Budget-Constrained Item Cold-Start Handling in Collaborative Filtering Recommenders via Optimal Design

It is well known that collaborative filtering (CF) based recommender systems provide better modeling of users and items associated with considerable rating history. The lack of historical ratings results in the user and the item cold-start problems. The latter is the main focus of this work. Most of the current literature addresses this problem by integrating content-based recommendation techniques to model the new item. However, in many cases such content is not available, and the question arises is whether this problem can be mitigated using CF techniques only. We formalize this problem as an optimization problem: given a new item, a pool of available users, and a budget constraint, select which users to assign with the task of rating the new item in order to minimize the prediction error of our model. We show that the objective function is monotone-supermodular, and propose efficient optimal design based algorithms that attain an approximation to its optimum. Our findings are verified by an empirical study using the Netflix dataset, where the proposed algorithms outperform several baselines for the problem at hand.Comment: 11 pages, 2 figure

Diversity and Novelty: Measurement, Learning and Optimization

The primary objective of this dissertation is to investigate research methods to answer the question: ``How (and why) does one measure, learn and optimize novelty and diversity of a set of items?" The computational models we develop to answer this question also provide foundational mathematical techniques to throw light on the following three questions: 1. How does one reliably measure the creativity of ideas? 2. How does one form teams to evaluate design ideas? 3. How does one filter good ideas out of hundreds of submissions? Solutions to these questions are key to enable the effective processing of a large collection of design ideas generated in a design contest. In the first part of the dissertation, we discuss key qualities needed in design metrics and propose new diversity and novelty metrics for judging design products. We show that the proposed metrics have higher accuracy and sensitivity compared to existing alternatives in literature. To measure the novelty of a design item, we propose learning from human subjective responses to derive low dimensional triplet embeddings. To measure diversity, we propose an entropy-based diversity metric, which is more accurate and sensitive than benchmarks. In the second part of the dissertation, we introduce the bipartite b-matching problem and argue the need for incorporating diversity in the objective function for matching problems. We propose new submodular and supermodular objective functions to measure diversity and develop multiple matching algorithms for diverse team formation in offline and online cases. Finally, in the third part, we demonstrate filtering and ranking of ideas using diversity metrics based on Determinantal Point Processes as well as submodular functions. In real-world crowd experiments, we demonstrate that such ranking enables increased efficiency in filtering high-quality ideas compared to traditionally used methods

Constrained Learning And Inference

Data and learning have become core components of the information processing and autonomous systems upon which we increasingly rely on to select job applicants, analyze medical data, and drive cars. As these systems become ubiquitous, so does the need to curtail their behavior. Left untethered, they are susceptible to tampering (adversarial examples) and prone to prejudiced and unsafe actions. Currently, the response of these systems is tailored by leveraging domain expert knowledge to either construct models that embed the desired properties or tune the training objective so as to promote them. While effective, these solutions are often targeted to specific behaviors, contexts, and sometimes even problem instances and are typically not transferable across models and applications. What is more, the growing scale and complexity of modern information processing and autonomous systems renders this manual behavior tuning infeasible. Already today, explainability, interpretability, and transparency combined with human judgment are no longer enough to design systems that perform according to specifications. The present thesis addresses these issues by leveraging constrained statistical optimization. More specifically, it develops the theoretical underpinnings of constrained learning and constrained inference to provide tools that enable solving statistical problems under requirements. Starting with the task of learning under requirements, it develops a generalization theory of constrained learning akin to the existing unconstrained one. By formalizing the concept of probability approximately correct constrained (PACC) learning, it shows that constrained learning is as hard as its unconstrained learning and establishes the constrained counterpart of empirical risk minimization (ERM) as a PACC learner. To overcome challenges involved in solving such non-convex constrained optimization problems, it derives a dual learning rule that enables constrained learning tasks to be tackled by through unconstrained learning problems only. It therefore concludes that if we can deal with classical, unconstrained learning tasks, then we can deal with learning tasks with requirements. The second part of this thesis addresses the issue of constrained inference. In particular, the issue of performing inference using sparse nonlinear function models, combinatorial constrained with quadratic objectives, and risk constraints. Such models arise in nonlinear line spectrum estimation, functional data analysis, sensor selection, actuator scheduling, experimental design, and risk-aware estimation. Although inference problems assume that models and distributions are known, each of these constraints pose serious challenges that hinder their use in practice. Sparse nonlinear functional models lead to infinite dimensional, non-convex optimization programs that cannot be discretized without leading to combinatorial, often NP-hard, problems. Rather than using surrogates and relaxations, this work relies on duality to show that despite their apparent complexity, these models can be fit efficiently, i.e., in polynomial time. While quadratic objectives are typically tractable (often even in closed form), they lead to non-submodular optimization problems when subject to cardinality or matroid constraints. While submodular functions are sometimes used as surrogates, this work instead shows that quadratic functions are close to submodular and can also be optimized near-optimally. The last chapter of this thesis is dedicated to problems involving risk constraints, in particular, bounded predictive mean square error variance estimation. Despite being non-convex, such problems are equivalent to a quadratically constrained quadratic program from which a closed-form estimator can be extracted. These results are used throughout this thesis to tackle problems in signal processing, machine learning, and control, such as fair learning, robust learning, nonlinear line spectrum estimation, actuator scheduling, experimental design, and risk-aware estimation. Yet, they are applicable much beyond these illustrations to perform safe reinforcement learning, sensor selection, multiresolution kernel estimation, and wireless resource allocation, to name a few

Dynamic Constrained Submodular Optimization with Polylogarithmic Update Time

Maximizing a monotone submodular function under cardinality constraint $k$ is a core problem in machine learning and database with many basic applications, including video and data summarization, recommendation systems, feature extraction, exemplar clustering, and coverage problems. We study this classic problem in the fully dynamic model where a stream of insertions and deletions of elements of an underlying ground set is given and the goal is to maintain an approximate solution using a fast update time. A recent paper at NeurIPS'20 by Lattanzi, Mitrovic, Norouzi{-}Fard, Tarnawski, Zadimoghaddam claims to obtain a dynamic algorithm for this problem with a $\frac{1}{2} -\epsilon$ approximation ratio and a query complexity bounded by $\mathrm{poly}(\log(n),\log(k),\epsilon^{-1})$. However, as we explain in this paper, the analysis has some important gaps. Having a dynamic algorithm for the problem with polylogarithmic update time is even more important in light of a recent result by Chen and Peng at STOC'22 who show a matching lower bound for the problem -- any randomized algorithm with a $\frac{1}{2}+\epsilon$ approximation ratio must have an amortized query complexity that is polynomial in $n$. In this paper, we develop a simpler algorithm for the problem that maintains a $(\frac{1}{2}-\epsilon)$-approximate solution for submodular maximization under cardinality constraint $k$ using a polylogarithmic amortized update time

Best-Arm Identification in Linear Bandits

We study the best-arm identification problem in linear bandit, where the rewards of the arms depend linearly on an unknown parameter $\theta^*$ and the objective is to return the arm with the largest reward. We characterize the complexity of the problem and introduce sample allocation strategies that pull arms to identify the best arm with a fixed confidence, while minimizing the sample budget. In particular, we show the importance of exploiting the global linear structure to improve the estimate of the reward of near-optimal arms. We analyze the proposed strategies and compare their empirical performance. Finally, as a by-product of our analysis, we point out the connection to the $G$-optimality criterion used in optimal experimental design.Comment: In Advances in Neural Information Processing Systems 27 (NIPS), 201

Emergency rapid mapping with drones: models and solution approaches for offline and online mission planning

Die Verfügbarkeit von unbemannten Luftfahrzeugen (unmanned aerial vehicles oder UAVs) und die Fortschritte in der Entwicklung leichtgewichtiger Sensorik eröffnen neue Möglichkeiten für den Einsatz von Fernerkundungstechnologien zur Schnellerkundung in Großschadenslagen. Hier ermöglichen sie es beispielsweise nach Großbränden, Einsatzkräften in kurzer Zeit ein erstes Lagebild zur Verfügung zu stellen. Die begrenzte Flugdauer der UAVs wie auch der Bedarf der Einsatzkräfte nach einer schnellen Ersteinschätzung bedeuten jedoch, dass die betroffenen Gebiete nur stichprobenartig überprüft werden können. In Kombination mit Interpolationsverfahren ermöglichen diese Stichproben anschließend eine Abschätzung der Verteilung von Gefahrstoffen. Die vorliegende Arbeit befasst sich mit dem Problem der Planung von UAV-Missionen, die den Informationsgewinn im Notfalleinsatz maximieren. Das Problem wird dabei sowohl in der Offline-Variante, die Missionen vor Abflug bestimmt, als auch in der Online-Variante, bei der die Pläne während des Fluges der UAVs aktualisiert werden, untersucht. Das übergreifende Ziel ist die Konzeption effizienter Modelle und Verfahren, die Informationen über die räumliche Korrelation im beobachteten Gebiet nutzen, um in zeitkritischen Situationen Lösungen von hoher Vorhersagegüte zu bestimmen. In der Offline-Planung wird das generalized correlated team orienteering problem eingeführt und eine zweistufige Heuristik zur schnellen Bestimmung explorativer UAV-Missionen vorgeschlagen. In einer umfangreichen Studie wird die Leistungsfähigkeit und Konkurrenzfähigkeit der Heuristik hinsichtlich Rechenzeit und Lösungsqualität bestätigt. Anhand von in dieser Arbeit neu eingeführten Benchmarkinstanzen wird der höhere Informationsgewinn der vorgeschlagenen Modelle im Vergleich zu verwandten Konzepten aufgezeigt. Im Bereich der Online-Planung wird die Kombination von lernenden Verfahren zur Modellierung der Schadstoffe mit Planungsverfahren, die dieses Wissen nutzen, um Missionen zu verbessern, untersucht. Hierzu wird eine breite Spanne von Lösungsverfahren aus unterschiedlichen Disziplinen klassifiziert und um neue effiziente Modellierungsvarianten für die Schnellerkundung ergänzt. Die Untersuchung im Rahmen einer ereignisdiskreten Simulation zeigt, dass vergleichsweise einfache Approximationen räumlicher Zusammenhänge in sehr kurzer Zeit Lösungen hoher Qualität ermöglichen. Darüber hinaus wird die höhere Robustheit genauerer, aber aufwändigerer Modelle und Lösungskonzepte demonstriert

Optimization and Communication in UAV Networks

UAVs are becoming a reality and attract increasing attention. They can be remotely controlled or completely autonomous and be used alone or as a fleet and in a large set of applications. They are constrained by hardware since they cannot be too heavy and rely on batteries. Their use still raises a large set of exciting new challenges in terms of trajectory optimization and positioning when they are used alone or in cooperation, and communication when they evolve in swarm, to name but a few examples. This book presents some new original contributions regarding UAV or UAV swarm optimization and communication aspects