Lazy Lagrangians with Predictions for Online Learning

We consider the general problem of online convex optimization with time-varying additive constraints in the presence of predictions for the next cost and constraint functions. A novel primal-dual algorithm is designed by combining a Follow-The-Regularized-Leader iteration with prediction-adaptive dynamic steps. The algorithm achieves $\mathcal O(T^{{\frac{3-\beta}{4}})$} regret and $\mathcal O(T^{{\frac{1+\beta}{2}})$} constraint violation bounds that are tunable via parameter $\beta!\in![1/2,1)$ and have constant factors that shrink with the predictions quality, achieving eventually $\mathcal O(1)$ regret for perfect predictions. Our work extends the FTRL framework for this constrained OCO setting and outperforms the respective state-of-the-art greedy-based solutions, without imposing conditions on the quality of predictions, the cost functions or the geometry of constraints, beyond convexity.