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

by   Minchao Wu, et al.

We propose a novel approach to interactive theorem-proving (ITP) using deep reinforcement learning. Unlike previous work, our framework is able to prove theorems both end-to-end and from scratch (i.e., without relying on example proofs from human experts). We formulate the process of ITP as a Markov decision process (MDP) in which each state represents a set of potential derivation paths. The agent learns to select promising derivations as well as appropriate tactics within each derivation using deep policy gradients. 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. Experimental results show that the framework provides comparable performance to that of the approaches that use human experts, and that it is also capable of proving theorems that it has never seen during training. We further elaborate the role of each component of the framework using ablation studies.



There are no comments yet.


page 1

page 2

page 3

page 4


End-to-End Learning of Proactive Handover Policy for Camera-Assisted mmWave Networks Using Deep Reinforcement Learning

For mmWave networks, this paper proposes an image-to-decision proactive ...

Effective Medical Test Suggestions Using Deep Reinforcement Learning

Effective medical test suggestions benefit both patients and physicians ...

Deep reinforcement learning for portfolio management

The objective of this paper is to verify that current cutting-edge artif...

Graph Contrastive Pre-training for Effective Theorem Reasoning

Interactive theorem proving is a challenging and tedious process, which ...

Designing Game of Theorems

"Theorem proving is similar to the game of Go. So, we can probably impro...

Learning to Prove from Synthetic Theorems

A major challenge in applying machine learning to automated theorem prov...

Calculating a backtracking algorithm: an exercise in monadic program derivation

Equational reasoning is among the most important tools that functional p...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.