Lazy Lagrangians for Optimistic Learning With Budget Constraints

We consider the general problem of online convex optimization with time-varying budget constraints in presence predictions for next cost and constraint functions, that arises a plethora network resource management problems. A novel saddle-point algorithm is designed by combining Follow-The-Regularized-Leader iteration prediction-adaptive dynamic steps. The achieves $\c O(T^{(3-\beta)/4})$ regret O(T^{(1+\beta)/2})$ violation bounds are tunable via parameter notation="LaTeX">$\beta\!\in\![1/2,1)$ have constant factors shrink quality, achieving eventually O(1)$ perfect predictions. Our work extends seminal FTRL framework this new OCO setting outperforms respective state-of-the-art greedy-based solutions which naturally cannot benefit from predictions, without imposing conditions on (unknown) quality functions or geometry constraints, beyond convexity.