Lemma: Bootstrapping High-Level Mathematical Reasoning with Learned Symbolic Abstractions

Humans tame the complexity of mathematical reasoning by developing hierarchies of abstractions.With proper abstractions, solutions to hard problems can be expressed concisely, thus making them more likely to be found.In this paper, we propose Learning Mathematical Abstractions (LEMMA): an algorithm that implements this idea forreinforcement learning agents in mathematical domains.LEMMA augments Expert Iterationwith an abstraction step, where solutions found so far are revisitedand rewritten in terms of new higher-level actions, which thenbecome available to solve new problems.We evaluate LEMMA on two mathematicalreasoning tasks--equation solving and fraction simplification--ina step-by-step fashion.In these two domains,LEMMA improves the ability of an existing agent, bothsolving more problems and generalizing more effectively to harderproblems than those seen during training.