  In Reinforcement Learning (RL), the goal of agents is to discover an optimal
policy that maximizes the expected cumulative rewards. This objective may also
be viewed as finding a policy that optimizes a linear function of its
state-action occupancy measure, hereafter referred as Linear RL. However, many
supervised and unsupervised RL problems are not covered in the Linear RL
framework, such as apprenticeship learning, pure exploration and variational
intrinsic control, where the objectives are non-linear functions of the
occupancy measures. RL with non-linear utilities looks unwieldy, as methods
like Bellman equation, value iteration, policy gradient, dynamic programming
that had tremendous success in Linear RL, fail to trivially generalize. In this
paper, we derive the policy gradient theorem for RL with general utilities. The
policy gradient theorem proves to be a cornerstone in Linear RL due to its
elegance and ease of implementability. Our policy gradient theorem for RL with
general utilities shares the same elegance and ease of implementability. Based
on the policy gradient theorem derived, we also present a simple sample-based
algorithm. We believe our results will be of interest to the community and
offer inspiration to future works in this generalized setting.
