Reinforcement Learning of Theorem Proving

Cezary Kaliszyk, Josef Urban, Henryk Michalewski, Mirek Olsák

Advances in Neural Information Processing Systems, 31, pp. 8836 – 8847, 2018.


We introduce a theorem proving algorithm that uses practically no domain heuristics for guiding its connection-style proof search. Instead, it runs many Monte-Carlo simulations guided by reinforcement learning from previous proof attempts. We produce several versions of the prover, parameterized by different learning and guiding algorithms. The strongest version of the system is trained on a large corpus of mathematical problems and evaluated on previously unseen problems. The trained system solves within the same number of inferences over 40% more problems than a baseline prover, which is an unusually high improvement in this hard AI domain. To our knowledge this is the first time reinforcement learning has been convincingly applied to solving general mathematical problems on a large scale.




title = {Reinforcement Learning of Theorem Proving},
author = {Kaliszyk, Cezary and Urban, Josef and Michalewski, Henryk and
Ol\v{s}\'{a}k, Miroslav},
booktitle = {Advances in Neural Information Processing Systems 31},
editor = {S. Bengio and H. Wallach and H. Larochelle and K. Grauman and
N. Cesa-Bianchi and R. Garnett},
pages = {8836--8847},
year = {2018},
publisher = {Curran Associates, Inc.},
url = {}
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