TacticZero: Learning to Prove Theorems from Scratch with Deep Reinforcement Learning

Minchao Wu, Michael Norrish, Christian Walder, Amir Dezfouli

Keywords: interactive theorem proving, reinforcement learning, HOL4

TL;DR: Applying deep reinforcement learning to interactive theorem proving. The framwork supports the learning of both proof search strategies and tactic prediction, without using human examples.

Abstract: We propose a novel approach to interactive theorem-proving (ITP) using deep reinforcement learning. The proposed framework is able to learn proof search strategies as well as tactic and arguments prediction in an end-to-end manner. We formulate the process of ITP as a Markov decision process (MDP) in which each state represents a set of potential derivation paths. This structure allows us to introduce a novel backtracking mechanism which enables the agent to efficiently discard (predicted) dead-end derivations and restart the derivation from promising alternatives. We implement the framework in the HOL theorem prover. Experimental results show that the framework using learned search strategies outperforms existing automated theorem provers (i.e., hammers) available in HOL when evaluated on unseen problems. We further elaborate the role of key components of the framework using ablation studies.

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