  In this work we study how to learn good algorithms for selecting reasoning
steps in theorem proving. We explore this in the connection tableau calculus
implemented by leanCoP where the partial tableau provides a clean and compact
notion of a state to which a limited number of inferences can be applied. We
start by incorporating a state-of-the-art learning algorithm -- a graph neural
network (GNN) -- into the plCoP theorem prover. Then we use it to observe the
system's behaviour in a reinforcement learning setting, i.e., when learning
inference guidance from successful Monte-Carlo tree searches on many problems.
Despite its better pattern matching capability, the GNN initially performs
worse than a simpler previously used learning algorithm. We observe that the
simpler algorithm is less confident, i.e., its recommendations have higher
entropy. This leads us to explore how the entropy of the inference selection
implemented via the neural network influences the proof search. This is related
to research in human decision-making under uncertainty, and in particular the
probability matching theory. Our main result shows that a proper entropy
regularisation, i.e., training the GNN not to be overconfident, greatly
improves plCoP's performance on a large mathematical corpus.
