Representation-Space Transition Kernels for Markov Chain Choice Models at Catalog Scale

A retailer deciding which products to offer must consider substitution and co-purchase effects simultaneously. These effects are typically modeled using a parameter for each ordered pair of products. In addition, since assortments change slowly, each category may offer only a few distinct assortments. Therefore, at catalog scale, there are far fewer observations than parameters. As a result, the model is not identifiable. We parameterize the transition kernels of a $K$-stage Markov chain choice model using frozen pretrained image and text encoders, reducing the number of transition parameters from $O(n^2)$ to $O(p^2)$ where $p \ll n$. In addition, we develop a two-level model whose likelihood decomposes across categories and whose constrained assortment problem reduces to one value curve per category plus an allocation across them. We show that the two-level full problem inherits the per-category approximation ratio. On 72,969 articles across 132 categories of a fashion retailer, our experiments show that a model that used the proposed parametrization is able to generalize to unseen data while an item-indexed model cannot. Moreover, holding shelf space fixed, the optimized assortments have 74,4% higher predicted revenue than the assortments the retailer actually realized.