Optimal Stopping with a Predicted Prior

TL;DR

This paper introduces a new model for optimal stopping that incorporates machine-learned priors, balancing the benefits of accurate predictions with robustness to errors, and proposes algorithms with improved trade-offs.

Contribution

It formulates the optimal stopping problem with predicted priors and develops bi-criteria algorithms that enhance the trade-off between consistency and robustness.

Findings

Bi-criteria algorithms outperform existing methods in trade-offs.

No single algorithm can simultaneously optimize both consistency and robustness.

Algorithms improve expected value and probability of accepting the maximum value.

Abstract

There are two major models of value uncertainty in the optimal stopping literature: the secretary model, which assumes no prior knowledge, and the prophet inequality model, which assumes full information about value distributions. In practice, decision makers often rely on machine-learned priors that may be erroneous. Motivated by this gap, we formulate the model of optimal stopping with a predicted prior to design algorithms that are both consistent, exploiting the prediction when accurate, and robust, retaining worst-case guarantees when it is not. Existing secretary and prophet inequality algorithms are either pessimistic in consistency or not robust to misprediction. A randomized combination only interpolates their guarantees linearly. We show that a family of bi-criteria algorithms achieves improved consistency-robustness trade-offs, both for maximizing the expected accepted value and for maximizing the probability of accepting the maximum value. We further prove that for the latter objective, no algorithm can simultaneously match the best prophet inequality algorithm in consistency, and the best secretary algorithm in robustness.