  It is well known that quantifying uncertainty in the action-value estimates
is crucial for efficient exploration in reinforcement learning. Ensemble
sampling offers a relatively computationally tractable way of doing this using
randomized value functions. However, it still requires a huge amount of
computational resources for complex problems. In this paper, we present an
alternative, computationally efficient way to induce exploration using index
sampling. We use an indexed value function to represent uncertainty in our
action-value estimates. We first present an algorithm to learn parameterized
indexed value function through a distributional version of temporal difference
in a tabular setting and prove its regret bound. Then, in a computational point
of view, we propose a dual-network architecture, Parameterized Indexed Networks
(PINs), comprising one mean network and one uncertainty network to learn the
indexed value function. Finally, we show the efficacy of PINs through
computational experiments.
