Learning Augmented Exact Exponential Algorithms
Machine-learned predictions augment exact exponential subset-selection algorithms, reducing search space and runtime smoothly with prediction quality under weak independence or unknown-accuracy settings.
Published 2026Sydney Poster Session 4 · Wed, Dec 9, 5:00 PM–8:00 PM local time · Hall 1-4arXiv ↗OpenReview ↗
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A rigorous framework proves marginally-better-than-random predictions shrink exact exponential bases for subset selection without accuracy calibration, though the family of algorithms remains underspecified and lacks empirical benchmarks or released code.
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.