  Modifying the reward-biased maximum likelihood method originally proposed in
the adaptive control literature, we propose novel learning algorithms to handle
the explore-exploit trade-off in linear bandits problems as well as generalized
linear bandits problems. We develop novel index policies that we prove achieve
order-optimality, and show that they achieve empirical performance competitive
with the state-of-the-art benchmark methods in extensive experiments. The new
policies achieve this with low computation time per pull for linear bandits,
and thereby resulting in both favorable regret as well as computational
efficiency.
