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Pure exploration in multi-armed bandits has emerged as an important framework for modeling decision making and search under uncertainty. In modern applications however, one is often faced with a tremendously large number of options and even obtaining one observation per option may be too costly rendering traditional pure exploration algorithms ineffective. Fortunately, one often has access to similarity relationships amongst the options that can be leveraged. In this paper, we consider the pure exploration problem in stochastic multi-armed bandits where the similarities between the arms is captured by a graph and the rewards may be represented as a smooth signal on this graph. In particular, we consider the problem of finding the arm with the maximum reward (i.e., the maximizing problem) or one that has sufficiently high reward (i.e., the satisficing problem) under this model. We propose novel algorithms GRUB (GRaph based UcB) and zeta-GRUB for these problems and provide theoretical characterization of their performance which specifically elicits the benefit of the graph side information. We also prove a lower bound on the data requirement that shows a large class of problems where these algorithms are near-optimal. We complement our theory with experimental results that show the benefit of capitalizing on such side information. 

This is a Complete Research paper. Understanding models is important for engineering students, but not often taught explicitly in first-year courses. Although there are many types of models in engineering, studies have shown that engineering students most commonly identify prototyping or physical models when asked about modeling. In order to evaluate students’ understanding of different types of models used in engineering and the effectiveness of interventions designed to teach modeling, a survey was developed. This paper describes development of a framework to categorize the types of engineering models that first-year engineering students discuss based on both previous literature and students’ responses to survey questions about models. In Fall 2019, the survey was administered to first-year engineering students to investigate their awareness of types of models and understanding of how to apply different types of models in solving engineering problems. Students’ responses to three questions from the survey were analyzed in this study: 1. What is a model in science, technology, engineering, and mathematics (STEM) fields?, 2. List different types of models that you can think of., and 3. Describe each different type of model you listed. Responses were categorized by model type and the framework was updated through an iterative coding process. After four rounds of analysis of 30 different students’ responses, an acceptable percentage agreement was reached between independent researchers coding the data. Resulting frequencies of the various model types identified by students are presented along with representative student responses to provide insight into students’ understanding of models in STEM. This study is part of a larger project to understand the impact of modeling interventions on students’ awareness of models and their ability to build and apply models. 

To succeed in engineering careers, students must be able to create and apply models to certain problems. The different types of modeling skills include physical, mathematical, computational, graphing, and financial. However, many students struggle to define and form relevant models in their engineering courses. We are hoping that the students are able to better define and apply models in their engineering courses after they have completed the MATLAB and/or CATIA courses. We also are hoping to see a difference in model identification between the MATLAB and CATIA courses. All students in the MATLAB and CATIA courses must be able to understand and create models in order to solve problems and think critically in engineering. Students need foundational knowledge about basic modeling skills that will be effective in their course. The goal is for students to create an approach to help them solve problems logically and apply different modeling skills.