Prophet Inequality with Conservative Prediction

2026-02-19

AI Summary

This work investigates how conservative predictions of the maximum value can enhance performance in online stopping decisions while preserving theoretical guarantees when predictions fail. Focusing on the prophet inequality problem with conservative predictions, the authors propose a threshold-based strategy that requires no prior knowledge of the prediction quality parameter α. The algorithm achieves a competitive ratio of 1/2 when α = 0 and smoothly improves to 3/4 as α approaches 1, establishing a Pareto-optimal trade-off between robustness and consistency that cannot be surpassed. When α is known in advance, the paper provides a tight competitive ratio of 1/(2 − α). Collectively, these results delineate the optimal performance boundaries for both known and unknown α settings, enabling a smooth transition in competitive ratio from 1/2 to 3/4.

Technology Category

• Machine Learning: Online Learning & Bandits
• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Learning to Search

Application Category

• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

Prophet inequalities compare online stopping strategies against an omniscient "prophet" using distributional knowledge. In this work, we augment this model with a conservative prediction of the maximum realized value. We quantify the quality of this prediction using a parameter $α\in [0,1]$, ranging from inaccurate to perfect. Our goal is to improve performance when predictions are accurate (consistency) while maintaining theoretical guarantees when they are not (robustness). We propose a threshold-based strategy oblivious to $α$ (i.e., with $α$ unknown to the algorithm) that matches the classic competitive ratio of $1/2$ at $α=0$ and improves smoothly to $3/4$ at $α=1$. We further prove that simultaneously achieving better than $3/4$ at $α=1$ while maintaining $1/2$ at $α=0$ is impossible. Finally, when $α$ is known in advance, we present a strategy achieving a tight competitive ratio of $\frac{1}{2-α}$.

Problem

• prophet inequality
• conservative prediction
• competitive ratio
• online stopping
• robustness

Innovation

• prophet inequality
• conservative prediction
• competitive ratio
• threshold-based strategy
• robustness-consistency tradeoff