Large Language Models (LLMs)  have demonstrated impressive capability in many natural language tasks. However, the auto-regressive generation process makes LLMs prone to produce errors, hallucinations and inconsistent statements when performing multi-step reasoning.
In this paper, by casting multi-step reasoning of LLMs as a heuristic search problem, we aim to alleviate the pathology by introducing Q*, a general, versatile and agile framework for guiding LLMs decoding process with deliberative planning. By learning a plug-and-play Q-value model as heuristic function for estimating expected future rewards, our Q* can effectively guide LLMs to select the most promising next reasoning step without fine-tuning LLMs for the current task, which avoids the significant computational overhead and potential risk of performance degeneration on other tasks. Extensive experiments on GSM8K, MATH and MBPP demonstrate the superiority of our method, contributing to improving the reasoning performance of existing open-source LLMs.