# Learning Augmented Exact Exponential Algorithms

arXiv: https://arxiv.org/abs/2606.18807 · HTML: https://mlsanity.com/paper/2606.18807/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 21 references that are in the map.
- First posted on arXiv 17 Jun 2026.

## Builds on (most cited first, 14 of 14)

- [Competitive caching with machine learned advice](https://mlsanity.com/paper/1802.05399/) (2018)
- [Algorithms with Predictions](https://mlsanity.com/paper/2006.09123/) (2020)
- [Improving Online Algorithms via ML Predictions](https://mlsanity.com/paper/2407.17712/) (2024)
- [Learning-Augmented Dynamic Power Management with Multiple States via New Ski Rental Bounds](https://mlsanity.com/paper/2110.13116/) (2021)
- [Beyond Black-Box Advice: Learning-Augmented Algorithms for MDPs with Q-Value Predictions](https://mlsanity.com/paper/2307.10524/) (2023)
- [Learning-Augmented Algorithms with Explicit Predictors](https://mlsanity.com/paper/2403.07413/) (2024)
- [Overcoming Brittleness in Pareto-Optimal Learning-Augmented Algorithms](https://mlsanity.com/paper/2408.04122/) (2024)
- [Approximation Algorithms for Combinatorial Optimization with Predictions](https://mlsanity.com/paper/2411.16600/) (2024)
- [Parsimonious Learning-Augmented Approximations for Dense Instances of NP-hard Problems](https://mlsanity.com/paper/2402.02062/) (2024)
- [Learning-Augmented Algorithms for the Bahncard Problem](https://mlsanity.com/paper/2410.15257/) (2024)
- [Constraint Satisfaction Problems with Advice](https://mlsanity.com/paper/2403.02212/) (2024)
- [Improved Approximations for Hard Graph Problems using Predictions](https://mlsanity.com/paper/2505.23967/) (2025)
- [Exact Algorithms via Monotone Local Search](https://mlsanity.com/paper/1512.01621/) (2015)
- [Mechanism design augmented with output advice](https://mlsanity.com/paper/2406.14165/) (2024)

## Abstract (arXiv)

The field of learning-augmented algorithms has demonstrated that machine-learned predictions can bypass worst-case lower bounds across a wide range of problems. So far, however, the focus has been almost exclusively on polynomial-time algorithms, where predictions improve competitive ratios, approximation guarantees, or running times. In this paper, we raise the question of whether predictions can push the frontier of exact exponential-time algorithms for NP-hard problems. We answer this question affirmatively by proposing a general approach that augments an entire family of state-of-the-art exact algorithms for a variety of subset selection problems. We show that a noisy predictor that is only marginally better than random guessing suffices to provably reduce the search space, and that the resulting runtime speedup scales smoothly with the prediction quality. Importantly, our algorithms require only pairwise independence of predictions or, alternatively, do not require the knowledge of the predictor's accuracy - both strictly weaker and more realistic settings than typically assumed.