Learning Augmented Exact Exponential Algorithms
For researchers in exact exponential algorithms, this work provides a general method to leverage weak predictions for provable speedups, addressing a gap in learning-augmented algorithms beyond polynomial time.
This paper introduces learning-augmented exact exponential algorithms for NP-hard subset selection problems, showing that a noisy predictor slightly better than random can provably reduce search space and yield runtime speedup scaling with prediction quality, under weaker assumptions than typical.
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.