We consider the problem of learning optimal reserve price in repeated
auctions against non-myopic bidders, who may bid strategically in order to gain
in future rounds even if the single-round auctions are truthful. Previous
algorithms, e.g., empirical pricing, do not provide non-trivial regret rounds
in this setting in general. We introduce algorithms that obtain small regret
against non-myopic bidders either when the market is large, i.e., no bidder
appears in a constant fraction of the rounds, or when the bidders are
impatient, i.e., they discount future utility by some factor mildly bounded
away from one. Our approach carefully controls what information is revealed to
each bidder, and builds on techniques from differentially private online
learning as well as the recent line of works on jointly differentially private
algorithms.

本研究针对非近视竞标者在重复拍卖中可能会采取策略性出价以获得未来回合利益的情况下，研究了学习最优保留价格的问题和相关算法。我们提出的算法可以在市场较大（即没有竞标者出现在一组回合的固定比例）或竞标者不耐心的情况下（即他们将未来效用打折，其因子在 1 附近）实现小的后悔率，该方法精细控制每个标注者所可见的信息，并借鉴了差分隐私在线学习和联合差分隐私算法的技术。