An Efficient Partial-Order Characterization of Admissible Actions for Real-Time Scheduling of Sporadic Tasks

In many scheduling problems involving tasks with multiple deadlines, there is typically a large degree of flexibility in determining which tasks to serve at each time step. Given a cost function it is often possible to cast a scheduling problem as an optimization problem to obtain the most suitable schedule. However, in several applications, especially when the schedule has to be computed in-line or periodically adjusted, the cost function may not be completely known a priori but only partially. For example, in some applications only the cost of the current allocation of resources to the tasks could be available. Under this scenario, a sensible approach is to optimally allocate resources without compromising the schedulability of the tasks. This work follows this approach by introducing a notion of partial ordering on the set of feasible schedules. This partial ordering is particularly useful to characterize which allocations of resources at the current time preserve the feasibility of the problem in the future. This enables the realization of fast algorithms for real-time scheduling. The model and algorithm presented can be utilized in different applications such as electric vehicle charging, cloud computing and advertising on websites. [1

A unified framework for the scheduling of guaranteed targeted display advertising under reach and frequency requirements

Motivated by recent trends in online advertising and advancements made by online publishers, we consider a new form of contract that allows advertisers to specify the number of unique individuals that should see their ad (reach) and the minimum number of times each individual should be exposed (frequency). We develop an optimization framework that aims for minimal under-delivery and proper spread of each campaign over its targeted demographics. As well, we introduce a pattern-based delivery mechanism that allows us to integrate a variety of interesting features into a website's ad allocation optimization problem that have not been possible before. For example, our approach allows publishers to implement any desired pacing of ads over time at the user level or control the number of competing brands seen by each individual. We develop a two-phase algorithm that employs column generation in a hierarchical scheme with three parallelizable components. Numerical tests with real industry data show that our algorithm produces high-quality solutions and has promising run-time and scalability. Several extensions of the model are presented, e.g., to account for multiple ad positions on the webpage or randomness in the website visitors' arrivalprocess

A unified framework for the scheduling of guaranteed targeted display advertising under reach and frequency requirements

Motivated by recent trends in online advertising and advancements made by online publishers, we consider a new form of contract that allows advertisers to specify the number of unique individuals that should see their ad (reach) and the minimum number of times each individual should be exposed (frequency). We develop an optimization framework that aims for minimal under-delivery and proper spread of each campaign over its targeted demographics. As well, we introduce a pattern-based delivery mechanism that allows us to integrate a variety of interesting features into a website's ad allocation optimization problem that have not been possible before. For example, our approach allows publishers to implement any desired pacing of ads over time at the user level or control the number of competing brands seen by each individual. We develop a two-phase algorithm that employs column generation in a hierarchical scheme with three parallelizable components. Numerical tests with real industry data show that our algorithm produces high-quality solutions and has promising run-time and scalability. Several extensions of the model are presented, e.g., to account for multiple ad positions on the webpage or randomness in the website visitors' arrivalprocess

New Analytics Paradigms in Online Advertising and Fantasy Sports

Over the last two decades, digitization has been drastically shifting the way businesses operate and has provided access to high volume, variety, velocity, and veracity data. Naturally, access to such granular data has opened a wider range of possibilities than previously available. We leverage such data to develop application-driven models in order to evaluate current systems and make better decisions. We explore three application areas. In Chapter 1, we develop models and algorithms to optimize portfolios in daily fantasy sports (DFS). We use opponent-level data to predict behavior of fantasy players via a Dirichlet-multinomial process, and our predictions feed into a novel portfolio construction model. The model is solved via a sequence of binary quadratic programs, motivated by its connection to outperforming stochastic benchmarks, the submodularity of the objective function, and the theory of order statistics. In addition to providing theoretical guarantees, we demonstrate the value of our framework by participating in DFS contests. In Chapter 2, we develop an axiomatic framework for attribution in online advertising, i.e., assessing the contribution of individual ads to product purchase. Leveraging a user-level dataset, we propose a Markovian model to explain user behavior as a function of the ads she is exposed to. We use our model to illustrate limitations of existing heuristics and propose an original framework for attribution, which is motivated by causality and game theory. Furthermore, we establish that our framework coincides with an adjusted ``unique-uniform'' attribution scheme. This scheme is efficiently implementable and can be interpreted as a correction to the commonly used uniform attribution scheme. We supplement our theory with numerics using a real-world large-scale dataset. In Chapter 3, we propose a decision-making algorithm for personalized sequential marketing. As in attribution, using a user-level dataset, we propose a state-based model to capture user behavior as a function of the ad interventions. In contrast with existing approaches that model only the myopic value of an intervention, we also model the long-run value. The objective of the firm is to maximize the probability of purchase and a key challenge it faces is the lack of understanding of the state-specific effects of interventions. We propose a model-free learning algorithm for decision-making in such a setting. Our algorithm inherits the simplicity of Thompson sampling for a multi-armed bandit setting and we prove its asymptotic optimality. We supplement our theory with numerics on an email marketing dataset