Rewrite systems [6, 10, 12] have been widely employing equality saturation [9], which is an optimisation methodology that uses a saturated e-graph to represent all possible sequences of rewrite simultaneously, and then extracts the optimal one. As such, optimal results can be achieved by avoiding the phase-ordering problem. However, we observe that when the e-graph is not saturated, it cannot represent all possible rewrite opportunities and therefore the phase-ordering problem is re-introduced during the construction phase of the e-graph. To address this problem, we propose MCTS-GEB, a domain-general rewrite system that applies reinforcement learning (RL) to e-graph construction. At its core, MCTS-GEB uses a Monte Carlo Tree Search (MCTS) [3] to efficiently plan for the optimal e-graph construction, and therefore it can effectively eliminate the phase-ordering problem at the construction phase and achieve better performance within a reasonable time. Evaluation in two different domains shows MCTS-GEB can outperform the state-of-the-art rewrite systems by up to 49x, while the optimisation can generally take less than an hour, indicating MCTS-GEB is a promising building block for the future generation of rewrite systems.

翻译：重写系统[6,10,12]已广泛采用等式饱和[9]技术，这是一种通过饱和等价图同时表示所有可能重写序列，再从中提取最优解的优化方法。通过规避相位排序问题，该方法可获得最优结果。然而，我们观察到当等价图未饱和时，其无法表示所有可能的优化机会，因此等价图构建阶段会重新引入相位排序问题。针对该问题，我们提出MCTS-GEB——一种将强化学习(RL)应用于等价图构建的通用重写系统。MCTS-GEB的核心采用蒙特卡洛树搜索(MCTS)[3]高效规划最优等价图构建策略，从而在构建阶段有效消除相位排序问题，并在合理时间内实现更优性能。在两个不同领域的评估中，MCTS-GEB的性能可比现有最优重写系统提升最高49倍，且优化过程通常在一小时内完成，这表明MCTS-GEB有望成为新一代重写系统的基础构建模块。