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    • Online Distributed Nonconvex Optimization with Stochastic Objective Functions: High Probability Bound Analysis of Dynamic Regrets

    Hang Xu,Kaihong Lu,Yu-Long Wang

    International Conference on Control, Automation, Robotics and Vision（2024）

    Shandong Univ Sci & Technol

    Cited 1|Views6
    Abstract
    In this paper, the problem of online distributed optimization with stochastic and nonconvex objective functions is studied by employing a multi-agent system. When making decisions, each agent only has access to a noisy gradient of its own objective function in the previous time and can only communicate with its immediate neighbors via a time-varying digraph. To handle this problem, an online distributed stochastic projection-free algorithm is proposed. Of particular interest is that the dynamic regrets are employed to measure the performance of the online algorithm. Existing works on online distributed algorithms involving stochastic gradients only provide the sublinearity results of regrets in expectation. Different from them, we study the high probability bounds of dynamic regrets, i.e., the sublinear bounds of dynamic regrets are characterized by the natural logarithm of the failure probability's inverse. Under mild assumptions on the graph and objective functions, we prove that if the variations in both the objective function sequence and its gradient sequence grow within a certain rate, then the high probability bounds of the dynamic regrets grow sublinearly. Finally, a simulation example is carried out to demonstrate the effectiveness of our theoretical results. (c) 2024 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
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    Key words
    Online distributed optimization,Nonconvex optimization,Stochastic gradients,High probability
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