PASTA: Pessimistic Assortment Optimization

TL;DR

This paper introduces PASTA, a pessimistic offline learning algorithm for assortment optimization that effectively identifies optimal assortments from historical data, even with limited coverage, under the multinomial logit model.

Contribution

The paper presents PASTA, a novel offline assortment optimization algorithm based on pessimism, with theoretical guarantees and practical efficiency under general settings.

Findings

PASTA correctly identifies optimal assortments with limited data coverage.

The algorithm achieves a provable regret bound under the multinomial logit model.

Numerical results show PASTA outperforms existing baseline methods.

Abstract

We consider a class of assortment optimization problems in an offline data-driven setting. A firm does not know the underlying customer choice model but has access to an offline dataset consisting of the historically offered assortment set, customer choice, and revenue. The objective is to use the offline dataset to find an optimal assortment. Due to the combinatorial nature of assortment optimization, the problem of insufficient data coverage is likely to occur in the offline dataset. Therefore, designing a provably efficient offline learning algorithm becomes a significant challenge. To this end, we propose an algorithm referred to as Pessimistic ASsortment opTimizAtion (PASTA for short) designed based on the principle of pessimism, that can correctly identify the optimal assortment by only requiring the offline data to cover the optimal assortment under general settings. In particular, we establish a regret bound for the offline assortment optimization problem under the celebrated multinomial logit model. We also propose an efficient computational procedure to solve our pessimistic assortment optimization problem. Numerical studies demonstrate the superiority of the proposed method over the existing baseline method.