Bid Optimization by Multivariable Control in Display Advertising

Real-Time Bidding (RTB) is an important paradigm in display advertising, where advertisers utilize extended information and algorithms served by Demand Side Platforms (DSPs) to improve advertising performance. A common problem for DSPs is to help advertisers gain as much value as possible with budget constraints. However, advertisers would routinely add certain key performance indicator (KPI) constraints that the advertising campaign must meet due to practical reasons. In this paper, we study the common case where advertisers aim to maximize the quantity of conversions, and set cost-per-click (CPC) as a KPI constraint. We convert such a problem into a linear programming problem and leverage the primal-dual method to derive the optimal bidding strategy. To address the applicability issue, we propose a feedback control-based solution and devise the multivariable control system. The empirical study based on real-word data from Taobao.com verifies the effectiveness and superiority of our approach compared with the state of the art in the industry practices

Optimal Real-Time Bidding Strategies

The ad-trading desks of media-buying agencies are increasingly relying on complex algorithms for purchasing advertising inventory. In particular, Real-Time Bidding (RTB) algorithms respond to many auctions -- usually Vickrey auctions -- throughout the day for buying ad-inventory with the aim of maximizing one or several key performance indicators (KPI). The optimization problems faced by companies building bidding strategies are new and interesting for the community of applied mathematicians. In this article, we introduce a stochastic optimal control model that addresses the question of the optimal bidding strategy in various realistic contexts: the maximization of the inventory bought with a given amount of cash in the framework of audience strategies, the maximization of the number of conversions/acquisitions with a given amount of cash, etc. In our model, the sequence of auctions is modeled by a Poisson process and the \textit{price to beat} for each auction is modeled by a random variable following almost any probability distribution. We show that the optimal bids are characterized by a Hamilton-Jacobi-Bellman equation, and that almost-closed form solutions can be found by using a fluid limit. Numerical examples are also carried out

Control para sistemas continuos y discretos basado en la ingeniería dirigida por modelos

El control ha sido un factor fundamental para el desarrollo de la tecnología, siempre que se requiere ajustar una variable física a un valor específico se está realizando una acción de control. El control se puede encontrar en la vida cotidiana en actividades como ajustar la temperatura de la ducha o ajustar el nivel de luminosidad en un invernadero. En términos generales, un sistema de control es un componente de un sistema más complejo en el que se requiere producir una salida determinada o mantener un estado específico del sistema. Los sistemas que requieren de un proceso de control retroalimentado son cada vez más complejos, lo cual conlleva grandes desafíos. La presente investigación tiene como propósito proponer un enfoque de simple utilización, basado en la ingeniería dirigida por modelos para el control de sistemas continuos y sistemas con eventos discretos, que incluye la implementación de la propuesta en la plataforma VariaMos y su aplicación en dos pruebas de concepto. La implementación permite, de manera experimental, obtener el modelo analítico del sistema y las ganancias del controlador PID. Los resultados obtenidos evidencian la manera en la que el enfoque puede ser usado en sistemas con eventos continuos y discretos. Por lo tanto, se concluye que el enfoque propuesto permite producir sistemas con capacidades de retroalimentación. Además, la implementación del enfoque facilita su uso a usuarios que no son necesariamente expertos en control.The control has been a fundamental factor for the development of the technology, whenever a physical variable needs to be adjusted to a specific value, a control action is being performed. Control can be found in everyday life in activities like adjusting the temperature of the shower or adjusting the brightness in a greenhouse. In general terms, a control system is a component of a more complex system in which it is required to produce a certain output or maintain a specific system state Systems that require a feedback control process are becoming increasingly complex, which carries with it great challenges. This research aims to propose a simple model-driven engineering approach, for the control of continuous systems and discrete-event systems, which includes the implementation of the proposal on the VariaMos platform and its application in two proof of concept. The implementation allows in an experimental way, to obtain the analytical model of the system and the gains of the PID controller. The results obtained show how approach can be used in systems with continuous and discrete events. Therefore, it is concluded that the proposed approach allows producing systems with feedback capabilities. Furthermore, the implementation of the approach allows it to be used by users who are not necessarily experts in control

The value of data

Thesis: S.M., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2018.Cataloged from PDF version of thesis.Includes bibliographical references (pages 71-73).Data and information are integral to the modern economic system. Advances in technology have allowed companies to both collect and utilize vast amounts of data. At times this data can be very private and collected surreptitiously. Smartphones and other devices that keep us in constant contact with the internet provide companies like Google and Facebook with a wealth of information to sell. Despite all this, there currently does not exist a systematic way to value data. In the absence of such valuations, gross economic inefficiencies are inevitable. In this thesis, we seek to model ways in which data can be bought, sold, and used fairly in an economic environment. We also develop a theory to value data in different settings. Our models and results are applied to a variety of different domains to demonstrate their efficacy. Results from game theory and mathematical programming allow us to provide fair and efficient allocations of data. This research shows that there exists an efficient and fair method with which to determine the value of information and data and to trade it fairly.by Dalton James Jones.S.M