  The adaptive and surprising emergent properties of biological materials
self-assembled in far-from-equilibrium environments serve as an inspiration for
efforts to design nanomaterials and their properties. In particular,
controlling the conditions of self-assembly can modulate material properties,
but there is no systematic understanding of either how to parameterize this
control or how \emph{controllable} a given material can be. Here, we
demonstrate that branched actin networks can be encoded with
\textit{metamaterial} properties by dynamically controlling the applied force
under which they grow, and that the protocols can be selected using multi-task
reinforcement learning. These actin networks have tunable responses over a
large dynamic range depending on the chosen external protocol, providing a
pathway to encoding ``memory'' within these structures. Interestingly, we show
that encoding memory requires dissipation and the rate of encoding is
constrained by the flow of entropy -- both physical and information
theoretical. Taken together, these results emphasize the utility and necessity
of nonequilibrium control for designing self-assembled nanostructures.
