Lazy Lagrangians with Predictions for Online Learning

• URL: http://arxiv.org/abs/2201.02890v1
• Date: Sat, 8 Jan 2022 21:49:10 GMT
• Title: Lazy Lagrangians with Predictions for Online Learning
• Authors: Daron Anderson, George Iosifidis, and Douglas J. Leith
• Abstract summary: We consider the general problem of online convex optimization with time-varying additive constraints. A novel primal-dual algorithm is designed by combining a Follow-The-Regularized-Leader iteration with prediction-adaptive dynamic steps. Our work extends the FTRL framework for this constrained OCO setting and outperforms the respective state-of-the-art greedy-based solutions.
• Score: 24.18464455081512
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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