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Large Language Models (LLMs) have achieved tremendous progress, yet theystill often struggle with challenging reasoning problems. Current approachesaddress this challenge by sampling or searching detailed and low-levelreasoning chains. However, these methods are still limited in their explorationcapabilities, making it challenging for correct solutions to stand out in thehuge solution space. In this work, we unleash LLMs' creative potential forexploring multiple diverse problem solving strategies by framing an LLM as ahierarchical policy via in-context learning. This policy comprises of avisionary leader that proposes multiple diverse high-level problem-solvingtactics as hints, accompanied by a follower that executes detailedproblem-solving processes following each of the high-level instruction. Thefollower uses each of the leader's directives as a guide and samples multiplereasoning chains to tackle the problem, generating a solution group for eachleader proposal. Additionally, we propose an effective and efficienttournament-based approach to select among these explored solution groups toreach the final answer. Our approach produces meaningful and inspiring hints,enhances problem-solving strategy exploration, and improves the final answeraccuracy on challenging problems in the MATH dataset. Code will be released athttps://github.com/lz1oceani/LLM-As-Hierarchical-Policy.

Unleashing the Creative Mind: Language Model As Hierarchical Policy For Improved Exploration on Challenging Problem Solving