The Second-Price Knapsack Problem: Near-Optimal Real Time Bidding in
Internet Advertisement
release_lftybevglve5bjhl3dd7xdrnje
by
Jonathan Amar, Nicholas Renegar, Haihao Lu
2018
Abstract
In the past decade, Real Time Bidding (RTB) has become one of the most common
purchase mechanisms of the online advertisement market. Under RTB a unique
second-price auction between bidders is managed for every individual
advertisement slot. We consider the bidder's problem of maximizing the value of
the bundle of ads they purchase, subject to budget constraints, and assuming
the value of each ad is known. We generalize the problem as a
second-price knapsack problem with uncertain resource consumption: the
bidder wins an auction when they bid the highest amount, but they pay an amount
equal to the second-highest bid, unknown a priori. Surprisingly, because of the
second-price mechanism, we prove that a linear form of bidding yields a
near-optimal selection of ads. We extend to an implementable online one-shot
learning algorithm. We prove that key points of the random permutation
assumption hold in this setting, and that we can apply algorithms for the
online-knapsack problem to this setting. Through this we recover a competitive
ratio of 1-6ϵ, where ϵ is the training ratio and is small in
general, yielding a strong theoretical result on an important variation of the
standard online knapsack problem. Numerical results from the iPinYou dataset
verify our results, recovering a bundle of ads with 99.5
optimal value.
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