Greedy Selection under Independent Increments: A Toy Model Analysis
Probability
2025-06-24 v1 Artificial Intelligence
Machine Learning
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.
Cite
@article{arxiv.2506.17941,
title = {Greedy Selection under Independent Increments: A Toy Model Analysis},
author = {Huitao Yang},
journal= {arXiv preprint arXiv:2506.17941},
year = {2025}
}