  We introduce the study of fairness in multi-armed bandit problems. Our
fairness definition can be interpreted as demanding that given a pool of
applicants (say, for college admission or mortgages), a worse applicant is
never favored over a better one, despite a learning algorithm's uncertainty
over the true payoffs. We prove results of two types.
  First, in the important special case of the classic stochastic bandits
problem (i.e., in which there are no contexts), we provide a provably fair
algorithm based on "chained" confidence intervals, and provide a cumulative
regret bound with a cubic dependence on the number of arms. We further show
that any fair algorithm must have such a dependence. When combined with regret
bounds for standard non-fair algorithms such as UCB, this proves a strong
separation between fair and unfair learning, which extends to the general
contextual case.
  In the general contextual case, we prove a tight connection between fairness
and the KWIK (Knows What It Knows) learning model: a KWIK algorithm for a class
of functions can be transformed into a provably fair contextual bandit
algorithm, and conversely any fair contextual bandit algorithm can be
transformed into a KWIK learning algorithm. This tight connection allows us to
provide a provably fair algorithm for the linear contextual bandit problem with
a polynomial dependence on the dimension, and to show (for a different class of
functions) a worst-case exponential gap in regret between fair and non-fair
learning algorithms
