# Lazy Lagrangians with Predictions for Online Learning

arXiv: https://arxiv.org/abs/2201.02890 · HTML: https://mlsanity.com/paper/2201.02890/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 36 references that are in the map.
- First posted on arXiv 8 Jan 2022.

## Builds on (most cited first, 13 of 13)

- [Introduction to Online Convex Optimization](https://mlsanity.com/paper/1909.05207/) (2019)
- [Competitive caching with machine learned advice](https://mlsanity.com/paper/1802.05399/) (2018)
- [Optimization, Learning, and Games with Predictable Sequences](https://mlsanity.com/paper/1311.1869/) (2013)
- [Online Convex Optimization with Stochastic Constraints](https://mlsanity.com/paper/1708.03741/) (2017)
- [Adversarial Bandits with Knapsacks](https://mlsanity.com/paper/1811.11881/) (2018)
- [Adaptive Algorithms for Online Convex Optimization with Long-term Constraints](https://mlsanity.com/paper/1512.07422/) (2015)
- [Online convex optimization for cumulative constraints](https://mlsanity.com/paper/1802.06472/) (2018)
- [An Online Convex Optimization Approach to Dynamic Network Resource Allocation](https://mlsanity.com/paper/1701.03974/) (2017)
- [Online Learning with Imperfect Hints](https://mlsanity.com/paper/2002.04726/) (2020)
- [Distributed Online Convex Optimization with Time-Varying Coupled Inequality Constraints](https://mlsanity.com/paper/1903.04277/) (2019)
- [Online Convex Optimization Using Predictions](https://mlsanity.com/paper/1504.06681/) (2015)
- [Online Convex Optimization with Perturbed Constraints](https://mlsanity.com/paper/1906.00049/) (2019)
- [Online Optimization with Predictions and Non-convex Losses](https://mlsanity.com/paper/1911.03827/) (2019)

## Built on by (most cited first, 4 of 4)

- [An Optimistic Algorithm for Online Convex Optimization with Adversarial Constraints](https://mlsanity.com/paper/2412.08060/) (2024)
- [Optimistic No-regret Algorithms for Discrete Caching](https://mlsanity.com/paper/2208.06414/) (2022)
- [Online Omniprediction with Long-Term Constraints](https://mlsanity.com/paper/2509.11357/) (2025)
- [Dynamic Regret Bounds for Online Omniprediction with Long Term Constraints](https://mlsanity.com/paper/2510.07266/) (2025)

## Abstract (arXiv)

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^frac3-β4) regret and mathcal O(T^frac1+β2) constraint violation bounds that are tunable via parameter β!∈![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.