Allocating online advertisement space with unreliable estimates

We study the problem of optimally allocating online advertisement space to budget-constrained advertisers. This problem was defined and studied from the perspective of worst-case online competitive analysis by Mehta et al. Our objective is to find an algorithm that takes advantage of the given estimates of the frequencies of keywords to compute a near optimal solution when the estimates are accurate, while at the same time maintaining a good worst-case competitive ratio in case the estimates are totally incorrect. This is motivated by real-world situations where search engines have stochastic information that provide reasonably accurate estimates of the frequency of search queries except in certain highly unpredictable yet economically valuable spikes in the search pattern. Our approach is a black-box approach: we assume we have access to an oracle that uses the given estimates to recommend an advertiser everytime a query arrives. We use this oracle to design an algorithm that provides two performance guarantees: the performance guarantee in the case that the oracle gives an accurate estimate, and its worst-case performance guarantee. Our algorithm can be fine tuned by adjusting a parameter α, giving a tradeoff curve between the two performance measures with the best competitive ratio for the worst-case scenario at one end of the curve and the optimal solution for the scenario where estimates are accurate at the other en. Finally, we demonstrate the applicability of our framework by applying it to two classical online problems, namely the lost cow and the ski rental problems.