In the context of online education, designing an automatic solver for
geometric problems has been considered a crucial step towards general math
Artificial Intelligence (AI), empowered by natural language understanding and
traditional logical inference. In most instances, problems are addressed by
adding auxiliary components such as lines or points. However, adding auxiliary
components automatically is challenging due to the complexity in selecting
suitable auxiliary components especially when pivotal decisions have to be
made. The state-of-the-art performance has been achieved by exhausting all
possible strategies from the category library to identify the one with the
maximum likelihood. However, an extensive strategy search have to be applied to
trade accuracy for ef-ficiency. To add auxiliary components automatically and
efficiently, we present deep reinforcement learning framework based on the
language model, such as BERT. We firstly apply the graph attention mechanism to
reduce the strategy searching space, called AttnStrategy, which only focus on
the conclusion-related components. Meanwhile, a novel algorithm, named
Automatically Adding Auxiliary Components using Reinforcement Learning
framework (A3C-RL), is proposed by forcing an agent to select top strategies,
which incorporates the AttnStrategy and BERT as the memory components. Results
from extensive experiments show that the proposed A3C-RL algorithm can
substantially enhance the average precision by 32.7% compared to the
traditional MCTS. In addition, the A3C-RL algorithm outperforms humans on the
geometric questions from the annual University Entrance Mathematical
Examination of China.

在在线教育领域，设计一个几何问题的自动求解器被认为是通往普适数学人工智能的关键一步。本研究提出了一种基于深度强化学习框架的图形注意力机制和 BERT 等语言模型的算法 A3C-RL，通过在特定空间中选择最佳策略，显著提高了准确性和效率，并在中国高考几何问题上超越了人类的表现。