  Imitation learning (IL) is a popular approach in the continuous control
setting as among other reasons it circumvents the problems of reward
mis-specification and exploration in reinforcement learning (RL). In IL from
demonstrations, an important challenge is to obtain agent policies that are
smooth with respect to the inputs. Learning through imitation a policy that is
smooth as a function of a large state-action ($s$-$a$) space (typical of high
dimensional continuous control environments) can be challenging. We take a
first step towards tackling this issue by using smoothness inducing
regularizers on \textit{both} the policy and the cost models of adversarial
imitation learning. Our regularizers work by ensuring that the cost function
changes in a controlled manner as a function of $s$-$a$ space; and the agent
policy is well behaved with respect to the state space. We call our new smooth
IL algorithm \textit{Smooth Policy and Cost Imitation Learning} (SPaCIL,
pronounced 'Special'). We introduce a novel metric to quantify the smoothness
of the learned policies. We demonstrate SPaCIL's superior performance on
continuous control tasks from MuJoCo. The algorithm not just outperforms the
state-of-the-art IL algorithm on our proposed smoothness metric, but, enjoys
added benefits of faster learning and substantially higher average return.
