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Anytime Model Selection in Linear Bandits
Parnian Kassraie · Aldo Pacchiano · Nicolas Emmenegger · Andreas Krause

Fri Jul 28 06:30 PM -- 06:40 PM (PDT) @
Event URL: https://openreview.net/forum?id=uvJjhYhqLQ »
Model selection in the context of bandit optimization is a challenging problem, as it requires balancing exploration and exploitation not only for action selection, but also for model selection. One natural approach is to rely on online learning algorithms that treat different models as experts. Existing methods, however, scale poorly ($\mathrm{poly}M$) with the number of models $M$ in terms of their regret. We develop ALEXP, an anytime algorithm, which has an exponentially improved ($\log M$) dependence on $M$ for its regret. We neither require knowledge of the horizon $n$, nor rely on an initial purely exploratory stage. Our approach utilizes a novel time-uniform analysis of the Lasso, by defining a self-normalized martingale sequence based on the empirical process error, establishing a new connection between interactive learning and high-dimensional statistics.

Author Information

Parnian Kassraie (ETH Zurich)

RA at LAS

Aldo Pacchiano (Broad Institute)
Nicolas Emmenegger (Department of Computer Science, ETHZ - ETH Zurich)
Andreas Krause (ETH Zurich)
Andreas Krause

Andreas Krause is a Professor of Computer Science at ETH Zurich, where he leads the Learning & Adaptive Systems Group. He also serves as Academic Co-Director of the Swiss Data Science Center and Chair of the ETH AI Center, and co-founded the ETH spin-off LatticeFlow. Before that he was an Assistant Professor of Computer Science at Caltech. He received his Ph.D. in Computer Science from Carnegie Mellon University (2008) and his Diplom in Computer Science and Mathematics from the Technical University of Munich, Germany (2004). He is a Max Planck Fellow at the Max Planck Institute for Intelligent Systems, an ELLIS Fellow, a Microsoft Research Faculty Fellow and a Kavli Frontiers Fellow of the US National Academy of Sciences. He received the Rössler Prize, ERC Starting Investigator and ERC Consolidator grants, the German Pattern Recognition Award, an NSF CAREER award as well as the ETH Golden Owl teaching award. His research has received awards at several premier conferences and journals, including the ACM SIGKDD Test of Time award 2019 and the ICML Test of Time award 2020. Andreas Krause served as Program Co-Chair for ICML 2018, and currently serves as General Chair for ICML 2023 and as Action Editor for the Journal of Machine Learning Research.

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