  Using a model heat engine, we show that neural network-based reinforcement
learning can identify thermodynamic trajectories of maximal efficiency. We
consider both gradient and gradient-free reinforcement learning. We use an
evolutionary learning algorithm to evolve a population of neural networks,
subject to a directive to maximize the efficiency of a trajectory composed of a
set of elementary thermodynamic processes; the resulting networks learn to
carry out the maximally-efficient Carnot, Stirling, or Otto cycles. When given
an additional irreversible process, this evolutionary scheme learns a
previously unknown thermodynamic cycle. Gradient-based reinforcement learning
is able to learn the Stirling cycle, whereas an evolutionary approach achieves
the optimal Carnot cycle. Our results show how the reinforcement learning
strategies developed for game playing can be applied to solve physical problems
conditioned upon path-extensive order parameters.
