abstract: Researchers have postulated that math academic achievement increases student success in college (Lee, 2012; Silverman & Seidman, 2011; Vigdor, 2013), yet 80% of universities and 98% of community colleges require many of their first-year students to be placed in remedial courses (Bettinger & Long, 2009). Many high school graduates are entering college ill prepared for the rigors of higher education, lacking understanding of basic and important principles (ACT, 2012). The desire to increase academic achievement is a wide held aspiration in education and the idea of adapting instruction to individuals is one approach to accomplish this goal (Lalley & Gentile, 2009a). Frequently, adaptive learning environments rely on a mastery learning approach, it is thought that when students are afforded the opportunity to master the material, deeper and more meaningful learning is likely to occur. Researchers generally agree that the learning environment, the teaching approach, and the students' attributes are all important to understanding the conditions that promote academic achievement (Bandura, 1977; Bloom, 1968; Guskey, 2010; Cassen, Feinstein & Graham, 2008; Changeiywo, Wambugu & Wachanga, 2011; Lee, 2012; Schunk, 1991; Van Dinther, Dochy & Segers, 2011). The present study investigated the role of college students' affective attributes and skills, such as academic competence and academic resilience, in an adaptive mastery-based learning environment on their academic performance, while enrolled in a remedial mathematics course. The results showed that the combined influence of students' affective attributes and academic resilience had a statistically significant effect on students' academic performance. Further, the mastery-based learning environment also had a significant effect on their academic competence and academic performance. / Dissertation/Thesis / Ph.D. Educational Technology 2013

L’Internet des Objets (IoT) est envisagé pour interconnecter des objets communicants et autonomes au sein du même réseau, qui peut être le réseau Internet ou un réseau de communication sans fil. Les objets autonomes qui composent les réseaux IoT possèdent des caractéristiques très différentes, que ce soit en terme d’application, de connectivité, de puissance de calcul, de mobilité ou encore de consommation de puissance. Le fait que tant d’objets hétérogènes partagent un même réseau soulève de nombreux défis tels que : l’identification des objets, l’efficacité énergétique, le contrôle des interférences du réseau, la latence ou encore la fiabilité des communications. La densification du réseau couplée à la limitation des ressources spectrales (partagées entre les objets) et à l’efficacité énergétique obligent les objets à optimiser l’utilisation des ressources fréquentielles et de puissance de transmission. De plus, la mobilité des objets au sein du réseau ainsi que la grande variabilité de leur comportement changent la dynamique du réseau qui devient imprévisible. Dans ce contexte, il devient difficile pour les objets d’utiliser des algorithmes d’allocation de ressources classiques, qui se basent sur une connaissance parfaite ou statistique du réseau. Afin de transmettre de manière efficace, il est impératif de développer de nouveaux algorithmes d’allocation de ressources qui sont en mesure de s’adapter aux évolutions du réseau. Pour cela, nous allons utiliser des outils d’optimisation en ligne et des techniques d’apprentissage. Dans ce cadre nous allons exploiter la notion du regret qui permet de comparer l’efficacité d’une allocation de puissance dynamique à la meilleure allocation de puissance fixe calculée à posteriori. Nous allons aussi utiliser la notion de non-regret qui garantit que l’allocation de puissance dynamique donne des résultats asymptotiquement optimaux . Dans cette thèse, nous nous sommes concentrés sur le problème de minimisation de puissance sous contrainte de débit. Ce type de problème permet de garantir une certaine efficacité énergétique tout en assurant une qualité de service minimale des communications. De plus, nous considérons des réseaux de type IoT et ne faisons donc aucune hypothèse quant aux évolutions du réseau. Un des objectifs majeurs de cette thèse est la réduction de la quantité d’information nécessaire à la détermination de l’allocation de puissance dynamique. Pour résoudre ce problème, nous avons proposé des algorithmes inspirés du problème du bandit manchot, problème classique de l’apprentissage statistique. Nous avons montré que ces algorithmes sont efficaces en terme du regret lorsque l’objet a accès à un vecteur, le gradient ou l’estimateur non-biaisé du gradient, comme feedback d’information. Afin de réduire d’avantage la quantité d’information reçue par l’objet, nous avons proposé une méthode de construction d’un estimateur du gradient basé uniquement sur une information scalaire. En utilisant cet estimateur nous avons présenté un algorithme efficace d’allocation de puissance. / One of the key challenges in Internet of Things (IoT) networks is to connect numerous, heterogeneous andautonomous devices. These devices have different types of characteristics in terms of: application, computational power, connectivity, mobility or power consumption. These characteristics give rise to challenges concerning resource allocation such as: a) these devices operate in a highly dynamic and unpredictable environments; b) the lack of sufficient information at the device end; c) the interference control due to the large number of devices in the network. The fact that the network is highly dynamic and unpredictable implies that existing solutions for resource allocation are no longer relevant because classical solutions require a perfect or statistical knowledge of the network. To address these issues, we use tools from online optimization and machine learning. In the online optimization framework, the device only needs to have strictly causal information to define its online policy. In order to evaluate the performance of a given online policy, the most commonly used notion is that of the regret, which compares its performance in terms of loss with a benchmark policy, i.e., the best fixed strategy computed in hindsight. Otherwise stated, the regret measures the performance gap between an online policy and the best mean optimal solution over a fixed horizon. In this thesis, we focus on an online power minimization problem under rate constraints in a dynamic IoT network. To address this issue, we propose a regret-based formulation that accounts for arbitrary network dynamics, using techniques used to solve the multi-armed bandit problem. This allows us to derive an online power allocation policy which is provably capable of adapting to such changes, while relying solely on strictly causal feedback. In so doing, we identify an important tradeoff between the amount of feedback available at the transmitter side and the resulting system performance. We first study the case in which the device has access to a vector, either the gradient or an unbiased estimated of the gradient, as information feedback. To limit the feedback exchange in the network our goal is to reduce it as mush as possible. Therefore, we study the case in which the device has access to only a loss-based information (scalar feedback). In this case, we propose a second online algorithm to determine an efficient and adaptative power allocation policy.

Recent decades have witnessed the phenomenal success of model predictive control (MPC) in a wide spectrum of domains, such as process industries, intelligent transportation, automotive applications, power systems, cyber security, and robotics. For constrained dynamic systems subject to uncertainties, robust MPC is attractive due to its capability of effectively dealing with various types of uncertainties while ensuring optimal performance concerning prescribed performance indices. But most robust MPC schemes require prior knowledge on the uncertainty, which may not be satisfied in practical applications. Therefore, it is desired to design robust MPC algorithms that proactively update the uncertainty description based on the history of inputs and measurements, motivating the development of adaptive MPC. This dissertation investigates four problems in robust and adaptive MPC from theoretical and application points of view. New algorithms are developed to address these issues efficiently with theoretical guarantees of closed-loop performance. Chapter 1 provides an overview of robust MPC, adaptive MPC, and self-triggered MPC, where the recent advances in these fields are reviewed. Chapter 2 presents notations and preliminary results that are used in this dissertation. Chapter 3 investigates adaptive MPC for a class of constrained linear systems with unknown model parameters. Based on the recursive least-squares (RLS) technique, we design an online set-membership system identification scheme to estimate unknown parameters. Then a novel integration of the proposed estimator and homothetic tube MPC is developed to improve closed-loop performance and reduce conservatism. In Chapter 4, a self-triggered adaptive MPC method is proposed for constrained discrete-time nonlinear systems subject to parametric uncertainties and additive disturbances. Based on the zonotope-based reachable set computation, a set-membership parameter estimator is developed to refine a set-valued description of the time-varying parametric uncertainty under the self-triggered scheduling. We leverage this estimation scheme to design a novel self-triggered adaptive MPC approach for uncertain nonlinear systems. The resultant adaptive MPC method can reduce the average sampling frequency further while preserving comparable closed-loop performance compared with the periodic adaptive MPC method. Chapter 5 proposes a robust nonlinear MPC scheme for the visual servoing of quadrotors subject to external disturbances. By using the virtual camera approach, an image-based visual servoing (IBVS) system model is established with decoupled image kinematics and quadrotor dynamics. A robust MPC scheme is developed to maintain the visual target stay within the field of view of the camera, where the tightened state constraints are constructed based on the Lipschitz condition to tackle external disturbances. In Chapter 6, an adaptive MPC scheme is proposed for the trajectory tracking of perturbed autonomous ground vehicles (AGVs) subject to input constraints. We develop an RLS-based set-membership based parameter to improve the prediction accuracy. In the proposed adaptive MPC scheme, a robustness constraint is designed to handle parametric and additive uncertainties. The proposed constraint has the offline computed shape and online updated shrinkage rate, leading to further reduced conservatism and slightly increased computational complexity compared with the robust MPC methods. Chapter 7 shows some conclusion remarks and future research directions. / Graduate

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<p> Direct policy search (DPS) has been shown to be an efficient method for identifying optimal rules (i.e., policies) for adapting a system in response to changing conditions. This dissertation describes three major advances in the usage of DPS for long-range infrastructure planning, using a specific application domain of flood risk management. We first introduce a new adaptive way to incorporate learning into DPS. The standard approach identifies policies by optimizing their average performance over a large ensemble of future states of the world (SOW). Our approach exploits information gained over time, regarding what kind of SOW is being experienced, to further improve performance via adaptive meta-policies defining how control of the system should switch between policies identified by a standard DPS approach (but trained on different SOWs). We outline the general method and illustrate it using a case study of optimal dike heightening extending the work of Garner and Keller (2018). The meta-policies identified by the adaptive algorithm show Pareto-dominance in two objectives over the standard DPS, with an overall 68% improvement in hypervolume. We also see the improved performance over three grouped SOWs based on future extreme water levels, with the hypervolume improvements of 90%, 46%, and 35% for low, medium, and high water level SOWs respectively. Additionally, we evaluate the degree of improvement achieved by different ways of implementing the algorithm (i.e., different hyperparameter values). This provides guidance for decision makers with different degrees of risk aversion, and computational budgets. </p> <p>Due to simplifying assumptions and limitations of the adaptive DPS model used in the chapter, such as uniform levee design heights, the Surge and Waves Model for Protection Systems (SWaMPS) is presented as a more realistic application of the DPS framework. SWaMPS is a process-based model of surge-based flood risk. This chapter marks the first implementation of DPS using a realistic process-based risk model. The physical process of storm surge and rainfall is simulated independently over multiple reaches, and different frequencies are explored to manage the production system in SWaMPS. The performance of the DPS algorithm is evaluated versus a static intertemporal optimization.</p> <p>The computational burden of evaluating the large ensemble of SOWs to include possible future events in DPS motivates us to apply scenario reduction methods to select representative scenarios that more efficiently span an uncertain parameter space. This allows us to reduce the runtime of the optimization process. We explore a range of data-mining tools, including principal component analysis (PCA) and clustering to reduce the scenarios. We compare the computational efficiency and quality of policies to this optimization problem with reduced ensembles of SOWs.</p>

Machine learning (ML) has become ubiquitous in various disciplines and applications, serving as a powerful tool for developing predictive models to analyze diverse variables of interest. With the advent of the digital era, the proliferation of data has presented numerous opportunities for growth and expansion across various domains. However, along with these opportunities, there is a unique set of challenges that arises due to the dynamic and ever-changing nature of data. These challenges include concept drift, which refers to shifting data distributions over time, and other data-related issues that can be framed as learning problems. Traditional static models are inadequate in handling these issues, underscoring the need for novel approaches to enhance the performance robustness and reliability of ML models to effectively navigate the inherent non-stationarity in the online world. The field of concept drift is characterized by several intricate aspects that challenge learning algorithms, including the analysis of model performance, which requires evaluating and understanding how the ML model's predictive capability is affected by different problem settings. Additionally, determining the magnitude of drift necessary for change detection is an indispensable task, as it involves identifying substantial shifts in data distributions. Moreover, the integration of adaptive methodologies is essential for updating ML models in response to data dynamics, enabling them to maintain their effectiveness and reliability in evolving environments. In light of the significance and complexity of the topic, this dissertation offers a fresh perspective on the performance robustness and adaptivity of ML models in non-stationary environments. The main contributions of this research include exploring and organizing the literature, analyzing the performance of ML models in the presence of different types of drift, and proposing innovative methodologies for drift detection and adaptation that solve real-world problems. By addressing these challenges, this research paves the way for the development of more robust and adaptive ML solutions capable of thriving in dynamic and evolving data landscapes. / Machine learning (ML) is widely used in various disciplines as a powerful tool for developing predictive models to analyze diverse variables. In the digital era, the abundance of data has created growth opportunities, but it also brings challenges due to the dynamic nature of data. One of these challenges is concept drift, the shifting data distributions over time. Consequently, traditional static models are inadequate for handling these challenges in the online world. Concept drift, with its intricate aspects, presents a challenge for learning algorithms. Analyzing model performance and detecting substantial shifts in data distributions are crucial for integrating adaptive methodologies to update ML models in response to data dynamics, maintaining effectiveness and reliability in evolving environments. In this dissertation, a fresh perspective is offered on the robustness and adaptivity of ML models in non-stationary environments. This research explores and organizes existing literature, analyzes ML model performance in the presence of drift, and proposes innovative methodologies for detecting and adapting to drift in real-world problems. The aim is to develop more robust and adaptive ML solutions capable of thriving in dynamic and evolving data landscapes.

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We consider unconstrained Simulation Optimization (SO) problems, that is, optimization problems where the underlying objective function is unknown but can be estimated at any chosen point by repeatedly executing a Monte Carlo (stochastic) simulation. SO, introduced more than six decades ago through the seminal work of Robbins and Monro (and later by Kiefer and Wolfowitz), has recently generated much attention. Such interest is primarily because of SOs flexibility, allowing the implicit specification of functions within the optimization problem, thereby providing the ability to embed virtually any level of complexity. The result of such versatility has been evident in SOs ready adoption in fields as varied as finance, logistics, healthcare, and telecommunication systems. While SO has become popular over the years, Robbins and Monros original stochastic approximation algorithm and its numerous modern incarnations have seen only mixed success in solving SO problems. The primary reason for this is stochastic approximations explicit reliance on a sequence of algorithmic parameters to guarantee convergence. The theory for choosing such parameters is now well-established, but most such theory focuses on asymptotic performance. Automatically choosing parameters to ensure good finite-time performance has remained vexingly elusive, as evidenced by continuing efforts six decades after the introduction of stochastic approximation! The other popular paradigm to solve SO is what has been called sample-average approximation. Sample-average approximation, more a philosophy than an algorithm to solve SO, attempts to leverage advances in modern nonlinear programming by first constructing a deterministic approximation of the SO problem using a fixed sample size, and then applying an appropriate nonlinear programming method. Sample-average approximation is reasonable as a solution paradigm but again suffers from finite-time inefficiency because of the simplistic manner in which sample sizes are prescribed. It turns out that in many SO contexts, the effort expended to execute the Monte Carlo oracle is the single most computationally expensive operation. Sample-average approximation essentially ignores this issue since, irrespective of where in the search space an incumbent solution resides, prescriptions for sample sizes within sample-average approximation remain the same. Like stochastic approximation, notwithstanding beautiful asymptotic theory, sample-average approximation suffers from the lack of automatic implementations that guarantee good finite-time performance. In this dissertation, we ask: can advances in algorithmic nonlinear programming theory be combined with intelligent sampling to create solution paradigms for SO that perform well in finite-time while exhibiting asymptotically optimal convergence rates? We propose and study a general solution paradigm called Sampling Controlled Stochastic Recursion (SCSR). Two simple ideas are central to SCSR: (i) use any recursion, particularly one that you would use (e.g., Newton and quasi- Newton, fixed-point, trust-region, and derivative-free recursions) if the functions involved in the problem were known through a deterministic oracle; and (ii) estimate objects appearing within the recursions (e.g., function derivatives) using Monte Carlo sampling to the extent required. The idea in (i) exploits advances in algorithmic nonlinear programming. The idea in (ii), with the objective of ensuring good finite-time performance and optimal asymptotic rates, minimizes Monte Carlo sampling by attempting to balance the estimated proximity of an incumbent solution with the sampling error stemming from Monte Carlo. This dissertation studies the theoretical and practical underpinnings of SCSR, leading to implementable algorithms to solve SO. We first analyze SCSR in a general context, identifying various sufficient conditions that ensure convergence of SCSRs iterates to a solution. We then analyze the nature of such convergence. For instance, we demonstrate that in SCSRs which guarantee optimal convergence rates, the speed of the underlying (deterministic) recursion and the extent of Monte Carlo sampling are intimately linked, with faster recursions permitting a wider range of Monte Carlo effort. With the objective of translating such asymptotic results into usable algorithms, we formulate a family of SCSRs called Adaptive SCSR (A-SCSR) that adaptively determines how much to sample as a recursion evolves through the search space. A-SCSRs are dynamic algorithms that identify sample sizes to balance estimated squared bias and variance of an incumbent solution. This makes the sample size (at every iteration of A-SCSR) a stopping time, thereby substantially complicating the analysis of the behavior of A-SCSRs iterates. That A-SCSR works well in practice is not surprising" the use of an appropriate recursion and the careful sample size choice ensures this. Remarkably, however, we show that A-SCSRs are convergent to a solution and exhibit asymptotically optimal convergence rates under conditions that are no less general than what has been established for stochastic approximation algorithms. We end with the application of a certain A-SCSR to a parameter estimation problem arising in the context of brain-computer interfaces (BCI). Specifically, we formulate and reduce the problem of probabilistically deciphering the electroencephalograph (EEG) signals recorded from the brain of a paralyzed patient attempting to perform one of a specified set of tasks. Monte Carlo simulation in this context takes a more general view, as the act of drawing an observation from a large dataset accumulated from the recorded EEG signals. We apply A-SCSR to nine such datasets, showing that in most cases A-SCSR achieves correct prediction rates that are between 5 and 15 percent better than competing algorithms. More importantly, due to the incorporated adaptive sampling strategies, A-SCSR tends to exhibit dramatically better efficiency rates for comparable prediction accuracies. / Ph. D.

The advent of the Internet has not only enabled traditional brick-and-mortar retailers to open online channels, but also provided a platform that facilitated consumer-to-consumer information exchange on retailers and/or products. As a result, the purchasing decisions of today's consumers are often affected by the purchasing decisions of other consumers. In this dissertation, we adopt an interdisciplinary approach that brings together tools and concepts from operations management, economics, systems dynamics and marketing literatures to create analytical models in order to address a dual-channel retailer's optimal demand shaping strategy, through e-commerce advertisement efforts, store service levels, and pricing, in this new environment. Our findings show that the retailer's optimal demand shaping strategy, in terms of store service levels and e-commerce advertisement effort, critically depends on the product's e-commerce adoption phase. We also show that in the presence of higher operating costs for the store channel compared to the online channels, a channel-tailored pricing policy always dominates a uniform pricing strategy. Our work sheds light on the benefits of channel integration for multi-channel retailers. We show that the retailer can leverage the online channels to provide in-store pricing and inventory availability information in order to enable a more transparent shopping experience for consumers, and this strategy results in a "win-win" situation for all parties. / Ph. D.