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An Adaptive Primal-Dual Subgradient Algorithm for Online Distributed Constrained Optimization
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AI
DOI：10.1109/TCYB.2017.2755720.png)
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In this paper, we consider the problem of solving distributed constrained optimization over a multiagent network that consists of multiple interacting nodes in online setting, where the objective functions of nodes are time-varying and the constraint set is characterized by an inequality. Through introducing a regularized convex-concave function, we present a consensus-based adaptive primal-dual subgradient algorithm that removes the need for knowing the total number of iterations T in advance. We show that the proposed algorithm attains an O(T1/2+c) [where c is an element of (0, 1/ 2)] regret bound and an O(T1-c/2) bound on the violation of constraints; in addition, we show an improvement to an O(T-c) regret bound when the objective functions are strongly convex. The proposed algorithm allows a novel trade-offs between the regret and the violation of constraints. Finally, a numerical example is provided to illustrate the effectiveness of the algorithm.
Keyword:
Adaptive regularization
distributed optimization
online convex optimization
regret bound
violation of constraints
期刊
IF:
10.5
论文数:
1.1W
被引数:
5.0W
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