  We consider the combinatorial bandits problem with semi-bandit feedback under
finite sampling budget constraints, in which the learner can carry out its
action only for a limited number of times specified by an overall budget. The
action is to choose a set of arms, whereupon feedback for each arm in the
chosen set is received. Unlike existing works, we study this problem in a
non-stochastic setting with subset-dependent feedback, i.e., the semi-bandit
feedback received could be generated by an oblivious adversary and also might
depend on the chosen set of arms. In addition, we consider a general feedback
scenario covering both the numerical-based as well as preference-based case and
introduce a sound theoretical framework for this setting guaranteeing sensible
notions of optimal arms, which a learner seeks to find. We suggest a generic
algorithm suitable to cover the full spectrum of conceivable arm elimination
strategies from aggressive to conservative. Theoretical questions about the
sufficient and necessary budget of the algorithm to find the best arm are
answered and complemented by deriving lower bounds for any learning algorithm
for this problem scenario.

Machine Learning;Machine Learning