  Thompson sampling is a well-known approach for balancing exploration and
exploitation in reinforcement learning. It requires the posterior distribution
of value-action functions to be maintained; this is generally intractable for
tasks that have a high dimensional state-action space. We derive a variational
Thompson sampling approximation for DQNs which uses a deep network whose
parameters are perturbed by a learned variational noise distribution. We
interpret the successful NoisyNets method \cite{fortunato2018noisy} as an
approximation to the variational Thompson sampling method that we derive.
Further, we propose State Aware Noisy Exploration (SANE) which seeks to improve
on NoisyNets by allowing a non-uniform perturbation, where the amount of
parameter perturbation is conditioned on the state of the agent. This is done
with the help of an auxiliary perturbation module, whose output is state
dependent and is learnt end to end with gradient descent. We hypothesize that
such state-aware noisy exploration is particularly useful in problems where
exploration in certain \textit{high risk} states may result in the agent
failing badly. We demonstrate the effectiveness of the state-aware exploration
method in the off-policy setting by augmenting DQNs with the auxiliary
perturbation module.
