This work addresses the problem of revenue maximization in a repeated, unlimited supply item-pricing auction while preserving buyer privacy. We present a novel algorithm that provides differential privacy with respect to the buyer's input pair: item selection and bid. Notably, our algorithm is the first to offer a sublinear $O(\sqrt{T}\log{T})$ regret with a privacy guarantee. Our method is based on an exponential weights meta-algorithm, and we mitigate the issue of discontinuities in revenue functions via small random perturbations. As a result of its structural similarity to the exponential mechanism, our method inherently secures differential privacy. We also extend our algorithm to accommodate scenarios where buyers strategically bid over successive rounds. The inherent differential privacy allows us to adapt our algorithm with minimal modification to ensure a sublinear regret in this setting.

翻译：本文研究在重复、无限供应的商品定价拍卖中，如何在保护买家隐私的同时实现收益最大化。我们提出了一种新颖的算法，该算法针对买方的输入对（商品选择与出价）提供差分隐私保护。值得注意的是，我们的算法是首个在隐私保证下实现亚线性$O(\sqrt{T}\log{T})$遗憾值的方案。该方法基于指数权重元算法，并通过引入小随机扰动来缓解收益函数的不连续性问题。由于其结构类似于指数机制，我们的方法天然具备差分隐私特性。此外，我们将算法扩展至买方在连续轮次中策略性出价的场景。这种内在的差分隐私特性使我们能够以最小修改量适应算法，从而在该场景下实现亚线性遗憾值。