  Contextual sequential decision problems with categorical or numerical
observations are ubiquitous and Generalized Linear Bandits (GLB) offer a solid
theoretical framework to address them. In contrast to the case of linear
bandits, existing algorithms for GLB have two drawbacks undermining their
applicability. First, they rely on excessively pessimistic concentration bounds
due to the non-linear nature of the model. Second, they require either
non-convex projection steps or burn-in phases to enforce boundedness of the
estimators. Both of these issues are worsened when considering non-stationary
models, in which the GLB parameter may vary with time. In this work, we focus
on self-concordant GLB (which include logistic and Poisson regression) with
forgetting achieved either by the use of a sliding window or exponential
weights. We propose a novel confidence-based algorithm for the maximum-likehood
estimator with forgetting and analyze its perfomance in abruptly changing
environments. These results as well as the accompanying numerical simulations
highlight the potential of the proposed approach to address non-stationarity in
GLB.
