Budget Feasible Mechanisms

We study a novel class of mechanism design problems in which the outcomes are constrained by the payments. This basic class of mechanism design problems captures many common economic situations, and yet it has not been studied, to our knowledge, in the past. We focus on the case of procurement auctions in which sellers have private costs, and the auctioneer aims to maximize a utility function on subsets of items, under the constraint that the sum of the payments provided by the mechanism does not exceed a given budget. Standard mechanism design ideas such as the VCG mechanism and its variants are not applicable here. We show that, for general functions, the budget constraint can render mechanisms arbitrarily bad in terms of the utility of the buyer. However, our main result shows that for the important class of submodular functions, a bounded approximation ratio is achievable. Better approximation results are obtained for subclasses of the submodular functions. We explore the space of budget feasible mechanisms in other domains and give a characterization under more restricted conditions

Multiplicative Bidding in Online Advertising

In this paper, we initiate the study of the multiplicative bidding language adopted by major Internet search companies. In multiplicative bidding, the effective bid on a particular search auction is the product of a base bid and bid adjustments that are dependent on features of the search (for example, the geographic location of the user, or the platform on which the search is conducted). We consider the task faced by the advertiser when setting these bid adjustments, and establish a foundational optimization problem that captures the core difficulty of bidding under this language. We give matching algorithmic and approximation hardness results for this problem; these results are against an information-theoretic bound, and thus have implications on the power of the multiplicative bidding language itself. Inspired by empirical studies of search engine price data, we then codify the relevant restrictions of the problem, and give further algorithmic and hardness results. Our main technical contribution is an $O(\log n)$-approximation for the case of multiplicative prices and monotone values. We also provide empirical validations of our problem restrictions, and test our algorithms on real data against natural benchmarks. Our experiments show that they perform favorably compared with the baseline.Comment: 25 pages; accepted to EC'1

Bid Optimization in Broad-Match Ad auctions

Ad auctions in sponsored search support ``broad match'' that allows an advertiser to target a large number of queries while bidding only on a limited number. While giving more expressiveness to advertisers, this feature makes it challenging to optimize bids to maximize their returns: choosing to bid on a query as a broad match because it provides high profit results in one bidding for related queries which may yield low or even negative profits. We abstract and study the complexity of the {\em bid optimization problem} which is to determine an advertiser's bids on a subset of keywords (possibly using broad match) so that her profit is maximized. In the query language model when the advertiser is allowed to bid on all queries as broad match, we present an linear programming (LP)-based polynomial-time algorithm that gets the optimal profit. In the model in which an advertiser can only bid on keywords, ie., a subset of keywords as an exact or broad match, we show that this problem is not approximable within any reasonable approximation factor unless P=NP. To deal with this hardness result, we present a constant-factor approximation when the optimal profit significantly exceeds the cost. This algorithm is based on rounding a natural LP formulation of the problem. Finally, we study a budgeted variant of the problem, and show that in the query language model, one can find two budget constrained ad campaigns in polynomial time that implement the optimal bidding strategy. Our results are the first to address bid optimization under the broad match feature which is common in ad auctions.Comment: World Wide Web Conference (WWW09), 10 pages, 2 figure

On the stability of generalized second price auctions with budgets

The Generalized Second Price (GSP) auction used typically to model sponsored search auctions does not include the notion of budget constraints, which is present in practice. Motivated by this, we introduce the different variants of GSP auctions that take budgets into account in natural ways. We examine their stability by focusing on the existence of Nash equilibria and envy-free assignments. We highlight the differences between these mechanisms and find that only some of them exhibit both notions of stability. This shows the importance of carefully picking the right mechanism to ensure stable outcomes in the presence of budgets.Peer ReviewedPostprint (author's final draft

Stochastic Budget Optimization in Internet Advertising

Internet advertising is a sophisticated game in which the many advertisers "play" to optimize their return on investment. There are many "targets" for the advertisements, and each "target" has a collection of games with a potentially different set of players involved. In this paper, we study the problem of how advertisers allocate their budget across these "targets". In particular, we focus on formulating their best response strategy as an optimization problem. Advertisers have a set of keywords ("targets") and some stochastic information about the future, namely a probability distribution over scenarios of cost vs click combinations. This summarizes the potential states of the world assuming that the strategies of other players are fixed. Then, the best response can be abstracted as stochastic budget optimization problems to figure out how to spread a given budget across these keywords to maximize the expected number of clicks. We present the first known non-trivial poly-logarithmic approximation for these problems as well as the first known hardness results of getting better than logarithmic approximation ratios in the various parameters involved. We also identify several special cases of these problems of practical interest, such as with fixed number of scenarios or with polynomial-sized parameters related to cost, which are solvable either in polynomial time or with improved approximation ratios. Stochastic budget optimization with scenarios has sophisticated technical structure. Our approximation and hardness results come from relating these problems to a special type of (0/1, bipartite) quadratic programs inherent in them. Our research answers some open problems raised by the authors in (Stochastic Models for Budget Optimization in Search-Based Advertising, Algorithmica, 58 (4), 1022-1044, 2010).Comment: FINAL versio

Програмна система управління інформаційними потоками в медійній рекламі

Кваліфікаційна робота включає пояснювальну записку (51 сторінку, 17 рисунків, 2 графіки) Об’єкт розробки – створення комп’ютерної системи автоматизації управління процесом продажу медійної реклами яка дозволяє завантажувати рекламні пропозиції та налаштовувати порядок та правила їх показу. Комп’ютерна система дозволяє: завантажувати медіа рекламу та забезпечувати їх збереження; створення рекламних кампаній, в основі яких лежать попередньо завантажені рекламні креативи; в автоматичному режимі вибрати оптимальну рекламну пропозицію з запропонованих рекламним запитом. В процесі розробки було використано стандарт OpenRTB версії 2.3. Всі описані сервіси було розроблено мовою програмування Node.js. В якості бази даних використовувалась MySQL. В ході розробки: − проведено аналіз стандарту OpenRTB; − сформульовані вимоги до комп’ютерної системи автоматизації управління продажу медійної реклами; − розроблена система автоматизації вибору оптимальної пропозиції з запропонованих варіантів рекламного запиту; − розроблено користувацький додаток для завантаження рекламних банерів та створення рекламних кампаній задля їх просування; − розроблено веб-сервіс для автоматичного завантаження даних створених через додаток та оперування цими даними для вибору оптимальної пропозиції; − розроблено програмне забезпечення для створення тестового навантаження на веб-сервіс.Qualification work includes explanatory note (51 page, 17 images, 2 graphs) Subject of development is creation of computer system that automates the selling process of advertisements and which handles creation if ad inventory and targeting rules. Developed computer system allows: to download ad banners and handles it’s storage; creation of ad campaigns, which are based on previously created ad banners; automatically select optimal ad position from provided ad request. Developed system is based on open-source standard OpenRTB version 2.3. All services were developed using Node.js. MySQL was used as main storage. During development process: − OpenRTB version 2.3 was analyzed ; − formulated requirements for the computer system that automates selling process of advertisements; − create automatization system for optimal deal selection from provided ad request; − developed user application for ad inventory and ad campaign creation; − developed web-service to handle automatic download of user provided data and using them to select an optimal deal; − Created software to perform load tests of main syste

Efficient regret bounds for online bid optimisation in budget-limited sponsored search auctions

We study the problem of an advertising agent who needs to intelligently distribute her budget across a sequence of online keyword bidding auctions. We assume the closing price of each auction is governed by the same unknown distribution, and study the problem of making provably optimal bidding decisions. Learning the distribution is done under censored observations, i.e. the closing price of an auction is revealed only if the bid we place is above it. We consider three algorithms, namely ε—First, Greedy Product-Limit (GPL) and LuekerLearn, respectively, and we show that these algorithms provably achieve Hannan-consistency. In particular, we show that the regret bound of ε—First is at most O(T⅔) with high probability. For the other two algorithms, we first prove that, by using a censored data distribution estimator proposed by Zeng [19], the empirical distribution of the closing market price converges in probability to its true distribution with a O(1/√t) rate, where t is the number of updates. Based on this result, we prove that both GPL and LuekerLearn achieve O(√T) regret bound with high probability. This in fact provides an affirmative answer to the research question raised in [1]. We also evaluate the abovementioned algorithms using real bidding data, and show that although GPL achieves the best performance on average (up to 90% of the optimal solution), its long running time may limit its suitability in practice. By contrast, LuekerLearn and ε— First proposed in this paper achieve up to 85% of the optimal, but with an exponential reduction in computational complexity (a saving up to 95%, compared to GPL)