解决匹配推荐中因历史数据衰减导致的偏好学习偏差问题。
From Recency Bias to Stable Convergence Block Kaczmarz Methods for Online Preference Learning in Matchmaking Applications
- 用正则化投影替代归一化，避免交互历史被指数级遗忘。
- 块版本算法在6400次滑动中实现0.698的偏好对齐度，稳定性达0.994。
- 自适应筛选候选集可提升长期对齐效果，但可能延缓校准恢复。
我们提出一类基于Kaczmarz的偏好学习算法，用于实时个性化匹配推荐。传统在线学习中的后步L2归一化会引发指数级近期偏差：第t次交互的影响随eta^(n-t)衰减，在eta=0.5时仅20次滑动后即降至约1e-6。为此，我们改用Tikhonov正则化投影分母，实现解析上界步长且不丢失历史。当候选标签向量未预归一化时（真实场景中候选标签密度各异），该分母||a||^2 + alpha产生真正与候选相关的自适应步长，结构上区别于固定学习率的在线梯度下降。进一步提出块变体，将整轮滑动会话作为单一格拉姆矩阵求解。大规模模拟显示，结合批次格拉姆求解与会话后归一化的块标准化Kaczmarz（BlockNK）在6400次滑动下达到最高偏好对齐（Align@20 = 0.698）、最强会话间方向稳定性（delta = 0.994），并在标签噪声翻转率p_flip ∈ [0.10, 0.35]下表现最稳健。在余弦相似度子采样下，自适应过滤候选池以靠近当前偏好方向能显著提升渐进对齐效果，代价是引入反馈环，可能延迟从误校准中恢复。序列Tikhonov-Kaczmarz在模拟条件下性能接近K-NoNorm，表明相比归一化Kaczmarz的主要优势在于移除每步归一化而非Tikhonov常数alpha本身。
原文摘要 · Abstract (English)
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.
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