Neural Scaling Laws for Customer Choice Prediction

Neural scaling laws are empirical relationships between the predictive performance of neural networks and the scale of training data, model capacity, or computation. They have been observed across multiple domains, including language modeling, computer vision, and speech recognition. Yet whether comparable scaling laws hold for prediction tasks in operations remains largely unexplored. We study neural scaling laws relating predictive loss to training-data size in customer choice prediction, a central problem in operations that underlies assortment planning, pricing, and product design. In particular, we train a neural network on an Expedia hotel-search interaction dataset to predict customer bookings across a range of training-set sizes. We establish a power-law relationship between prediction loss and training-set size, and provide an explicit functional form for this relationship. We then examine how this law changes when real choice data are supplemented with synthetic choice data generated by a large language model (LLM). We show that synthetic data improve prediction when real data are scarce, but their benefits shrink as real-data scale grows and can reverse when too much synthetic data is added. We provide an explicit joint scaling law that captures how predictive loss changes with the amount of real and synthetic choice data. Together, these laws can help firms anticipate the predictive returns to additional choice data and assess when and how much synthetic data are likely to improve prediction.