  Query rewrite systems perform graph substitutions using rewrite rules to
generate optimal SQL query plans. Rewriting logical and physical relational
query plans is proven to be an NP-hard sequential decision-making problem with
a search space exponential in the number of rewrite rules. In this paper, we
address the query rewrite problem by interleaving Equality Saturation and Graph
Reinforcement Learning (RL). The proposed system, Aurora, rewrites relational
queries by guiding Equality Saturation, a method from compiler literature to
perform non-destructive graph rewriting, with a novel RL agent that embeds both
the spatial structure of the query graph as well as the temporal dimension
associated with the sequential construction of query plans. Our results show
Graph Reinforcement Learning for non-destructive graph rewriting yields SQL
plans orders of magnitude faster than existing equality saturation solvers,
while also achieving competitive results against mainstream query optimisers.
