A tractable online learning algorithm for the multinomial logit contextual bandit

In this paper, we consider the contextual variant of MNL-Bandit problem. More specifically, a dynamic set optimization problem, where decision-maker offers subset (assortment) products to consumer and observes response in every round. Consumers purchase maximize their utility. We assume that attributes describe products, mean utility product is linear values these attributes. model choice behavior using widely used Multinomial Logit (MNL) decision makers problem dynamically learning parameters while optimizing cumulative revenue over selling horizon T. Though has recently attracted considerable attention, many existing methods often involve solving an intractable non-convex Their theoretical performance guarantees depend on problem-dependent parameter which could be prohibitively large. particular, current algorithms for have regret bounded by O(κdT), κ constant may exponential dependency number attributes, d. propose optimistic algorithm show O(dT+κ), significantly improving methods. Further, convex relaxation step, allows tractable decision-making retaining favorable guarantee. also demonstrate our robust varying through numerical experiments.