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Poster
Leveraging Good Representations in Linear Contextual Bandits
Matteo Papini · Andrea Tirinzoni · Marcello Restelli · Alessandro Lazaric · Matteo Pirotta

Thu Jul 22 09:00 PM -- 11:00 PM (PDT) @ Virtual #None
The linear contextual bandit literature is mostly focused on the design of efficient learning algorithms for a given representation. However, a contextual bandit problem may admit multiple linear representations, each one with different characteristics that directly impact the regret of the learning algorithm. In particular, recent works showed that there exist ``good'' representations for which constant problem-dependent regret can be achieved. In this paper, we first provide a systematic analysis of the different definitions of ``good'' representations proposed in the literature. We then propose a novel selection algorithm able to adapt to the best representation in a set of $M$ candidates. We show that the regret is indeed never worse than the regret obtained by running \textsc{LinUCB} on best representation (up to a $\ln M$ factor). As a result, our algorithm achieves constant regret if a ``good'' representation is available in the set. Furthermore, we show the algorithm may still achieve constant regret by implicitly constructing a ``good'' representation, even when none of the initial representations is ``good''. Finally, we validate our theoretical findings in a number of standard contextual bandit problems.

Author Information

Matteo Papini (Universitat Pompeu Fabra)
Andrea Tirinzoni (Inria)
Marcello Restelli (Politecnico di Milano)
Alessandro Lazaric (Facebook AI Research)
Matteo Pirotta (Facebook AI Research)

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