Predicting and understanding how people make decisions has been a long-standing goal in many fields, with quantitative models of human decision-making informing research in both the social sciences and engineering. We show how progress toward this goal can be accelerated by using large datasets to power machine-learning algorithms that are constrained to produce interpretable psychological theories. Conducting the largest experiment on risky choice to date and analyzing the results using gradient-based optimization of differentiable decision theories implemented through artificial neural networks, we were able to recapitulate historical discoveries, establish that there is room to improve on existing theories, and discover a new, more accurate model of human decision-making in a form that preserves the insights from centuries of research.