Online Optimization with Feedback Delay and Nonlinear Switching Cost

We study a variant of online optimization in which the learner receives k-round delayed feedback about hitting cost and there is multi-step nonlinear switching cost, i.e., costs depend on multiple previous actions manner. Our main result shows that novel Iterative Regularized Online Balanced Descent (iROBD) algorithm has constant, dimension-free competitive ratio O(L2k), where L Lipschitz constant cost. Additionally, we provide lower bounds illustrate condition required dependencies k are tight. Finally, via reductions, show this setting closely related to control problems with delay, dynamics, adversarial disturbances, iROBD directly offers constant-competitive policies. This extended abstract an abridged version [2].