Inspired by online ad allocation, we study online stochastic packing linear programs from theoretical and practical standpoints. We first present a near-optimal online algorithm for a general class of packing linear programs which model various online resource allocation problems including online variants of routing, ad allocations, generalized assignment, and combinatorial auctions. As our main theoretical result, we prove that a simple primal-dual training-based algorithm achieves a (1 - o(1))-approximation guarantee in the random order stochastic model. This is a significant improvement over logarithmic or constant-factor approximations for the adversarial variants of the same problems (e.g. factor 1 - 1 e for online ad allocation, and m for online routing). We then focus on the online display ad allocation problem and study the efficiency and fairness of various training-based and online allocation algorithms on data sets collected from real-life display ad allocation system. Our experimental evaluation confirms the effectiveness of training-based primal-dual algorithms on real data sets, and also indicate an intrinsic trade-off between fairness and efficiency.
We consider the problem of a search engine trying to assign a sequence of search keywords to a set of competing bidders, each with a daily spending limit. The goal is to maximize the revenue generated by these keyword sales, bearing in mind that, as some bidders may eventually exceed their budget, not all keywords should be sold to the highest bidder. We assume that the sequence of keywords (or equivalently, of bids) is revealed on-line. Our concern will be the competitive ratio for this problem versus the off-line optimum. We extend the current literature on this problem by considering the setting where the keywords arrive in a random order. In this setting we are able to achieve a competitive ratio of 1-e under some mild, but necessary, assumptions. In contrast, it is already known that when the keywords arrive in an adversarial order, the best competitive ratio is bounded away from 1. Our algorithm is motivated by PAC learning, and proceeds in two parts: a training phase, and an exploitation phase.