Low-Rank Online Dynamic Assortment with Dual Contextual Information

As e-commerce expands, delivering real-time personalized recommendations from vast catalogs poses a critical challenge for retail platforms. Maximizing revenue requires careful consideration of both individual customer characteristics and available item features to optimize assortments over time. In this paper, we consider the dynamic assortment problem with dual contexts -- user and item features. In high-dimensional scenarios, the quadratic growth of dimensions complicates computation and estimation. To tackle this challenge, we introduce a new low-rank dynamic assortment model to transform this problem into a manageable scale. Then we propose an efficient algorithm that estimates the intrinsic subspaces and utilizes the upper confidence bound approach to address the exploration-exploitation trade-off in online decision making. Theoretically, we establish a regret bound of $\tilde{O}((d_1+d_2)r\sqrt{T})$, where $d_1, d_2$ represent the dimensions of the user and item features respectively, $r$ is the rank of the parameter matrix, and $T$ denotes the time horizon. This bound represents a substantial improvement over prior literature, made possible by leveraging the low-rank structure. Extensive simulations and an application to the Expedia hotel recommendation dataset further demonstrate the advantages of our proposed method.

RTB Formulation Using Point Process

We propose a general stochastic framework for modelling repeated auctions in the Real Time Bidding (RTB) ecosystem using point processes. The flexibility of the framework allows a variety of auction scenarios including configuration of information provided to player, determination of auction winner and quantification of utility gained from each auctions. We propose theoretical results on how this formulation of process can be approximated to a Poisson point process, which enables the analyzer to take advantage of well-established properties. Under this framework, we specify the player's optimal strategy under various scenarios. We also emphasize that it is critical to consider the joint distribution of utility and market condition instead of estimating the marginal distributions independently.

Addressing Distribution Shift in RTB Markets via Exponential Tilting

Distribution shift in machine learning models can be a primary cause of performance degradation. This paper delves into the characteristics of these shifts, primarily motivated by Real-Time Bidding (RTB) market models. We emphasize the challenges posed by class imbalance and sample selection bias, both potent instigators of distribution shifts. This paper introduces the Exponential Tilt Reweighting Alignment (ExTRA) algorithm, as proposed by Marty et al. (2023), to address distribution shifts in data. The ExTRA method is designed to determine the importance weights on the source data, aiming to minimize the KL divergence between the weighted source and target datasets. A notable advantage of this method is its ability to operate using labeled source data and unlabeled target data. Through simulated real-world data, we investigate the nature of distribution shift and evaluate the applicacy of the proposed model.