  Contextual bandits have the same exploration-exploitation trade-off as
standard multi-armed bandits. On adding positive externalities that decay with
time, this problem becomes much more difficult as wrong decisions at the start
are hard to recover from. We explore existing policies in this setting and
highlight their biases towards the inherent reward matrix. We propose a
rejection based policy that achieves a low regret irrespective of the structure
of the reward probability matrix.
