隐私保护下的核上下文老虎机，新算法误差更优且对隐私参数依赖更小。
Differentially Private Kernelized Contextual Bandits
- 设计新型低敏感度奖励估计器，兼顾高效学习与强隐私保护。
- 理论证明误差为 $\mathcal{O}\left(\sqrt{\frac{γ_T}{T}} + \frac{γ_T}{T \varepsilon}\right)$，优于现有方法。
- 适合关注隐私强化机器学习的科研人员与工程师参考。
我们研究具有随机上下文的核上下文老虎机问题，其中奖励函数属于已知再生核希尔伯特空间（RKHS）。在此基础上引入联合差分隐私约束，要求查询点序列对上下文和奖励序列均满足差分隐私。提出一种新算法，在一大类核函数下，经过 $T$ 次查询后，达到 $\mathcal{O}\left(\sqrt{\frac{γ_T}{T}} + \frac{γ_T}{T \varepsilon}\right)$ 的误差率，其中 $γ_T$ 表示核的有效维度，$\varepsilon > 0$ 为隐私参数。该结果基于一种新型奖励函数估计器，兼具高效性与低敏感性，是实现最优学习性能并改善隐私参数依赖性的关键。
原文摘要 · Abstract (English)
We consider the problem of contextual kernel bandits with stochastic contexts, where the underlying reward function belongs to a known Reproducing Kernel Hilbert Space (RKHS). We study this problem under the additional constraint of joint differential privacy, where the agents needs to ensure that the sequence of query points is differentially private with respect to both the sequence of contexts and rewards. We propose a novel algorithm that improves upon the state of the art and achieves an error rate of $\mathcal{O}\left(\sqrt{\frac{γ_T}{T}} + \frac{γ_T}{T \varepsilon}\right)$ after $T$ queries for a large class of kernel families, where $γ_T$ represents the effective dimensionality of the kernel and $\varepsilon > 0$ is the privacy parameter. Our results are based on a novel estimator for the reward function that simultaneously enjoys high utility along with a low-sensitivity to observed rewards and contexts, which is crucial to obtain an order optimal learning performance with improved dependence on the privacy parameter.
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