# Dynamic Assortment Personalization in High Dimensions

arXiv: https://arxiv.org/abs/1610.05604 · HTML: https://mlsanity.com/paper/1610.05604/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Oct 2016.

## Built on by (most cited first, 14 of 14)

- [Post-Contextual-Bandit Inference](https://mlsanity.com/paper/2106.00418/) (2021)
- [Transfer Learning for Contextual Multi-armed Bandits](https://mlsanity.com/paper/2211.12612/) (2022)
- [Policy Learning with Adaptively Collected Data](https://mlsanity.com/paper/2105.02344/) (2021)
- [Risk Minimization from Adaptively Collected Data: Guarantees for Supervised and Policy Learning](https://mlsanity.com/paper/2106.01723/) (2021)
- [Doubly High-Dimensional Contextual Bandits: An Interpretable Model for Joint Assortment-Pricing](https://mlsanity.com/paper/2309.08634/) (2023)
- [Distributionally Robust Policy Learning under Concept Drifts](https://mlsanity.com/paper/2412.14297/) (2024)
- [Speed Up the Cold-Start Learning in Two-Sided Bandits with Many Arms](https://mlsanity.com/paper/2210.00340/) (2022)
- [Low-Rank Online Dynamic Assortment with Dual Contextual Information](https://mlsanity.com/paper/2404.17592/) (2024)
- [PASTA: A Unified Framework for Offline Assortment Learning](https://mlsanity.com/paper/2510.01693/) (2025)
- [The Sign Estimator: LLM Alignment in the Face of Choice Heterogeneity](https://mlsanity.com/paper/2510.23965/) (2025)
- [Demistifying Inference after Adaptive Experiments](https://mlsanity.com/paper/2405.01281/) (2024)
- [MNL-Bandits under Inventory and Limited Switches Constraints](https://mlsanity.com/paper/2204.10787/) (2022)
- [Minimax-optimal trust-aware multi-armed bandits](https://mlsanity.com/paper/2410.03651/) (2024)
- [Scalable Multi-Task Inverse Reinforcement Learning](https://mlsanity.com/paper/2610.00758/) (2026)

## Abstract (arXiv)

We study the problem of dynamic assortment personalization with large, heterogeneous populations and wide arrays of products, and demonstrate the importance of structural priors for effective, efficient large-scale personalization. Assortment personalization is the problem of choosing, for each individual (type), a best assortment of products, ads, or other offerings (items) so as to maximize revenue. This problem is central to revenue management in e-commerce and online advertising where both items and types can number in the millions. We formulate the dynamic assortment personalization problem as a discrete-contextual bandit with m contexts (types) and exponentially many arms (assortments of the n items). We assume that each type's preferences follow a simple parametric model with n parameters. In all, there are mn parameters, and existing literature suggests that order optimal regret scales as mn. However, the data required to estimate so many parameters is orders of magnitude larger than the data available in most revenue management applications; and the optimal regret under these models is unacceptably high. In this paper, we impose a natural structure on the problem -- a small latent dimension, or low rank. In the static setting, we show that this model can be efficiently learned from surprisingly few interactions, using a time- and memory-efficient optimization algorithm that converges globally whenever the model is learnable. In the dynamic setting, we show that structure-aware dynamic assortment personalization can have regret that is an order of magnitude smaller than structure-ignorant approaches. We validate our theoretical results empirically.