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Multi-Selection for Recommendation Systems

Sahasrajit Sarmasarkar, Zhihao Jiang, Ashish Goel, Aleksandra Korolova, Kamesh Munagala

TL;DR

This work tackles privacy in recommender systems by combining geographic differential privacy with a local-trust framework and a multi-selection paradigm. The server returns $k$ candidate items plus a compact local model, enabling the user to pick the best item using their true features on-device, thereby improving utility under privacy constraints. The approach employs posterior sampling over training-user feature vectors, greedy submodular maximization to select results, and a PCA-based frugal model to assist local decision-making, all evaluated on the MovieLens-25M dataset. Results show the multi-selection method yields about $97\%$ of the optimal utility under $\epsilon \approx 1$ GDP/LDP, outperforming single-result baselines and demonstrating a favorable privacy-utility tradeoff for private recommendations.

Abstract

We present the construction of a multi-selection model to answer differentially private queries in the context of recommendation systems. The server sends back multiple recommendations and a ``local model'' to the user, which the user can run locally on its device to select the item that best fits its private features. We study a setup where the server uses a deep neural network (trained on the Movielens 25M dataset as the ground truth for movie recommendation. In the multi-selection paradigm, the average recommendation utility is approximately 97\% of the optimal utility (as determined by the ground truth neural network) while maintaining a local differential privacy guarantee with $ε$ ranging around 1 with respect to feature vectors of neighboring users. This is in comparison to an average recommendation utility of 91\% in the non-multi-selection regime under the same constraints.

Multi-Selection for Recommendation Systems

TL;DR

This work tackles privacy in recommender systems by combining geographic differential privacy with a local-trust framework and a multi-selection paradigm. The server returns candidate items plus a compact local model, enabling the user to pick the best item using their true features on-device, thereby improving utility under privacy constraints. The approach employs posterior sampling over training-user feature vectors, greedy submodular maximization to select results, and a PCA-based frugal model to assist local decision-making, all evaluated on the MovieLens-25M dataset. Results show the multi-selection method yields about of the optimal utility under GDP/LDP, outperforming single-result baselines and demonstrating a favorable privacy-utility tradeoff for private recommendations.

Abstract

We present the construction of a multi-selection model to answer differentially private queries in the context of recommendation systems. The server sends back multiple recommendations and a ``local model'' to the user, which the user can run locally on its device to select the item that best fits its private features. We study a setup where the server uses a deep neural network (trained on the Movielens 25M dataset as the ground truth for movie recommendation. In the multi-selection paradigm, the average recommendation utility is approximately 97\% of the optimal utility (as determined by the ground truth neural network) while maintaining a local differential privacy guarantee with ranging around 1 with respect to feature vectors of neighboring users. This is in comparison to an average recommendation utility of 91\% in the non-multi-selection regime under the same constraints.

Paper Structure

This paper contains 36 sections, 2 theorems, 9 equations, 13 figures, 5 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Local Differential privacy (LDP)
  4. Multi-Selection
  5. Homomorphic encryption
  6. Overview of Multi-Selection Architecture
  7. Geographic Differential Privacy
  8. Architecture Details
  9. User Agent's action $\mathcal{A}$
  10. Server's action.
  11. Measuring Utility of Results
  12. Instantiating server actions
  13. Posterior Distribution
  14. Greedy Result Selection
  15. Construction of Frugal Model $\mathfrak{m}$
  16. ...and 21 more sections

Key Result

Proposition 1

Let $s: \mathcal{U} \times \mathcal{Y} \rightarrow \mathbbm{R}$ by $L$-Lipschitz in $\mathcal{U}$. Then the mechanism $Q$ with density is $\epsilon L$ geographic differentially private.

Figures (13)

  • Figure 1: Overall architecture for multi-selection.
  • Figure 2: Ratings predicted under Deep-NN model
  • Figure 3: Difference of mean ratings of neighboring users.
  • Figure 4: Duplicated preferred movies of users in a cluster
  • Figure 5: Histogram plot of diameters of 5,10 and 15 sized clusters
  • ...and 8 more figures

Theorems & Definitions (4)

  • Definition 1: adapted from 6686179koufogiannis2015optimality
  • Definition 2: adapted from koufogiannis2015optimality
  • Proposition 1: adapted from koufogiannis2015optimality
  • Theorem 1: nemhauser1978analysis