Learning Algorithms in Strategic Environments
Learning algorithms are often analyzed under the assumption their inputs are drawn
from stochastic or adversarial sources. Increasingly, these algorithms are being applied
in strategic settings, where we can hope for stronger guarantees. This thesis aims to
understand the performance of existing learning algorithms in these settings, and to
design new algorithms that perform well in these settings.
This thesis is divided into three parts. In Part I, we address the question of how
agents should learn to bid in repeated non-truthful auctions – and conversely, how
should we design auctions whose participants are learning agents.
In Part II, we study the dynamic pricing problem: the question of how should a
large retailer learn how to set prices for a sequence of disparate goods over time, based
on observing demands for goods at various prices. Previous work has demonstrated
how to obtain O(log T) regret for this problem. We show how to achieve regret
O(log log T), which is tight. Our algorithm uses ideas from integral geometry (most
notably the concept of intrinsic volumes).
Finally, in Part III, we study how to learn the ranking of a set of N items from
pairwise comparisons that may be strategic or noisy. In particular, we design mechanisms
for a variety of settings (choosing the winner of a round-robin tournament,
aggregating the top-K items under the strong stochastic transitivity noise model)
which outperform the naive rule of ranking items according to the total number of
pairwise comparisons won.