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arXiv · 2506.17941

Greedy Selection under Independent Increments: A Toy Model Analysis

Huitao Yang
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Abstract

We study an iterative selection problem over N i.i.d. discrete-time stochastic processes with independent increments. At each stage, a fixed number of processes are retained based on their observed values. Under this simple model, we prove that the optimal strategy for selecting the final maximum-value process is to apply greedy selection at each stage. While the result relies on strong independence assumptions, it offers a clean justification for greedy heuristics in multi-stage elimination settings and may serve as a toy example for understanding related algorithms in high-dimensional applications.

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Huitao Yang. 2025-06-22. Greedy Selection under Independent Increments: A Toy Model Analysis. https://arxiv.org/abs/2506.17941

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