Simultaneously achieving sublinear regret and constraint violations for online convex optimization with time-varying constraints

In this paper, we develop a novel virtual-queue-based online algorithm for convex optimization (OCO) problems with long-term and time-varying constraints conduct performance analysis respect to the dynamic regret constraint violations. We design new update rule of dual variables way incorporating functions into variables. To best our knowledge, is first parameter-free simultaneously achieve sublinear Our proposed also outperforms state-of-the-art results in many aspects, e.g., does not require Slater condition. Meanwhile, group practical widely-studied constrained OCO which variation consecutive smooth enough across time, achieves O ( 1 ) Furthermore, extend case when time horizon T unknown. Finally, numerical experiments are conducted validate theoretical guarantees algorithm, some applications framework will be outlined.