  Large Language Models (LLMs) have driven substantial progress in artificial
intelligence in recent years, exhibiting impressive capabilities across a wide
range of tasks, including mathematical problem-solving. Inspired by the success
of subgoal-based methods, we propose a novel framework called
\textbf{SE}quential sub\textbf{G}oal \textbf{O}ptimization (SEGO) to enhance
LLMs' ability to solve mathematical problems. By establishing a connection
between the subgoal breakdown process and the probability of solving problems,
SEGO aims to identify better subgoals with theoretical guarantees. Addressing
the challenge of identifying suitable subgoals in a large solution space, our
framework generates problem-specific subgoals and adjusts them according to
carefully designed criteria. Incorporating these optimized subgoals into the
policy model training leads to significant improvements in problem-solving
performance. We validate SEGO's efficacy through experiments on two benchmarks,
GSM8K and MATH, where our approach outperforms existing methods, highlighting
the potential of SEGO in AI-driven mathematical problem-solving.
  Data and code associated with this paper will be available at
https://github.com/zhaoxlpku/SEGO
