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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2604.09964 |
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| _version_ | 1866911584828260352 |
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| author | Nguyen, James |
| author_facet | Nguyen, James |
| contents | We present a family of Kaczmarz-based preference learning algorithms for real-time personalized matchmaking in reciprocal recommender systems. Post-step L2 normalization, common in Kaczmarz-inspired online learners, induces exponential recency bias: the influence of the t-th interaction decays as eta^(n - t), reaching approximately 1e-6 after just 20 swipes at eta = 0.5. We resolve this by replacing the normalization step with a Tikhonov-regularized projection denominator that bounds step size analytically without erasing interaction history. When candidate tag vectors are not pre-normalized, as in realistic deployments where candidates vary in tag density, the Tikhonov denominator ||a||^2 + alpha produces genuinely per-candidate adaptive step sizes, making it structurally distinct from online gradient descent with any fixed learning rate. We further derive a block variant that processes full swipe sessions as a single Gram matrix solve. Population-scale simulation over 6,400 swipes reveals that Block Normalized Kaczmarz (BlockNK), which combines the batch Gram solve with post-session L2 normalization, achieves the highest preference alignment (Align@20 = 0.698), the strongest inter-session direction stability (delta = 0.994), and the flattest degradation profile under label noise across flip ratios p_flip in [0.10, 0.35]. Experiments under cosine similarity subsampling further show that adaptively filtering the candidate pool toward the current preference direction substantially improves asymptotic alignment, at the cost of introducing a feedback loop that may slow recovery from miscalibration. The sequential Tikhonov-Kaczmarz method performs comparably to K-NoNorm under our simulation conditions, suggesting the dominant practical gain over normalized Kaczmarz is the removal of per-step normalization rather than the Tikhonov constant alpha itself. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_09964 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | From Recency Bias to Stable Convergence Block Kaczmarz Methods for Online Preference Learning in Matchmaking Applications Nguyen, James Machine Learning We present a family of Kaczmarz-based preference learning algorithms for real-time personalized matchmaking in reciprocal recommender systems. Post-step L2 normalization, common in Kaczmarz-inspired online learners, induces exponential recency bias: the influence of the t-th interaction decays as eta^(n - t), reaching approximately 1e-6 after just 20 swipes at eta = 0.5. We resolve this by replacing the normalization step with a Tikhonov-regularized projection denominator that bounds step size analytically without erasing interaction history. When candidate tag vectors are not pre-normalized, as in realistic deployments where candidates vary in tag density, the Tikhonov denominator ||a||^2 + alpha produces genuinely per-candidate adaptive step sizes, making it structurally distinct from online gradient descent with any fixed learning rate. We further derive a block variant that processes full swipe sessions as a single Gram matrix solve. Population-scale simulation over 6,400 swipes reveals that Block Normalized Kaczmarz (BlockNK), which combines the batch Gram solve with post-session L2 normalization, achieves the highest preference alignment (Align@20 = 0.698), the strongest inter-session direction stability (delta = 0.994), and the flattest degradation profile under label noise across flip ratios p_flip in [0.10, 0.35]. Experiments under cosine similarity subsampling further show that adaptively filtering the candidate pool toward the current preference direction substantially improves asymptotic alignment, at the cost of introducing a feedback loop that may slow recovery from miscalibration. The sequential Tikhonov-Kaczmarz method performs comparably to K-NoNorm under our simulation conditions, suggesting the dominant practical gain over normalized Kaczmarz is the removal of per-step normalization rather than the Tikhonov constant alpha itself. |
| title | From Recency Bias to Stable Convergence Block Kaczmarz Methods for Online Preference Learning in Matchmaking Applications |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2604.09964 |