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Distributed online stochastic gradient tracking
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AI
DOI：10.1016/j.jfranklin.2025.107902.png)
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Abstract
En 中文
We study the distributed online stochastic optimization, where networked nodes cooperatively track the optimal solutions of the time-varying global cost function online. Each node acts as a local optimizer with access only to its own local cost function. The global cost function is the sum of these time-varying local cost functions, and each local optimizer can only obtain an unbiased stochastic gradient estimate of its current local cost function. We propose a distributed online stochastic gradient tracking algorithm that incorporates the prediction of the dynamic optimal solutions. Firstly, we derive an upper bound on the mean square of the average tracking error, indicating that our algorithm can effectively track the dynamic global optimal solutions in mean square. Then, we establish an upper bound of the dynamic regret for the proposed algorithm. This bound depends on two regularity measures, which quantify the path length of the dynamic optimal solutions and the accumulation of gradient variation errors at the optimal solutions, respectively. It is worth noting that this upper bound will decrease as the network size increases. Next, we prove that with a fixed step size of PKD/K, the dynamic regret satisfies RKd=O(KPKD), where RKd is the dynamic regret, K is the total tracking time, and PKD is the path length of the dynamic optimal solutions. This conclusion is consistent with that of the centralized online algorithm. Finally, we demonstrate our theoretical results through a numerical simulation.
Keywords:
distributed online optimization
stochastic gradient tracking
dynamic regret
networked nodes
time-varying cost functions
Journal
J
IF:
4.2
Papers:
822
Citations:
0