We propose computationally efficient algorithms foronline linear optimization with bandit feedback, in which a player chooses anaction vectorfrom a given (possibly infinite) setA Rd, and then suffers a loss that can be expressed as a linear function in action vectors.

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/

Weconsider afinite-horizon multi-armed bandit (MAB) problem inaBayesian setting, for which we propose aninformation relaxation samplingframework.

In this paper, we propose an online convex optimization approach with two different levels of adaptivity. On a higher level, our approach is agnostic to the unknown types and curvatures of the online functions, while at a lower level, it can exploit the unknown niceness of the environments and attain problem-dependent guarantees.

In practice, however, such biased training data are commonly encountered.

Toaddressthis, we need simple'normative' assumptions, which cannot be deduced exclusively fromobservations.