  We propose a fully distributed actor-critic algorithm approximated by deep
neural networks, named \textit{Diff-DAC}, with application to single-task and
to average multitask reinforcement learning (MRL). Each agent has access to
data from its local task only, but it aims to learn a policy that performs well
on average for the whole set of tasks. During the learning process, agents
communicate their value-policy parameters to their neighbors, diffusing the
information across the network, so that they converge to a common policy, with
no need for a central node. The method is scalable, since the computational and
communication costs per agent grow with its number of neighbors. We derive
Diff-DAC's from duality theory and provide novel insights into the standard
actor-critic framework, showing that it is actually an instance of the dual
ascent method that approximates the solution of a linear program. Experiments
suggest that Diff-DAC can outperform the single previous distributed MRL
approach (i.e., Dist-MTLPS) and even the centralized architecture.
