  Efficient allocation of impressions to advertisers in display advertising has
a significant impact on advertisers' utility and the browsing experience of
users. The problem becomes particularly challenging in the presence of
advertisers with limited budgets as this creates a complex interaction among
advertisers in the optimal impression assignment. In this paper, we study
online impression allocation in display advertising with budgeted advertisers.
That is, upon arrival of each impression, cost and revenue vectors are revealed
and the impression should be assigned to an advertiser almost immediately.
Without any assumption on the distribution/arrival of impressions, we propose a
framework to capture the risk to the ad network for each possible allocation;
impressions are allocated to advertisers such that the risk of ad network is
minimized. In practice, this translates to starting with an initial estimate of
dual prices and updating them according to the belief of the ad network toward
the future demand and remaining budgets. We apply our algorithms to a real data
set, and we empirically show that Kullback-Leibler divergence risk measure has
the best performance in terms of revenue and balanced budget delivery.
