Learning in Prophet Inequalities with Noisy Observations
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 ...
| Authors | Jung-hun Kim, Vianney Perchet |
|---|---|
| Primary category | stat.ML |
| Published | 2 April 2026 |
| Last updated at source | 2 April 2026 |
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