Assortment Planning with Sponsored Products

Assortment optimization is a fundamental problem in revenue management, typically addressed using parametric choice models such as the multinomial logit (MNL) and its variants. While these models enable tractable formulations, their performance is sensitive to model misspecification and often struggles to capture complex customer behavior. In this paper, we propose a model-agnostic framework for assortment optimization based on guided discrete diffusion. We represent assortments as binary vectors and perform stochastic search via a learned reverse diffusion process, avoiding explicit combinatorial enumeration. To incorporate decision objectives, we introduce a reward-guided mechanism that biases local transitions using estimates of expected revenue. This allows the method to effectively balance exploration and exploitation during generation. Empirically, we show that the proposed approach consistently identifies high-quality assortments and remains robust under model misspecification, often recovering near-optimal solutions in high-dimensional settings. Moreover, the generative nature of diffusion enables the production of diverse high-performing assortments, offering flexibility beyond a single deterministic solution. These results highlight the potential of generative modeling as a scalable and robust paradigm for combinatorial optimization in data-driven decision-making.

We study online learning for new products on a platform that makes capacity-constrained assortment decisions on which products to offer. For a newly listed product, its quality is initially unknown, and quality information propagates through social learning: when a customer purchases a new product and leaves a review, its quality is revealed to both the platform and future customers. Since reviews require purchases, the platform must feature new products in the assortment ("explore") to generate reviews to learn about new products. Such exploration is costly because customer demand for new products is lower than for incumbent products. We characterize the optimal assortments for exploration to minimize regret, addressing two questions. (1) Should the platform offer a new product alone or alongside incumbent products? The former maximizes the purchase probability of the new product but yields lower short-term revenue. Despite the lower purchase probability, we show it is always optimal to pair the new product with the top incumbent products. (2) With multiple new products, should the platform explore them simultaneously or one at a time? We show that the optimal number of new products to explore simultaneously has a simple threshold structure: it increases with the "potential" of the new products and, surprisingly, does not depend on their individual purchase probabilities. We also show that two canonical bandit algorithms, UCB and Thompson Sampling, both fail in this setting for opposite reasons: UCB over-explores while Thompson Sampling under-explores. Our results provide structural insights on how platforms should learn about new products through assortment decisions.

We study a dynamic assortment problem on a two-sided service platform with incomplete information and heterogeneous customers in a discrete-time setting. In each period, a customer arrives seeking service, and the platform chooses an assortment of sellers to display. The customer then proposes a transaction to at most one seller in the assortment according to a multinomial logit choice model. After a fixed number of periods, sellers review the proposals they have received and each chooses at most one customer according to another multinomial logit choice model, after which the cycle repeats. A key challenge is that the platform does not know the choice-model parameters of either customers or sellers in advance. To our knowledge, this is the first study of a dynamic assortment problem in which both sides' choice parameters are unknown. We develop a data-driven algorithm that learns these parameters while optimizing the platform's objective over time. We evaluate performance using regret, which measures revenue loss relative to a clairvoyant benchmark that knows all parameters and customer arrivals in advance. We show that the algorithm's worst-case regret grows polylogarithmically over time, and we derive a matching lower bound, establishing its rate optimality.