewicz (P-Ł) 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-Ł 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.

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Section: A Literature Reviewmentioning

confidence: 99%

Section: A Literature Reviewmentioning

confidence: 99%

Zeroth-Order Algorithms for Stochastic Distributed Nonconvex Optimization

Yi¹,

Zhang²,

Yang³

et al. 2021

Preprint

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show abstract

“…Previous Work For both deterministic and stochastic scenarios of problem (1), a large body of literature is devoted to first-order gradient based methods with a consensus scheme (see the papers cited above and references therein). On the other hand, the study of zero-order methods was started only recently [27,29,28,11,37,35]. The works [27,37,35] are dealing with zero-order distributed methods in noise-free settings while the noisy setting is developed in [11,29,28].…”

Section: Introductionmentioning

confidence: 99%

Distributed Zero-Order Optimization under Adversarial Noise

Akhavan,

Pontil,

Tsybakov

2021

Preprint

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We study the problem of distributed zero-order optimization for a class of strongly convex functions. They are formed by the average of local objectives, associated to different nodes in a prescribed network of connections. We propose a distributed zero-order projected gradient descent algorithm to solve this problem. Exchange of information within the network is permitted only between neighbouring nodes. A key feature of the algorithm is that it can query only function values, subject to a general noise model, that does not require zero mean or independent errors. We derive upper bounds for the average cumulative regret and optimization error of the algorithm which highlight the role played by a network connectivity parameter, the number of variables, the noise level, the strong convexity parameter of the global objective and certain smoothness properties of the local objectives. When the bound is specified to the standard undistributed setting, we obtain an improvement over the state-of-the-art bounds, due to the novel gradient estimation procedure proposed here. We also comment on lower bounds and observe that the dependency over certain function parameters in the bound is nearly optimal.

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“…[13] focus on applying the push-sum technique in distributed ZO optimization in order to handle direct communication between agents. [14] provided distributed ZO mirror descent algorithm. [15] utilized the gradient tracking technique in distributed ZO optimization problems.…”

Section: Introductionmentioning

confidence: 99%

Accelerated Zeroth-order Algorithm for Stochastic Distributed Nonconvex Optimization

Zhang¹,

Bailey²

2021

Preprint

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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 O( √ p/ √ 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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Distributed Randomized Gradient-Free Mirror Descent Algorithm for Constrained Optimization

Cited by 8 publications

References 25 publications

Zeroth-Order Algorithms for Stochastic Distributed Nonconvex Optimization

Zeroth-Order Algorithms for Stochastic Distributed Nonconvex Optimization

Distributed Zero-Order Optimization under Adversarial Noise

Accelerated Zeroth-order Algorithm for Stochastic Distributed Nonconvex Optimization

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