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Fast Rates for Bandit Optimization with Upper-Confidence Frank-Wolfe

Neural Information Processing Systems

We consider the problem of bandit optimization, inspired by stochastic optimization and online learning problems with bandit feedback. In this problem, the objective is to minimize a global loss function of all the actions, not necessarily a cumulative loss. This framework allows us to study a very general class of problems, with applications in statistics, machine learning, and other fields. To solve this problem, we analyze the Upper-Confidence Frank-Wolfe algorithm, inspired by techniques for bandits and convex optimization. We give theoretical guarantees for the performance of this algorithm over various classes of functions, and discuss the optimality of these results.


The Download: the secrets of vitamin D, and an AI party in Africa

MIT Technology Review

Plus: Google's new image generator has extremely loose guardrails We're learning more about what vitamin D does to our bodies At a checkup a few years ago, a doctor told me I was deficient in vitamin D. But he wouldn't write me a prescription for supplements, simply because, as he put it, everyone in the UK is deficient. Putting the entire population on vitamin D supplements would be too expensive for the country's national health service, he told me. But supplementation--whether covered by a health-care provider or not--can be important. As those of us living in the Northern Hemisphere spend fewer of our waking hours in sunlight, let's consider the importance of vitamin D. Read the full story . This article first appeared in The Checkup, MIT Technology Review's weekly biotech newsletter. Here's why we don't have a cold vaccine.





On Optimal Generalizability in Parametric Learning

Neural Information Processing Systems

We consider the parametric learning problem, where the objective of the learner is determined by a parametric loss function. Employing empirical risk minimization with possibly regularization, the inferred parameter vector will be biased toward the training samples. Such bias is measured by the cross validation procedure in practice where the data set is partitioned into a training set used for training and a validation set, which is not used in training and is left to measure the out-of-sample performance. A classical cross validation strategy is the leave-one-out cross validation (LOOCV) where one sample is left out for validation and training is done on the rest of the samples that are presented to the learner, and this process is repeated on all of the samples. LOOCV is rarely used in practice due to the high computational complexity. In this paper, we first develop a computationally efficient approximate LOOCV (ALOOCV) and provide theoretical guarantees for its performance. Then we use ALOOCV to provide an optimization algorithm for finding the regularizer in the empirical risk minimization framework. In our numerical experiments, we illustrate the accuracy and efficiency of ALOOCV as well as our proposed framework for the optimization of the regularizer.



Parameter-Free Online Learning via Model Selection

Neural Information Processing Systems

Finally, we generalize these results by providing oracle inequalities for arbitrary non-linear classes in the online supervised learning model. These results are all derived through a unified meta-algorithm scheme using a novel "multi-scale" algorithm for prediction with expert advice based on random playout, which may be of