## Abstract

Algorithms often must solve sequences of closely related problems. If the algorithm runs a standard procedure with worst-case runtime guarantees on each instance, it will fail to take advantage of valuable structure shared across the problem instances. When a commuter drives from work to home, for example, there are typically only a handful of routes that will ever be the shortest path. A naïve algorithm that does not exploit this common structure may spend most of its time checking roads that will never be in the shortest path. More generally, we can often ignore large swaths of the search space that will likely never contain an optimal solution. We present an algorithm that learns to maximally prune the search space on repeated computations, thereby reducing runtime while provably outputting the correct solution each period with high probability. Our algorithm employs a simple explore-exploit technique resembling those used in online algorithms, though our setting is quite different. We prove that, with respect to our model of pruning search spaces, our approach is optimal up to constant factors. Finally, we illustrate the applicability of our model and algorithm to three classic problems: shortest-path routing, string search, and linear programming.

Original language | American English |
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Pages (from-to) | 30-33 |

Number of pages | 4 |

Journal | Proceedings of Machine Learning Research |

Volume | 99 |

State | Published - 2019 |

Event | 32nd Conference on Learning Theory, COLT 2019 - Phoenix, United States Duration: 25 Jun 2019 → 28 Jun 2019 |

### Bibliographical note

Funding Information:This work was supported in part by Israel Science Foundation (ISF) grant #1044/16, a subcontract on the DARPA Brandeis Project, and the Federmann Cyber Security Center in conjunction with the Israel national cyber directorate.

Publisher Copyright:

© 2019 D. Alabi, A.T. Kalai, K. Ligett, C. Musco, C. Tzamos & E. Vitercik.