Today, billions of display ad impressions are purchased on a daily basis through a public auction hosted by real time bidding (RTB) exchanges. A decision has to be made for advertisers to submit a bid for each selected RTB ad request in milliseconds. Restricted by the budget, the goal is to buy a set of ad impressions to reach as many targeted users as possible. A desired action (conversion), advertiser specific, includes purchasing a product, filling out a form, signing up for emails, etc. In addition, advertisers typically prefer to spend their budget smoothly over the time in order to reach a wider range of audience accessible throughout a day and have a sustainable impact. However, since the conversions occur rarely and the occurrence feedback is normally delayed, it is very challenging to achieve both budget and performance goals at the same time. In this paper, we present an online approach to the smooth budget delivery while optimizing for the conversion performance. Our algorithm tries to select high quality impressions and adjust the bid price based on the prior performance distribution in an adaptive manner by distributing the budget optimally across time. Our experimental results from real advertising campaigns demonstrate the effectiveness of our proposed approach.
Agrawal @cite_9 proposed an general online linear programming algorithm to solve many practical online problems. First they applied the standard linear programming solver to compute the optimal dual solution for the data which have been seen in the system. Then, the solution for the new instance can be decided by checking if the dual solution with the new instance satisfies the constraint. The problem is that the true value @math and cost @math for the incoming ad request is unknown when it arrives to the system. If @math and @math is estimated by some statistical models or other alternative solutions, the dual solution needs to be re-computed more frequently for each campaign in order to impose budget constraints accurately. This introduces high computational cost in the real time bidding system.
@cite_9
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We describe a real-time bidding algorithm for performance-based display ad allocation. A central issue in performance display advertising is matching campaigns to ad impressions, which can be formulated as a constrained optimization problem that maximizes revenue subject to constraints such as budget limits and inventory availability. The current practice is to solve the optimization problem offline at a tractable level of impression granularity (e.g., the page level), and to serve ads online based on the precomputed static delivery scheme. Although this offline approach takes a global view to achieve optimality, it fails to scale to ad allocation at the individual impression level. Therefore, we propose a real-time bidding algorithm that enables fine-grained impression valuation (e.g., targeting users with real-time conversion data), and adjusts value-based bids according to real-time constraint snapshots (e.g., budget consumption levels). Theoretically, we show that under a linear programming (LP) primal-dual formulation, the simple real-time bidding algorithm is indeed an online solver to the original primal problem by taking the optimal solution to the dual problem as input. In other words, the online algorithm guarantees the offline optimality given the same level of knowledge an offline optimization would have. Empirically, we develop and experiment with two real-time bid adjustment approaches to adapting to the non-stationary nature of the marketplace: one adjusts bids against real-time constraint satisfaction levels using control-theoretic methods, and the other adjusts bids also based on the statistically modeled historical bidding landscape. Finally, we show experimental results with real-world ad delivery data that support our theoretical conclusions. We study the online stochastic bipartite matching problem, in a form motivated by display ad allocation on the Internet. In the online, but adversarial case, the celebrated result of Karp, Vazirani and Vazirani gives an approximation ratio of @math , a very familiar bound that holds for many online problems; further, the bound is tight in this case. In the online, stochastic case when nodes are drawn repeatedly from a known distribution, the greedy algorithm matches this approximation ratio, but still, no algorithm is known that beats the @math bound.Our main result is a @math -approximation online algorithm for stochastic bipartite matching, breaking this @math barrier. Furthermore, we show that no online algorithm can produce a @math approximation for an arbitrarily small @math for this problem. Our algorithms are based on computing an optimal offline solution to the expected instance, and using this solution as a guideline in the process of online allocation. We employ a novel application of the idea of the power of two choices from load balancing: we compute two disjoint solutions to the expected instance, and use both of them in the online algorithm in a prescribed preference order. To identify these two disjoint solutions, we solve a max flow problem in a boosted flow graph, and then carefully decompose this maximum flow to two edge-disjoint (near-) matchings. In addition to guiding the online decision making, these two offline solutions are used to characterize an upper bound for the optimum in any scenario. This is done by identifying a cut whose value we can bound under the arrival distribution. At the end, we discuss extensions of our results to more general bipartite allocations that are important in a display ad application. We give a simple proof that the ranking algorithm of Karp, Vazirani and Vazirani [KVV90] is 1-1 e competitive for the online bipartite matching problem. The proof is via a randomized primal-dual argument. Primal-dual algorithms have been successfully used for many online algorithm problems, but the dual constraints are always satisfied deterministically. This is the first instance of a non-trivial randomized primal-dual algorithm in which the dual constraints only hold in expectation. The approach also generalizes easily to the vertex-weighted version considered by [AGKM11]. Further we show that the proof is very similar to the deterministic primal-dual argument for the online budgeted allocation problem with small bids (also called the AdWords problem) of [MSVV05]. Infrastructure-as-a-service (IaaS) clouds offer diverse instance purchasing options. A user can either run instances on demand and pay only for what it uses, or it can prepay to reserve instances for a long period, during which a usage discount is entitled. An important problem facing a user is how these two instance options can be dynamically combined to serve time-varying demands at minimum cost. Existing strategies in the literature, however, require either exact knowledge or the distribution of demands in the long-term future, which significantly limits their use in practice. Unlike existing works, we propose two practical online algorithms , one deterministic and another randomized, that dynamically combine the two instance options online without any knowledge of the future. We show that the proposed deterministic (resp., randomized) algorithm incurs no more than @math (resp., @math ) times the minimum cost obtained by an optimal offline algorithm that knows the exact future a priori , where @math is the entitled discount after reservation. Our online algorithms achieve the best possible competitive ratios in both the deterministic and randomized cases, and can be easily extended to cases when short-term predictions are reliable. Simulations driven by a large volume of real-world traces show that significant cost savings can be achieved with prevalent IaaS prices.