Delayed feedback in online non-convex optimization: A non-stationary approach with applications

We study non-convex online optimization problems with delay and noise by evaluating dynamic regret in the non-stationary setting when the loss functions are quasar-convex. In particular, we consider scenarios involving quasar-convex functions either with Lipschitz gradients or with weak smoothness, and in each case we establish bounded dynamic regret in terms of cumulative path variation, achieving sub-linear rates. Furthermore, we illustrate the flexibility of our framework by applying it to both thThe average execution time for each experiment is alsoincluded.eoretical settings, such as zeroth-order (bandit), and practical applications with quadratic fractional functions. Moreover, we provide new examples of non-convex functions that are quasar-convex by proving that the class of differentiable strongly quasiconvex functions is strongly quasar-convex on convex compact sets. Finally, several numerical experiments validate our theoretical findings, illustrating the effectiveness of our approach.