[2604.01789] Learning in Prophet Inequalities with Noisy Observations

Statistics > Machine Learning arXiv:2604.01789 (stat) [Submitted on 2 Apr 2026] Title:Learning in Prophet Inequalities with Noisy Observations Authors:Jung-hun Kim, Vianney Perchet View a PDF of the paper titled Learning in Prophet Inequalities with Noisy Observations, by Jung-hun Kim and 1 other authors View PDF HTML (experimental) Abstract:We study the prophet inequality, a fundamental problem in online decision-making and optimal stopping, in a practical setting where rewards are observed only through noisy realizations and reward distributions are unknown. At each stage, the decision-maker receives a noisy reward whose true value follows a linear model with an unknown latent parameter, and observes a feature vector drawn from a distribution. To address this challenge, we propose algorithms that integrate learning and decision-making via lower-confidence-bound (LCB) thresholding. In the i.i.d.\ setting, we establish that both an Explore-then-Decide strategy and an $\varepsilon$-Greedy variant achieve the sharp competitive ratio of $1 - 1/e$, under a mild condition on the optimal value. For non-identical distributions, we show that a competitive ratio of $1/2$ can be guaranteed against a relaxed benchmark. Moreover, with limited window access to past rewards, the tight ratio of $1/2$ against the optimal benchmark is achieved. Comments: Subjects: Machine Learning (stat.ML); Machine Learning (cs.LG) Cite as: arXiv:2604.01789 [stat.ML]   (or arXiv:2604.01789v1 [stat.ML] for...