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Safe Collaborative Filtering

Riku Togashi, Tatsushi Oka, Naoto Ohsaka, Tetsuro Morimura

TL;DR

This work addresses tail-risk in collaborative filtering by optimizing a CVaR objective over user losses, focusing on under-served users rather than the average. It introduces SAFER2, a smoothing-based MF algorithm that recasts CVaR optimization into a block-separable, parallelizable form using convolution-type smoothing, primal-dual splitting, and a re-weighted ALS update scheme. The approach achieves excellent tail performance with competitive or superior average performance and runtime compared to strong baselines such as iALS and CVaR-MF, demonstrated on large real-world datasets. Practically, SAFER2 provides a scalable path to safer recommender systems that protect the experience of low-satisfaction users while preserving overall efficiency, with publicly available code to foster adoption.

Abstract

Excellent tail performance is crucial for modern machine learning tasks, such as algorithmic fairness, class imbalance, and risk-sensitive decision making, as it ensures the effective handling of challenging samples within a dataset. Tail performance is also a vital determinant of success for personalized recommender systems to reduce the risk of losing users with low satisfaction. This study introduces a "safe" collaborative filtering method that prioritizes recommendation quality for less-satisfied users rather than focusing on the average performance. Our approach minimizes the conditional value at risk (CVaR), which represents the average risk over the tails of users' loss. To overcome computational challenges for web-scale recommender systems, we develop a robust yet practical algorithm that extends the most scalable method, implicit alternating least squares (iALS). Empirical evaluation on real-world datasets demonstrates the excellent tail performance of our approach while maintaining competitive computational efficiency.

Safe Collaborative Filtering

TL;DR

This work addresses tail-risk in collaborative filtering by optimizing a CVaR objective over user losses, focusing on under-served users rather than the average. It introduces SAFER2, a smoothing-based MF algorithm that recasts CVaR optimization into a block-separable, parallelizable form using convolution-type smoothing, primal-dual splitting, and a re-weighted ALS update scheme. The approach achieves excellent tail performance with competitive or superior average performance and runtime compared to strong baselines such as iALS and CVaR-MF, demonstrated on large real-world datasets. Practically, SAFER2 provides a scalable path to safer recommender systems that protect the experience of low-satisfaction users while preserving overall efficiency, with publicly available code to foster adoption.

Abstract

Excellent tail performance is crucial for modern machine learning tasks, such as algorithmic fairness, class imbalance, and risk-sensitive decision making, as it ensures the effective handling of challenging samples within a dataset. Tail performance is also a vital determinant of success for personalized recommender systems to reduce the risk of losing users with low satisfaction. This study introduces a "safe" collaborative filtering method that prioritizes recommendation quality for less-satisfied users rather than focusing on the average performance. Our approach minimizes the conditional value at risk (CVaR), which represents the average risk over the tails of users' loss. To overcome computational challenges for web-scale recommender systems, we develop a robust yet practical algorithm that extends the most scalable method, implicit alternating least squares (iALS). Empirical evaluation on real-world datasets demonstrates the excellent tail performance of our approach while maintaining competitive computational efficiency.
Paper Structure (72 sections, 2 theorems, 79 equations, 10 figures, 3 tables, 4 algorithms)

This paper contains 72 sections, 2 theorems, 79 equations, 10 figures, 3 tables, 4 algorithms.

Table of Contents

  1. Introduction
  2. Setting and Challenge
  3. Pairwise ranking optimization.
  4. Convex and separable upper bound.
  5. Conditional value at risk (CVaR).
  6. CVaR-MF.
  7. SAFER2: Smoothing Approach for Efficient Risk-averse Recommender
  8. Convolution-type smoothing for CVaR
  9. Convolution-type smoothed quantile estimation
  10. Efficient loss computation.
  11. Stochastic optimization for many users.
  12. Primal-dual splitting for parallel computation
  13. Dual-free optimization.
  14. Re-weighted alternating least squares.
  15. Tikhonov regularization.
  16. ...and 57 more sections

Key Result

Proposition C.0

If the kernel function $k_h$ is symmetric, the subproblem of $\xi$ is equivalent to the following, where $\rho_{1-\alpha}(u)=(1-\alpha - \ind{u < 0})u$.

Figures (10)

  • Figure 1: Illustration of CVaR
  • Figure 2: Convolution-type smoothing.
  • Figure 3: Relative performance of each method over iALS for each quantile level.
  • Figure 4: Distributions of relative performances of SAFER2 over ERM-MF and iALS on ML-1M.
  • Figure 5: Ranking quality vs. training epochs/wall time on ML-20M (top) and MSD (bottom).
  • ...and 5 more figures

Theorems & Definitions (5)

  • Proposition C.0
  • proof
  • proof
  • Proposition E.0
  • proof