  The statistical framework of Generalized Linear Models (GLM) can be applied
to sequential problems involving categorical or ordinal rewards associated, for
instance, with clicks, likes or ratings. In the example of binary rewards,
logistic regression is well-known to be preferable to the use of standard
linear modeling. Previous works have shown how to deal with GLMs in contextual
online learning with bandit feedback when the environment is assumed to be
stationary. In this paper, we relax this latter assumption and propose two
upper confidence bound based algorithms that make use of either a sliding
window or a discounted maximum-likelihood estimator. We provide theoretical
guarantees on the behavior of these algorithms for general context sequences
and in the presence of abrupt changes. These results take the form of high
probability upper bounds for the dynamic regret that are of order d^2/3 G^1/3
T^2/3 , where d, T and G are respectively the dimension of the unknown
parameter, the number of rounds and the number of breakpoints up to time T. The
empirical performance of the algorithms is illustrated in simulated
environments.
