Borrowing Strength Across Stores: Transfer Learning for Choice-Based Revenue Management
Authors: Recep Yusuf Bekci, Stefanus Jasin, Joline Uichanco
Organizations: Department of Management Science and Engineering, University of Waterloo, Waterloo, Ontario, Canada · Stephen M. Ross School of Business, University of Michigan, Ann Arbor, Michigan, USA · Department of Technology Management and Innovation, Tandon School of Engineering, New York University, Brooklyn, New York, USA
Large retail chains must tailor assortment and pricing decisions to local customer preferences, yet even retailers with extensive sales records often have limited data for estimating demand at the store or local market level, particularly in product categories with short selling windows. Local estimation (fitting a demand model for each store on its own) can therefore be unreliable, while pooling data across stores improves estimation precision at the cost of ignoring local demand heterogeneity. We study how retailers can balance these competing effects through transfer learning under a multinomial logit (MNL) demand model. We propose a shrinkage estimator that combines store-specific demand estimates with information pooled from other stores. Unlike the linear or quadratic settings underlying much of the existing theoretical literature on information transfer in operations, the nonlinear MNL likelihood does not admit a straightforward bias-variance decomposition. By exploiting its self-concordant-like properties, we establish finite-sample performance guarantees that characterize when information transfer improves demand estimation and how the appropriate degree of shrinkage depends on local sample size, feature dimensionality, and cross-store heterogeneity. We further derive regret bounds for downstream assortment and pricing decisions. Numerical experiments demonstrate the operational benefits of shrinkage across different data environments. An empirical study using data from several hundred stores of a European apparel retailer shows that shrinkage improves out-of-sample product prioritization and revenue capture relative to both local estimation and full pooling. Our findings demonstrate how retailers can leverage information across their store networks to improve revenue management decisions while preserving local demand differences.
Figures & tables
Figure 1: Reduction in expected excess risk that Theorem 5.5 guarantees for shrinkage relative to local estimation, over cross-store heterogeneity Δ and the local sample ratio nk/d . Blue marks where shrinkage is guaranteed to improve on local estimation, and red where the bound gives no such guarantee.
Figure 2: Percentage Regret for assortment (left) and pricing (right) decisions as cross-store heterogeneity Δ varies.
Figure 3: Percentage regret for assortment (left) and pricing (right) decisions as the local sample size nk varies.
Category
# Stores
# Products
Total Observations
Total Units Sold
Blazers
365
790
622,642
173,471
Dresses
371
4,182
1,669,206
781,011
Leggings
361
255
193,958
79,181
Trousers
372
3,394
1,552,620
614,147
T-shirts
375
3,984
2,783,502
1,894,169
Table 1: Dataset dimensions by product category.
Category
Avg. # products per store
Avg. assortment size per store-week
Avg. units sold per store-week
Blazers
178.7
9.7
4.7
Dresses
493.9
39.2
24.9
Leggings
48.8
5.5
3.8
Trousers
447.5
31.4
18.6
T-shirts
754.5
101.9
69.6
Table 2: Average store- and store-week-level scale by category.
Figure 4: Out-of-sample revenue capture across the five apparel categories, evaluated at a m=20% budget constraint. Store-level predictive performance is disaggregated by historical sales volume into Lower Volume stores (left), Medium Volume stores (center), and Higher Volume stores (right). Error bars represent standard errors.
Δstore vs. Store MLE
Δpool vs. Pooled MLE
Group
Mean lift (pp)
95% CI
Win rate
Mean lift (pp)
95% CI
Win rate
Overall
2.64
[2.17, 3.10]
86.6%
3.11
[2.55, 3.68]
83.6%
Category: Blazers
1.59
[-0.04, 3.20]
91.0%
4.21
[2.85, 5.58]
93.2%
Category: Dresses
1.44
[1.00, 1.95]
85.4%
3.13
[1.98, 4.23]
80.7%
Category: Leggings
7.53
[5.69, 9.66]
93.9%
4.15
[2.46, 5.81]
94.3%
Category: Trousers
2.48
[1.66, 3.27]
85.3%
2.41
[1.37, 3.39]
82.2%
Table 3: Mean lift from Shrinkage CV at m=20% . Lifts are reported in percentage points. Confidence intervals are clustered-bootstrap intervals resampling stores, and win rates report the fraction of store-weeks in which Shrinkage CV outperforms the corresponding benchmark.
Figure 5: Revenue capture by product category and local-information tercile at display budget m=10% .
Figure 6: Revenue capture by product category and local-information tercile at display budget m=30% .
Figure 7: Validation-selected shrinkage weights by category and local-information bucket.
Figure 8: Sensitivity of assortment (left) and pricing (right) regret to the number of nonprice features d−2 . In this sweep, nonprice features are rescaled by 1/d−2 so that the variance of the linear predictor remains approximately constant as dimension grows. The heterogeneity radius Δ is held fixed, so increasing d spreads a fixed amount of cross-store mismatch over more coordinates.
Item demand forecasting is an integral component of store assortment optimization. Existing literature focuses on learning a suitable customer choice model and using this model to determine the value of an objective function (i.e. expected demand) with respect to an assortment proposal. However, for large item universe with many categories, this approach can prove inefficient, needing a separate demand forecast for every possible item assortment. An alternate approach exists whereby we combine the efficiency of forecasting item demand independently, while at the same time applying adjustments to the independent forecasts that account for the relations between item demand and the availability of other similar items on the shelf. Central to this approach is the estimation of Demand Transfer (DT) coefficients. These DT coefficients represent the percent of a particular target item's (item that the customer walked in the store to buy) demand that is redirected to each other item in the universe should the target item be removed from the shelf. We introduce an approach that allows us to compute these DT coefficients on large item universes (assortments having 1 million+ items). Experiments on data as well as historical transaction data for multiple locations within categories demonstrate that when certain reasonable assumptions about substitution behavior are satisfied, our procedure is able to accurately estimate underlying DT coefficients and lead to improvements in demand forecasting.
Lakshya Garg, Deep Narayan Mishra, Swapnil Yadav +4
We study transfer learning for contextual joint assortment-pricing under a multinomial logit choice model with bandit feedback. A seller operates across multiple related markets and observes only posted prices and realized purchases. While data from source markets can accelerate learning in a target market, cross-market differences in customer preferences may introduce systematic bias if pooled indiscriminately. We model heterogeneity through a structured utility shift, where markets share a common contextual utility structure but differ along a sparse set of latent preference coordinates. Building on this, we develop Transfer Joint Assortment-Pricing (TJAP), a bias-aware framework that combines aggregate-then-debias estimation with a UCB-style policy. TJAP constructs two-radius confidence bounds that separately capture statistical uncertainty and transfer-induced bias, uniformly over continuous prices. We establish matching minimax regret bounds of order O~(d1+HT+s0T),revealing a transparent variance-bias tradeoff: transfer accelerates learning along shared preference directions, while heterogeneous components impose an irreducible adaptation cost. Numerical experiments corroborate the theory, showing that TJAP outperforms both target-only learning and naive pooling while remaining robust to cross-market differences.
Elynn Chen, Xi Chen, Yi Zhang
New York University, Stern School of Business · Tsinghua University, School of Economics and Management
Problem definition: This paper studies the problem of estimating consumer preferences from bundle sales data. Product bundling is a widely used pricing strategy in retail markets. To set profitable bundle selection and prices, the seller needs to learn the distribution of consumers' valuations for individual products from the transaction data. When customers purchase bundles or multiple products, classical methods such as discrete choice models cannot be used to estimate consumers' valuations. In this paper, we propose an approach to learn the distribution of consumers' valuations toward the products using bundle sales data. Methodology/results: Our approach is to define a utility model for customer choices and estimate the parameters of a valuation distribution that maximizes the likelihood of observing the transaction data. Our approach reduces this problem to an estimation problem where the samples are censored by polyhedral regions on the valuation space of customers. Using the EM algorithm and Monte Carlo simulation, our approach can recover the distribution of consumers' valuations. We extend the framework to allow for unobserved no-purchases, clustered market segments and to incorporate non-additive bundle utilities with synergy effects. In addition, we provide theoretical results on the identifiability of the probability model and sufficient conditions for local convergence of the EM algorithm. Moreover, the performance of the approach is also demonstrated numerically with synthetic and real datasets. Managerial implications: This study demonstrates the challenge to leverage the transaction data of bundle sales to learn customers' preferences. The proposed algorithm provides a practical guidance for retailers.
Ningyuan Chen, Setareh Farajollahzadeh, Qingwei Jin +2
University of Toronto · McGill University · Zhejiang University