  The lottery ticket hypothesis questions the role of overparameterization in
supervised deep learning. But how is the performance of winning lottery tickets
affected by the distributional shift inherent to reinforcement learning
problems? In this work, we address this question by comparing sparse agents who
have to address the non-stationarity of the exploration-exploitation problem
with supervised agents trained to imitate an expert. We show that feed-forward
networks trained with behavioural cloning compared to reinforcement learning
can be pruned to higher levels of sparsity without performance degradation.
This suggests that in order to solve the RL-specific distributional shift
agents require more degrees of freedom. Using a set of carefully designed
baseline conditions, we find that the majority of the lottery ticket effect in
both learning paradigms can be attributed to the identified mask rather than
the weight initialization. The input layer mask selectively prunes entire input
dimensions that turn out to be irrelevant for the task at hand. At a moderate
level of sparsity the mask identified by iterative magnitude pruning yields
minimal task-relevant representations, i.e., an interpretable inductive bias.
Finally, we propose a simple initialization rescaling which promotes the robust
identification of sparse task representations in low-dimensional control tasks.
