Optimal No-regret Learning in Repeated First-price Auctions
release_lk5tig7hyrc23amdlthmtsgyla
by
Yanjun Han, Zhengyuan Zhou, Tsachy Weissman
2020
Abstract
We study online learning in repeated first-price auctions with censored
feedback, where a bidder, only observing the winning bid at the end of each
auction, learns to adaptively bid in order to maximize her cumulative payoff.
To achieve this goal, the bidder faces a challenging dilemma: if she wins the
bid–the only way to achieve positive payoffs–then she is not able to observe
the highest bid of the other bidders, which we assume is iid drawn from an
unknown distribution. This dilemma, despite being reminiscent of the
exploration-exploitation trade-off in contextual bandits, cannot directly be
addressed by the existing UCB or Thompson sampling algorithms in that
literature, mainly because contrary to the standard bandits setting, when a
positive reward is obtained here, nothing about the environment can be learned.
In this paper, by exploiting the structural properties of first-price
auctions, we develop the first learning algorithm that achieves
O(√(T)log^2 T) regret bound when the bidder's private values are
stochastically generated. We do so by providing an algorithm on a general class
of problems, which we call monotone group contextual bandits, where the same
regret bound is established under stochastically generated contexts. Further,
by a novel lower bound argument, we characterize an Ω(T^2/3) lower
bound for the case where the contexts are adversarially generated, thus
highlighting the impact of the contexts generation mechanism on the fundamental
learning limit. Despite this, we further exploit the structure of first-price
auctions and develop a learning algorithm that operates sample-efficiently (and
computationally efficiently) in the presence of adversarially generated private
values. We establish an O(√(T)log^3 T) regret bound for this algorithm,
hence providing a complete characterization of optimal learning guarantees for
this problem.
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