Photonic neural network implementation has been gaining considerable attention as a potentially disruptive future technology. Demonstrating learning in large-scale neural networks is essential to establish photonic machine learning substrates as viable information processing systems. Realizing photonic neural networks with numerous nonlinear nodes in a fully parallel and efficient learning hardware has been lacking so far. We demonstrate a network of up to 2025 diffractively coupled photonic nodes, forming a large-scale recurrent neural network. Using a digital micro mirror device, we realize reinforcement learning. Our scheme is fully parallel, and the passive weights maximize energy efficiency and bandwidth. The computational output efficiently converges, and we achieve very good performance.