Zeroth-order Feedback Optimization for Cooperative Multi-Agent Systems

Tang, Yujie; Ren, Zhaolin; Li, Na

doi:10.1109/cdc42340.2020.9304302

Cited by 17 publications

(16 citation statements)

References 20 publications

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“…From Lemma 1(c), it is readily seen that the upper bound of ĝi,t (x) depends on the dimension m, which is essentially the penalty incurred by the use of zeroth-order oracle instead of the real subgradient. The dimension dependency of our algorithm is O(m), which is identical to that of [43], and better than O(m 2 ) in [11], [12], [28], [31], [32], [41]. The optimal dimension dependency O( √ m) is obtained in [33].…”

Section: B Dynamic Regret Analysismentioning

confidence: 97%

Distributed Online Optimization in Time-Varying Unbalanced Networks without Explicit Subgradients

Xiong¹,

Li²,

You³

et al. 2022

Preprint

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This paper studies a distributed online constrained optimization problem over time-varying unbalanced digraphs without explicit subgradients. In sharp contrast to the existing algorithms, we design a novel consensus-based distributed online algorithm with a local randomized zeroth-order oracle and then rescale the oracle by constructing row-stochastic matrices, which aims to address the unbalancedness of time-varying digraphs. Under mild conditions, the average dynamic regret over a time horizon is shown to asymptotically converge at a sublinear rate provided that the accumulated variation grows sublinearly with a specific order. Moreover, the counterpart of the proposed algorithm when subgradients are available is also provided, along with its dynamic regret bound, which reflects that the convergence of our algorithm is essentially not affected by the zeroth-order oracle. Simulations on distributed targets tracking problem and dynamic sparse signal recovery problem in sensor networks are employed to demonstrate the effectiveness of the proposed algorithm.

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Section: B Dynamic Regret Analysismentioning

confidence: 97%

Distributed Online Optimization in Time-Varying Unbalanced Networks without Explicit Subgradients

Xiong¹,

Li²,

You³

et al. 2022

Preprint

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show abstract

“…Over the past decade, considerable attention and effort have been paid to the consensus optimization problem [1], [2]. There is also some existing work where each agent keeps its own distinct decision variables [3], [4]. In this paper, we restrict our attention to a special case where the influences of other agents' strategies can be represented through some aggregative coupling structures [5].…”

Section: Imentioning

confidence: 99%

A Primal Decomposition Approach to Globally Coupled Aggregative Optimization over Networks

Huang¹,

Hu²

2021

Preprint

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We consider a class of multi-agent optimization problems, where each agent has a local objective function that depends on its own decision variables and the aggregate of others, and is willing to cooperate with other agents to minimize the sum of the local objectives. After associating each agent with an auxiliary variable and the related local estimates, we conduct primal decomposition to the globally coupled problem and reformulate it so that it can be solved distributedly. Based on the Douglas-Rachford method, an algorithm is proposed which ensures the exact convergence to a solution of the original problem. The proposed method enjoys desirable scalability by only requiring each agent to keep local estimates whose number grows linearly with the number of its neighbors. We illustrate our proposed algorithm by numerical simulations on a commodity distribution problem over a transport network.

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“…due to unreliable communication channels connecting the agents) [36,9,14,28,3], and because they may employ an approximate first-order information (e.g. in the case of stochastic gradient descent or zeroth order methods) [44,11].…”

Section: Introductionmentioning

confidence: 99%

A Stochastic Operator Framework for Inexact Static and Online Optimization

Bastianello¹,

Madden²,

Carli³

et al. 2021

Preprint

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This paper provides a unified stochastic operator framework to analyze the convergence of iterative optimization algorithms for both static problems and online optimization and learning. In particular, the framework is well suited for algorithms that are implemented in an inexact or stochastic fashion because of (i) stochastic errors emerging in algorithmic steps, and because (ii) the algorithm may feature random coordinate updates. To this end, the paper focuses on separable operators of the form T x = (T 1 x, . . . , Tnx), defined over the direct sum of possibly infinite-dimensional Hilbert spaces, and investigates the convergence of the associated stochastic Banach-Picard iteration. Results in terms of convergence in mean and in high-probability are presented when the errors affecting the operator follow a sub-Weibull distribution and when updates T i x are performed based on a Bernoulli random variable. In particular, the results are derived for the cases where T is contractive and averaged in terms of convergence to the unique fixed point and cumulative fixed-point residual, respectively. The results do not assume vanishing errors or vanishing parameters of the operator, as typical in the literature (this case is subsumed by the proposed framework), and links with exiting results in terms of almost sure convergence are provided. In the online optimization context, the operator changes at each iteration to reflect changes in the underlying optimization problem. This leads to an online Banach-Picard iteration, and similar results are derived where the bounds for the convergence in mean and high-probability further depend on the evolution of fixed points (i.e., optimal solutions of the time-varying optimization problem).

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Zeroth-order Feedback Optimization for Cooperative Multi-Agent Systems

Cited by 17 publications

References 20 publications

Distributed Online Optimization in Time-Varying Unbalanced Networks without Explicit Subgradients

Distributed Online Optimization in Time-Varying Unbalanced Networks without Explicit Subgradients

A Primal Decomposition Approach to Globally Coupled Aggregative Optimization over Networks

A Stochastic Operator Framework for Inexact Static and Online Optimization

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