Learning in Prophet Inequalities with Noisy Observations

• URL: http://arxiv.org/abs/2604.01789v1
• Date: Thu, 02 Apr 2026 08:55:56 GMT
• Title: Learning in Prophet Inequalities with Noisy Observations
• Abstract summary: We study the prophet inequality, a fundamental problem in online decision-making and optimal stopping.<n>We propose algorithms that integrate learning and decision-making via lower-confidence-bound thresholding.
• Score: 38.27113852163736
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

Related papers

• The Sample Complexity of Multiclass and Sparse Contextual Bandits [106.74652380822778]
  We aim to identify an approximately optimal policy from a given class based on bandit feedback.<n>Motivated by bandit multiclass classification with zero-one rewards, we focus on the emph$s$-sparse setting.<n>We show that, with $s$-sparse rewards, the induced model class admits a sharp DEC bound that scales with $s$ and directly yields the optimal rate.
  arXiv  Detail & Related papers  (2026-05-28T09:12:20Z)
• Robust and Consistent Ski Rental with Distributional Advice [13.811651343801579]
  The ski rental problem is a canonical model for online decision-making under uncertainty.<n>We propose a framework that integrates distributional advice of unknown quality into both deterministic and randomized algorithms.<n>We show that our framework improves consistency significantly over existing point-prediction baselines while maintaining comparable robustness.
  arXiv  Detail & Related papers  (2026-03-31T04:04:21Z)
• Active Bipartite Ranking with Smooth Posterior Distributions [1.9838140219494644]
  Bipartite ranking is a statistical learning problem involved in many applications and widely studied in the passive context.<n>We propose a novel algorithm, referred to as smooth-rank and designed for the continuous setting, which aims to minimise the distance between the ROC curve of the estimated ranking rule and the optimal one w.r.t. the $sup$ norm.<n>We provide a problem dependent upper bound on the expected sampling time of smooth-rank and establish a problem dependent lower bound on the expected sampling time of any PAC$(,)$ algorithm.
  arXiv  Detail & Related papers  (2026-02-27T18:32:08Z)
• Optimistic Feasible Search for Closed-Loop Fair Threshold Decision-Making [0.0]
  We study online learning of a one-dimensional threshold policy from bandit feedback.<n>We propose Optimistic Feasible Search (OFS), a simple grid-based method that maintains confidence bounds for reward and constraint residuals.
  arXiv  Detail & Related papers  (2025-12-26T10:44:40Z)
• EVaR-Optimal Arm Identification in Bandits [7.340828059560291]
  We study the fixed-confidence best arm identification problem within the multiarmed bandit (MAB) framework under the Entropic Value-at-Risk criterion.
  arXiv  Detail & Related papers  (2025-10-06T11:49:56Z)
• Regret Minimization and Statistical Inference in Online Decision Making with High-dimensional Covariates [7.21848268647674]
  We integrate the $varepsilon$-greedy bandit algorithm for decision-making with a hard thresholding algorithm for estimating sparse bandit parameters.<n>Under a margin condition, our method achieves either $O(T1/2)$ regret or classical $O(T1/2)$-consistent inference.
  arXiv  Detail & Related papers  (2024-11-10T01:47:11Z)
• Beyond Expectations: Learning with Stochastic Dominance Made Practical [88.06211893690964]
  dominance models risk-averse preferences for decision making with uncertain outcomes. Despite theoretically appealing, the application of dominance in machine learning has been scarce. We first generalize the dominance concept to enable feasible comparisons between any arbitrary pair of random variables. We then develop a simple and efficient approach for finding the optimal solution in terms of dominance.
  arXiv  Detail & Related papers  (2024-02-05T03:21:23Z)
• A Minimaximalist Approach to Reinforcement Learning from Human Feedback [49.45285664482369]
  We present Self-Play Preference Optimization (SPO), an algorithm for reinforcement learning from human feedback. Our approach is minimalist in that it does not require training a reward model nor unstable adversarial training. We demonstrate that on a suite of continuous control tasks, we are able to learn significantly more efficiently than reward-model based approaches.
  arXiv  Detail & Related papers  (2024-01-08T17:55:02Z)
• Autoregressive Bandits [58.46584210388307]
  We propose a novel online learning setting, Autoregressive Bandits, in which the observed reward is governed by an autoregressive process of order $k$. We show that, under mild assumptions on the reward process, the optimal policy can be conveniently computed. We then devise a new optimistic regret minimization algorithm, namely, AutoRegressive Upper Confidence Bound (AR-UCB), that suffers sublinear regret of order $widetildemathcalO left( frac(k+1)3/2sqrtnT (1-G
  arXiv  Detail & Related papers  (2022-12-12T21:37:36Z)
• Online Learning with Knapsacks: the Best of Both Worlds [54.28273783164608]
  We casting online learning problems in which a decision maker wants to maximize their expected reward without violating a finite set of $m$m resource constraints. Our framework allows the decision maker to handle its evidence flexibility and costoretic functions.
  arXiv  Detail & Related papers  (2022-02-28T12:10:48Z)
• Top $K$ Ranking for Multi-Armed Bandit with Noisy Evaluations [102.32996053572144]
  We consider a multi-armed bandit setting where, at the beginning of each round, the learner receives noisy independent evaluations of the true reward of each arm. We derive different algorithmic approaches and theoretical guarantees depending on how the evaluations are generated.
  arXiv  Detail & Related papers  (2021-12-13T09:48:54Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.