# Learning-Augmented Online Minimization with Dual Predictions

arXiv: https://arxiv.org/abs/2606.05380 · HTML: https://mlsanity.com/paper/2606.05380/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 73 references that are in the map.
- First posted on arXiv 3 Jun 2026.

## Builds on (most cited first, 30 of 33)

- [Competitive caching with machine learned advice](https://mlsanity.com/paper/1802.05399/) (2018)
- [Algorithms with Predictions](https://mlsanity.com/paper/2006.09123/) (2020)
- [The Primal-Dual method for Learning Augmented Algorithms](https://mlsanity.com/paper/2010.11632/) (2020)
- [Online metric algorithms with untrusted predictions](https://mlsanity.com/paper/2003.02144/) (2020)
- [Near-Optimal Bounds for Online Caching with Machine Learned Advice](https://mlsanity.com/paper/1910.12172/) (2019)
- [Improving Online Algorithms via ML Predictions](https://mlsanity.com/paper/2407.17712/) (2024)
- [Optimal Robustness-Consistency Trade-offs for Learning-Augmented Online Algorithms](https://mlsanity.com/paper/2010.11443/) (2020)
- [Faster Matchings via Learned Duals](https://mlsanity.com/paper/2107.09770/) (2021)
- [Online Computation with Untrusted Advice](https://mlsanity.com/paper/1905.05655/) (2019)
- [Faster Fundamental Graph Algorithms via Learned Predictions](https://mlsanity.com/paper/2204.12055/) (2022)
- [Better and Simpler Learning-Augmented Online Caching](https://mlsanity.com/paper/2005.13716/) (2020)
- [Online Algorithms for Weighted Paging with Predictions](https://mlsanity.com/paper/2006.09509/) (2020)
- [Learnable and Instance-Robust Predictions for Online Matching, Flows and Load Balancing](https://mlsanity.com/paper/2011.11743/) (2020)
- [Online Algorithms with Multiple Predictions](https://mlsanity.com/paper/2205.03921/) (2022)
- [Learning-Augmented Dynamic Power Management with Multiple States via New Ski Rental Bounds](https://mlsanity.com/paper/2110.13116/) (2021)
- [Chasing Convex Bodies and Functions with Black-Box Advice](https://mlsanity.com/paper/2206.11780/) (2022)
- [Chasing Convex Bodies Optimally](https://mlsanity.com/paper/1905.11968/) (2019)
- [Learning-Augmented Weighted Paging](https://mlsanity.com/paper/2011.09076/) (2020)
- [Chasing Convex Bodies with Linear Competitive Ratio](https://mlsanity.com/paper/1905.11877/) (2019)
- [Data-driven Competitive Algorithms for Online Knapsack and Set Cover](https://mlsanity.com/paper/2012.05361/) (2020)
- [Mixing predictions for online metric algorithms](https://mlsanity.com/paper/2304.01781/) (2023)
- [Algorithms for Caching and MTS with reduced number of predictions](https://mlsanity.com/paper/2404.06280/) (2024)
- [Metrical task systems on trees via mirror descent and unfair gluing](https://mlsanity.com/paper/1807.04404/) (2018)
- [Learning-Augmented Algorithms for Online Linear and Semidefinite Programming](https://mlsanity.com/paper/2209.10614/) (2022)
- [The Randomized k-Server Conjecture is False!](https://mlsanity.com/paper/2211.05753/) (2022)
- [Pure entropic regularization for metrical task systems](https://mlsanity.com/paper/1906.04270/) (2019)
- [Shortest Paths without a Map, but with an Entropic Regularizer](https://mlsanity.com/paper/2202.04551/) (2022)
- [A General Framework for Learning-Augmented Online Allocation](https://mlsanity.com/paper/2305.18861/) (2023)
- [Chasing Convex Functions with Long-term Constraints](https://mlsanity.com/paper/2402.14012/) (2024)
- [Best of Many in Both Worlds: Online Resource Allocation with Predictions under Unknown Arrival Model](https://mlsanity.com/paper/2402.13530/) (2024)

## Built on by (most cited first, 1 of 1)

- [Compressing Value Predictions for Learning-Augmented Metrical Task Systems](https://mlsanity.com/paper/2609.33580/) (2026)

## Abstract (arXiv)

We present learning-augmented algorithms for two general classes of online minimization problems: metrical task systems and laminar set cover. Both algorithms achieve improved theoretical guarantees using machine-learned predictions of an optimal solution to the dual linear program. Unlike optimal primal solutions, which can change drastically under tiny instance perturbations, these dual solutions are much more stable, which ensures the existence of good (and learnable) predictions for families of similar instances. While previous work has used dual predictions in offline settings and for online maximization problems, our algorithms are, to the best of our knowledge, the first demonstration that such dual predictions can be effective for online minimization. Our theoretical results are complemented by experiments on the k-server problem and the parking permit problem.