Learning Augmented Exact Exponential Algorithms

2026-06-17

AI Summary

This work investigates how to integrate machine learning predictions into exact exponential-time algorithms to surpass worst-case running time lower bounds for NP-hard subset selection problems. We propose the first learning-augmented exact exponential algorithm framework, which achieves substantial search space reduction using only weak predictors—such as those slightly better than random guessing or satisfying pairwise independence. Notably, our approach operates without prior knowledge of prediction accuracy, rendering the assumptions more realistic, and provides theoretical guarantees that the running time improvement smoothly correlates with prediction quality. Crucially, even when predictions are of low fidelity, the method still ensures a provable reduction in the effective search space.

Abstract

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.

Problem

• learning-augmented algorithms
• exact exponential algorithms
• NP-hard problems
• subset selection
• prediction-guided search

Innovation

• learning-augmented algorithms
• exact exponential algorithms
• subset selection
• noisy predictions
• pairwise independence