  In this paper, we propose a constant word (RAM model) algorithm for regret
minimisation for both finite and infinite Stochastic Multi-Armed Bandit (MAB)
instances. Most of the existing regret minimisation algorithms need to remember
the statistics of all the arms they encounter. This may become a problem for
the cases where the number of available words of memory is limited. Designing
an efficient regret minimisation algorithm that uses a constant number of words
has long been interesting to the community. Some early attempts consider the
number of arms to be infinite, and require the reward distribution of the arms
to belong to some particular family. Recently, for finitely many-armed bandits
an explore-then-commit based algorithm~\citep{Liau+PSY:2018} seems to escape
such assumption. However, due to the underlying PAC-based elimination their
method incurs a high regret. We present a conceptually simple, and efficient
algorithm that needs to remember statistics of at most $M$ arms, and for any
$K$-armed finite bandit instance it enjoys a $O(KM +K^{1.5}\sqrt{T\log
(T/MK)}/M)$ upper-bound on regret. We extend it to achieve sub-linear
\textit{quantile-regret}~\citep{RoyChaudhuri+K:2018} and empirically verify the
efficiency of our algorithm via experiments.
