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：本文研究了在重复进行的、无限供给的商品定价拍卖中，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，该算法对买方的输入对（即商品选择和出价）提供差分隐私保护。值得注意的是，我们的算法是首个在具有隐私保证的前提下实现次线性 $O(\sqrt{T}\log{T})$ 遗憾的方法。该方法基于指数权重元算法，并通过引入微小随机扰动来缓解收益函数中的不连续性。由于其结构与指数机制相似，该方法天然具备差分隐私保护能力。我们还将算法扩展至买家在连续轮次中策略性出价的场景。通过利用这种内在的差分隐私特性，我们仅需对算法进行最小限度的调整，便能在该场景下确保次线性遗憾。