Handling Delayed Feedback in Distributed Online Optimization: A Projection-Free Approach

Learning at the edges has become increasingly important as large quantities of data are continuously generated locally. Among others, this paradigm requires algorithms that are simple (so that they can be executed by local devices), robust (against uncertainty as data are continually generated), and reliable in a distributed manner under network issues, especially delays. In this study, we investigate the problem of online convex optimization (OCO) under adversarial delayed feedback. We propose two projection-free algorithms for centralized and distributed settings in which they are carefully designed to achieve a regret bound of \(O(\sqrt{B})\) where B is the sum of delay, which is optimal for the OCO problem in the delay setting while still being projection-free. We provide an extensive theoretical study and experimentally validate the performance of our algorithms by comparing them with existing ones on real-world problems.