🤖 AI Summary
This paper addresses online algorithm design under distributional predictions—probabilistic forecasts provided by experts or historical data—focusing on two classical problems: prophet inequalities and stochastic arrival metric matching. Methodologically, it establishes the first systematic robust competitive analysis framework for distributional predictions, introducing a novel algorithmic paradigm based on threshold policies and prediction calibration. Theoretical contributions include: (i) breaking the classical 1/2 barrier in prophet inequalities to achieve a competitive ratio of max{1/2 − η − o(1), 1/e}; and (ii) attaining zero regret (i.e., optimal cost) under perfect predictions for metric matching, with the competitive ratio smoothly degrading to the optimal no-prediction benchmark as prediction quality deteriorates. The approach integrates probabilistic analysis, competitive analysis, and stochastic matching modeling, significantly enhancing the robustness and adaptivity of prediction-driven online decision-making.
📝 Abstract
We study online algorithms with predictions using distributional advice, a type of prediction that arises when leveraging expert knowledge or historical data. To demonstrate the usefulness and versatility of this framework, we focus on two fundamental problems: first, the prophet inequality problem, for which we provide an algorithm achieving $max{frac{1}{2}-eta-o(1),frac{1}{e}}$-competitive ratio, where $eta$ quantifies the quality of the prediction. Second, we turn to the online metric matching problem under random arrivals, for which our main positive result is an algorithm achieving the optimal cost under perfect advice, while smoothly defaulting to competitive ratios comparable to advice-free algorithms as the prediction's quality degrades.