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 previously best known algorithm, and show that no algorithm in that family admits a strategic regret more favorable than Ω( √ 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 state of the art and show a consistent exponential improvement in several different scenarios.
This paper studies an established model of repeated posted-price auctions with a single, strategic agent with an unknown value for a good. The algorithm posts a price at each time step, and the agent makes a purchasing decision based on his surplus from the current stage and the effect of his purchasing decision on future prices. In particular, the agent may strategically choose to not buy the good in the hopes of lowering the prices offered in future rounds. The authors extend an existing price-exploration algorithm for the non-strategic buyer case to this strategic case and show that their algorithm achieves near optimal strategic regret. They provide limited empirical evaluation to demonstrate superior performance over the previous work in this model. This is a good paper and is a valuable contribution to the literature at the intersection of machine learning and algorithmic game theory. The techniques, and the associated technical exposition, are very clean and intuitive. Throughout the paper, the authors do a good job of providing the high level ideas and also do a good job of explaining the relationship between their methods and previous work. While the model studied might not be the most realistic one for the context of repeated ad auctions, the techniques and analysis in this paper are likely to helpful in the study of more realistic and complex models. One particularly nice aspect of the approach in this paper is that the technique feels like it can be used again in similar settings. As is noted, the discount rate of the buyer is really the only aspect of this model that a designer can use to enforce good incentive properties and the algorithm in this paper seems like a general technique for leveraging the discount rate in repeated games, e.g. in a model where buyers don’t have an explicit discount rate but have some sort of ad impression budget that they must satisfy before the end of the game.  The only minor complaint I have is regards the knowledge of the discount rate. While knowledge of such parameters is standard in theoretical models, robustness to such an assumption is a desirable property (e.g. the literature on prior-free mechanism design). The authors do show a few experimental examples where their method performs well even without knowledge of the discount rate but I didn’t find that section to be particularly convincing. Perhaps more extensive empirical work could have made this point better (although that would have been difficult due to space constraints). Still this is only a minor point. Side Notes: - In figure 2, it is not immediately obvious that the y-axis is on a different scale. So it initially appeared that the regret with a known discount parameter was actually higher than the unknown.