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We consider the problem of online nonparametric regression with arbitrary deterministic sequences. Using ideas from the chaining technique, we design an algorithm that achieves a Dudley-type regret bound similar to the one obtained in a non-constructive fashion by Rakhlin and Sridharan (2014). Our regret bound is expressed in terms of the metric entropy in the sup norm, which yields optimal guarantees when the metric and sequential entropies are of the same order of magnitude. In particular our algorithm is the first one that achieves optimal rates for online regression over Hölder balls.

We review some recent extensions of the so-called generalized empirical likelihood method, when the Kullback distance is replaced by some general convex divergence. We propose to use, instead of empirical likelihood, some regularized form or quasi-empirical likelihood method, corresponding to a convex combination of Kullback and chi2 discrepancies. We show that for some adequate choice of the weight in this combination, the corresponding quasi-empirical likelihood is Bartlett-correctable.

Adaptive clinical trial design methods have garnered growing attention in the recent years, in large part due to their greater flexibility over their traditional counterparts. One such design is the so-called covariate-adjusted, response-adaptive (CARA) randomized controlled trial (RCT).

The stochastic multi-armed bandit model is a simple abstraction that has proven useful in many different contexts in statistics and machine learning. Whereas the achievable limit in terms of regret minimization is now well known, our aim is to contribute to a better understanding of the performance in terms of identifying the m best arms. We introduce generic notions of complexity for the two dominant frameworks considered in the literature: fixed-budget and fixed-confidence settings.

We study some extensions of the empirical likelihood method, when the Kullback distance is replaced by some general convex divergence or phi-discrepancy. We show that this generalized empirical likelihood method is asymptotically valid for general Hadamard differentiable functionals.