Markov Chain Choice Model from Pairwise Comparisons

Recently, the Markov chain choice model has been introduced by Blanchet et al. to overcome the computational intractability for learning and revenue management for several modern choice models, including the mixed multinomial logit models. However, the known methods for learning the Markov models require almost all items to be offered in the learning stage, which is impractical. To address this challenge, we propose a new approach for learning the Markov chain models that only use pairwise comparisons. Thus learned Markov models provably enjoys the similar advantages of the original Markov chain choice models, such as recovering the multinomial logit model as a special case, approximation guarantees for mixed multinomial logit models, and tractable exact solutions to assortment optimization. We provide numerical simulations investigating the price we pay for the simplified learning approach, which is in the accuracy of the predicted probabilities.