# Greedy Selection under Independent Increments: A Toy Model Analysis

arXiv: https://arxiv.org/abs/2506.17941 · HTML: https://mlsanity.com/paper/2506.17941/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 5 references that are in the map.
- First posted on arXiv 22 Jun 2025.

## Builds on (most cited first, 1 of 1)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)

## Abstract (arXiv)

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.