Exploration-Exploitation Prompting: A Dual-Process Framework for Complex Mathematical Problem Solving

Aniket Deroy

Keywords: Exploration, Evaluation, Verification, Exploitation

TL;DR: This paper introduces Exploration-Exploitation Prompting (EEP), to help Large Language Models solve complex, high-dimensional math problems more effectively than traditional methods.

Abstract:

Solving high-dimensional mathematical problems
requires more than just sequential reasoning; it requires a
strategic balance between breadth of search and depth of computation. This paper introduces the Exploration-Exploitation
Prompting (EEP) strategy. Inspired by reinforcement learning’s Multi-Armed Bandit problem and human cognitive dual-process theory, EEP bifurcates the Large Language Model’s
(LLM) reasoning into two distinct phases: a “Global Exploration” phase to map potential solution spaces and a “Local
Exploitation” phase to refine and execute the most promising
path. We observe that our proposed Exploration-exploitation
prompting method provides better results than the chain-of-thoughts and tree-of-thoughts prompting method on the Math-NET dataset.

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Submission Number: 23