Department of Industrial Engineering & Decision Analytics [Joint IEDA/ISOM seminar] - Neural-Network Mixed Logit Choice Model: Statistical and Optimality Guarantees

The mixed logit model, widely used in operations, marketing, and econometrics, represents choice probabilities as mixtures of multinomial logits. This study explores the effectiveness of representing the mixed logit model using a single-hidden-layer neural network, which approximates the mixture distribution as an equally weighted distribution on finite consumer types. From the statistical perspective, we show that the approximation error of the neural network does not suffer from the curse of dimensionality, and that over-parameterization does not lead to overfitting. From the optimization perspective, we prove that the noisy gradient descent algorithm can find the global optimizer of the non-convex parameter learning problem up to an error. Experiments on synthetic and real datasets validate the algorithm’s superior in-sample and out-of-sample performance. These findings underscore the potential of even shallow neural network representations, coupled with over-parameterization and efficient training algorithms, to effectively learn complex choice models with strong statistical and optimality guarantees.