Near Instance Optimal Model Selection for Pure Exploration Linear
Bandits
- URL: http://arxiv.org/abs/2109.05131v1
- Date: Fri, 10 Sep 2021 22:56:58 GMT
- Title: Near Instance Optimal Model Selection for Pure Exploration Linear
Bandits
- Authors: Yinglun Zhu, Julian Katz-Samuels, Robert Nowak
- Abstract summary: We study the model selection problem in the pure exploration linear bandit setting.
Our goal is to automatically adapt to the instance-dependent complexity measure of the smallest hypothesis class.
Our algorithms define a new optimization problem based on experimental design.
- Score: 20.67688737534517
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: The model selection problem in the pure exploration linear bandit setting is
introduced and studied in both the fixed confidence and fixed budget settings.
The model selection problem considers a nested sequence of hypothesis classes
of increasing complexities. Our goal is to automatically adapt to the
instance-dependent complexity measure of the smallest hypothesis class
containing the true model, rather than suffering from the complexity measure
related to the largest hypothesis class. We provide evidence showing that a
standard doubling trick over dimension fails to achieve the optimal
instance-dependent sample complexity. Our algorithms define a new optimization
problem based on experimental design that leverages the geometry of the action
set to efficiently identify a near-optimal hypothesis class. Our fixed budget
algorithm uses a novel application of a selection-validation trick in bandits.
This provides a new method for the understudied fixed budget setting in linear
bandits (even without the added challenge of model selection). We further
generalize the model selection problem to the misspecified regime, adapting our
algorithms in both fixed confidence and fixed budget settings.
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