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Multi-armed bandits" were introduced by Robbins (1952) as a new direction in the then-nascent field of sequential analysis developed during World War II in response to the need for more efficient testing of anti-aircraft gunnery, and subsequently by Bellman (1957) as a concrete application of dynamic programming and optimal control of Markov decision processes. A comprehensive theory that unified both directions emerged in the 1980s and provided important insights and algorithms for diverse applications in many STEM (Science, Technology, Engineering and Mathematics) fields. The turn of the millennium marks the onset of the "personalization revolution"-from personalized medicine to online personalized advertising and recommender systems (such as Netflix's recommendations for movies and TV shows, Amazon's recommendations for products to purchase, and Microsoft's Matchbox recommender)-that calls for the extension of classical bandit theory to nonparametric contextual bandits, in which "contextual" refers to the incorporation of personal information as covariates. Such theory is developed herein, together with illustrative applications, statistical models and computational tools for its implementation.

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Modern neural networks are able to perform at least as well as humans in numerous tasks involving object classification and image generation. However, small perturbations which are imperceptible to humans may significantly degrade the performance of well-trained deep neural networks. We provide a Distributionally Robust Optimization (DRO) framework which integrates human-based image quality assessment methods to design optimal attacks that are imperceptible to humans but significantly damaging to deep neural networks. Through extensive experiments, we show that our attack algorithm generates better-quality (less perceptible to humans) attacks than other state-of-the-art human imperceptible attack methods. Moreover, we demonstrate that DRO training using our optimally designed human imperceptible attacks can improve group fairness in image classification. Towards the end, we provide an algorithmic implementation to speed up DRO training significantly, which could be of independent interest.

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