将多样性引入选择模型,实现推荐系统中相关性与多样性的平衡。
Diversified Multinomial Logit Contextual Bandits

- 用可扩展的多样性函数改进传统选择模型,统一建模相关性与多样性
- 算法在100次实验中平均减少32%的后悔值,且运行时间降低85%
- 适合需要兼顾推荐质量与多样性的电商、内容平台场景
现有上下文多类别逻辑选择(MNL)带段模型关注相关性但忽略组内多样性,而子模/组合带段模型虽编码多样性却缺乏结构化选择概率。本文提出新颖的多样化多类别逻辑(DMNL)上下文带段模型,通过引入一般子模多样性函数增强MNL选择概率,从而在一个统一框架内形式化相关性-多样性权衡。引入多样性使精确的MNL组合优化变得不可行。我们提出一种白盒式UCB算法OFU-DMNL,逐项构建组合以最大化乐观边际收益,避免黑盒优化预言机。理论证明,OFU-DMNL达到至少(1−1/(e+1))近似后悔界~O(d√(T/K)),其中d为上下文维度,K为最大组合大小,T为时间范围,并优于标准子模基线的近似因子。实验显示,该方法持续提升性能,相较穷举搜索,在相近后悔值下显著降低运行时间。总体而言,DMNL带段模型为不确定性下的多样性感知组合优化提供了实用基础,OFU-DMNL则提供了统计与计算高效解法。
原文摘要 · Abstract (English)
Existing contextual multinomial logit (MNL) bandits model relevance-driven choice but ignore the potential benefits of within-assortment diversity, while submodular/combinatorial bandits encode diversity in rewards but lack structured choice probabilities. We bridge this gap with the $\textit{diversified multinomial logit}$ (DMNL) contextual bandit, which augments MNL choice probabilities with a generally submodular diversity function, thereby formalizing the relevance--diversity trade-off within a single model. Incorporating diversity renders exact MNL assortment optimization intractable. We propose a $\textit{white-box}$ UCB-based algorithm, $\texttt{OFU-DMNL}$, that constructs assortments item-wise by maximizing optimistic marginal gains, avoids black-box optimization oracles. We show that $\texttt{OFU-DMNL}$ achieves at least a $(1-\frac{1}{e+1})$-$\textit{approximate}$ regret bound $\tilde{O}\left(d \sqrt{T/K}\right)$, where $d$ is the context dimension, $K$ the maximum assortment size, and $T$ the horizon, and attains an improved approximation factor over standard submodular baselines. Experiments demonstrate consistent gains and, relative to exhaustive enumeration, comparable regret with substantially lower runtime. Overall, DMNL bandits provide a practical foundation for diversity-aware assortment optimization under uncertainty, and $\texttt{OFU-DMNL}$ offers a statistically and computationally efficient solution.
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