Optimal Regret Minimization in Posted-Price Auctions with Strategic Buyers

We study revenue optimization learning algorithms for posted-price auctions with strategic buyers. We analyze a very broad family of monotone regret minimization algorithms for this problem, which includes the previous best known algorithm, and show that no algorithm in that family admits a strategic regret more favorable than $\Omega(\sqrt{T})$. We then introduce a new algorithm that achieves a strategic regret differing from the lower bound only by a factor in $O(\log T)$, an exponential improvement upon the previous best algorithm. Our new algorithm admits a natural analysis and simpler proofs, and the ideas behind its design are general. We also report the results of empirical evaluations comparing our algorithm with the previous best algorithm and show a consistent exponential improvement in several different scenarios.