Online Optimization with Feedback Delay and Nonlinear Switching Cost

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Abstract

We study a variant of online optimization in which the learner receives k-rounddelayed feedback about hitting cost and there is a multi-step nonlinear switching cost, i.e., costs depend on multiple previous actions in a nonlinear manner. Our main result shows that a novel Iterative Regularized Online Balanced Descent (iROBD) algorithm has a constant, dimension-free competitive ratio that is O(L 2k), where L is the Lipschitz constant of the switching cost. Additionally, we provide lower bounds that illustrate the Lipschitz condition is required and the dependencies on k and L are tight. Finally, via reductions, we show that this setting is closely related to online control problems with delay, nonlinear dynamics, and adversarial disturbances, where iROBD directly offers constant-competitive online policies.

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Pan, W., Shi, G., Lin, Y., & Wierman, A. (2022). Online Optimization with Feedback Delay and Nonlinear Switching Cost. In Proceedings of the ACM on Measurement and Analysis of Computing Systems (Vol. 6). Association for Computing Machinery. https://doi.org/10.1145/3508037

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