Bio: Jeffrey Negrea is a 5th year Ph.D. candidate and Vanier scholar at the University of Toronto in the department of Statistical Sciences, and a graduate student researcher at the Vector Institute, working with Daniel Roy on foundational problems in computational statistics, machine learning, and sequential decision making. His research focuses on questions of reliability and robustness for statistical and machine learning methods. His contributions are broad: he has recent work addressing robustness to the IID assumption in sequential decision making, the role of regularization in statistical learning, the connection between stochastic optimization and uncertainty quantification, and approximation methods in MCMC. Previously, Jeff completed his B.Math. at the University of Waterloo, and his M.Sc. in Statistics at the University of Toronto.
Talk Title: Adapting to failure of the IID assumption for sequential prediction
Talk Abstract: We consider sequential prediction with expert advice when data are generated from distributions varying arbitrarily within an unknown constraint set. We quantify relaxations of the classical IID assumption in terms of these constraint sets, with IID sequences at one extreme and adversarial mechanisms at the other. The Hedge algorithm, long known to be minimax optimal in the adversarial regime, was recently shown to be minimax optimal for IID data. We show that Hedge with deterministic learning rates is suboptimal between these extremes, and present new algorithms that adaptively achieve the minimax optimal rate of regret with respect to our relaxations of the IID assumption, and do so without knowledge of the underlying constraint set. We analyze our algorithm using the follow-the-regularized-leader framework, and prove it corresponds to Hedge with adaptive learning rates.