We consider bidding in repeated Bayesian first-price auctions. Bidding algorithms that achieve optimal regret have been extensively studied, but their strategic robustness to the seller's manipulation remains relatively underexplored. Bidding algorithms based on no-swap-regret algorithms achieve both desirable properties, but are suboptimal in terms of statistical and computational efficiency. In contrast, online gradient ascent is the only algorithm that achieves $O(\sqrt{TK})$ regret and strategic robustness [KSS24], where $T$ denotes the number of auctions and $K$ the number of bids. In this paper, we explore whether simple online linear optimization (OLO) algorithms suffice for bidding algorithms with both desirable properties. Our main result shows that sublinear linearized regret is sufficient for strategic robustness. Specifically, we construct simple black-box reductions that convert any OLO algorithm into a strategically robust no-regret bidding algorithm, in both known and unknown value distribution settings. For the known value distribution case, our reduction yields a bidding algorithm that achieves $O(\sqrt{T \log K})$ regret and strategic robustness (with exponential improvement on the $K$-dependence compared to [KSS24]). For the unknown value distribution case, our reduction gives a bidding algorithm with high-probability $O(\sqrt{T (\log K+\log(T/δ)})$ regret and strategic robustness, while removing the bounded density assumption made in [KSS24].

翻译：本文研究重复贝叶斯一价拍卖中的竞价问题。尽管实现最优遗憾的竞价算法已得到广泛研究，但其对卖方操纵的策略鲁棒性仍相对缺乏深入探讨。基于无交换遗憾算法的竞价算法虽能同时满足这两项理想特性，但在统计与计算效率方面存在不足。相比之下，在线梯度上升是唯一能实现$O(\sqrt{TK})$遗憾且具备策略鲁棒性的算法[KSS24]，其中$T$表示拍卖次数，$K$表示出价数量。本文旨在探究简单的在线线性优化（OLO）算法是否足以构建同时具备这两项理想特性的竞价算法。我们的主要结果表明，次线性的线性化遗憾条件即可保证策略鲁棒性。具体而言，我们构建了简单的黑盒归约方法，可将任意OLO算法转化为具备策略鲁棒性的无遗憾竞价算法，该转化同时适用于价值分布已知与未知两种场景。对于价值分布已知的情况，我们的归约产生的竞价算法可实现$O(\sqrt{T \log K})$遗憾并保持策略鲁棒性（相比[KSS24]在$K$依赖项上获得指数级改进）。对于价值分布未知的情况，我们的归约给出的竞价算法能以高概率实现$O(\sqrt{T (\log K+\log(T/δ)})$遗憾并保持策略鲁棒性，同时消除了[KSS24]中对概率密度有界的假设。