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We study the problem of estimating the expected reward of the optimal policyin the stochastic disjoint linear bandit setting. We prove that for certainsettings it is possible to obtain an accurate estimate of the optimal policyvalue even with a number of samples that is sublinear in the number that wouldbe required to \emph{find} a policy that realizes a value close to this optima.We establish nearly matching information theoretic lower bounds, showing thatour algorithm achieves near optimal estimation error. Finally, we demonstratethe effectiveness of our algorithm on joke recommendation and cancer inhibitiondosage selection problems using real datasets.

Sublinear Optimal Policy Value Estimation in Contextual Bandits