* 19 pages, 13 figures. To appear in AISTATS 2018. Corrected typos, and
made minor stylistic changes throughout. Main results unchanged. Added
section I (and Figure 13) in appendix Access Paper or Ask Questions
* Changes from previous version: (a) Corrected typos throughout. (b) In
earlier version, regret was defined as a conditional expectation (and hence
bounded w.h.p); this is changed to an expectation now resulting in minor
changes in statements of Lemma 1, Theorems 1,2 and Corollary 1. See Remark 1.
(c) Added Remark 3, and corrected statement of Proposition 3 Access Paper or Ask Questions
* To appear in Information and Inference: A Journal of the IMA. Made
following changes after review process: (a) Corrected typos throughout the
text. (b) Corrected choice of sampling distribution in Section 5, see eqs.
(5.2), (5.3). (c) More detailed comparison with existing work in Section 8.
(d) Added Section B in appendix on roots of cubic equation Access Paper or Ask Questions