A distributed optimization method with unknown cost function in a multi-agent system via randomized gradient-free method

Pang, Yipeng; Hu, Guoqiang

doi:10.1109/ascc.2017.8287157

Cited by 19 publications

(24 citation statements)

References 20 publications

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“…In this paper, we consider the online optimization problem where the gradient information is not available, but the value of the objective functions can be measured, and is only revealed after the decision is made at each time-step. Motivated by the work in [32] and our previous work in [31], we propose an online randomized gradient-free distributed projected gradient descent (oRGF-DPGD) algorithm, in which a randomized gradient-free oracle is built locally as a replacement of the local function derivative, followed by the update of the state variables at each time-step. With some standard assumptions on the graph connectivity and the local objective functions, we are able to prove that the dynamic regret is bounded by a small error term plus a product of a term depending on the variation of the optimal solution sequence and a sublinear function of the time duration.…”

Section: Introductionmentioning

confidence: 99%

Randomized Gradient-Free Distributed Online Optimization with Time-Varying Cost Functions

Pang

2019

2019 IEEE 58th Conference on Decision and Control (CDC)

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This paper presents a randomized gradient-free distributed online optimization algorithm, with a group of agents whose local objective functions are time-varying. It is worth noting that the value of the local objective function is only revealed to the corresponding agent after the decision is made at each time-step. Thus, each agent updates the decision variable using the local objective function value of its last decision and the information collected from its immediate in-neighbors. A randomized gradient-free oracle is built locally in replacement of the true gradient information in guiding the updates of the decision variable. The notion of dynamic regret is brought forward to measure the difference between the total cost incurred by the agent's state estimation and the offline centralized optimal solution where the objective functions are available a priori. Under the assumptions of strongly connected communication graph and bounded subgradients of the local objective functions, we characterize the dynamic regret associated with each agent as a function of the time duration T and the deviation of the minimizer sequence. Averaging the dynamic regret over the time duration, we establish the asymptotic convergence to a small neighborhood of zero with a rate of O(ln T / √ T ). The effectiveness of this algorithm is illustrated through numerical simulations.

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Section: Introductionmentioning

confidence: 99%

Randomized Gradient-Free Distributed Online Optimization with Time-Varying Cost Functions

Pang

2019

2019 IEEE 58th Conference on Decision and Control (CDC)

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“…(b) We design a class of distributed optimization algorithms by a way to combining conventional KW ideas and consensus based algorithms, which is a different technique compared to other existing gradient/subgradient-free algorithms c.f., [23]- [27]. We prove the consensus of estimates and achievement of the global minimization with probability one.…”

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confidence: 99%

Distributed Subgradient-Free Stochastic Optimization Algorithm for Nonsmooth Convex Functions over Time-Varying Networks

Wang¹,

Zhao²,

Ye³

et al. 2019

SIAM J. Control Optim.

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In this paper we consider a distributed stochastic optimization problem without the gradient/subgradient information for the local objective functions, subject to local convex constraints. The objective functions may be non-smooth and observed with stochastic noises, and the network for the distributed design is time-varying.By adding the stochastic dithers into the local objective functions and constructing the randomized differences motivated by the Kiefer-Wolfowitz algorithm, we propose a distributed subgradient-free algorithm to find the global minimizer with local observations. Moreover, we prove that the consensus of estimates and global minimization can be achieved with probability one over the time-varying network, and then obtain the convergence rate of the mean average of estimates as well. Finally, we give a numerical example to illustrate the effectiveness of the proposed algorithm.

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“…medicine [51], and earth sciences [52]. Recent research on gradient-free schemes has been reported in [53][54][55][56][57][58][59] based on extremum seeking, and [60][61][62][63][64][65][66][67][68][69][70] This type of methods, in general, is a continuous-time control-based approach, and usually presumes some smoothness in the cost function. On the other hand, the smoothing-based methods estimate the gradient of the cost function based on two point values.…”

Section: Literature Reviewmentioning

confidence: 99%

“…As reviewed in Chapter 1, recent studies on this topic have been reported in [60][61][62][63][64][65][66][67].…”

Section: Introductionmentioning

confidence: 99%

“…However, all these methods are endowed with a doubly-stochastic weighting matrix requirement, which is restrictive in a distributed setting. The doubly-stochastic assumption was removed in [65] by adopting a pushsum technique and [66,67] by introducing a surplus variable, respectively. Duchi et al in [68] introduced a smoothing technique which used two point gradient estimation to close the optimality gap between the final iterate and the optimal point by choosing appropriate parameters.…”

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Gradient-free distributed optimization and nash equilibrium seeking

Pang¹

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A distributed optimization method with unknown cost function in a multi-agent system via randomized gradient-free method

Cited by 19 publications

References 20 publications

Randomized Gradient-Free Distributed Online Optimization with Time-Varying Cost Functions

Randomized Gradient-Free Distributed Online Optimization with Time-Varying Cost Functions

Distributed Subgradient-Free Stochastic Optimization Algorithm for Nonsmooth Convex Functions over Time-Varying Networks

Gradient-free distributed optimization and nash equilibrium seeking

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