As a result of evolutionary selection, the subunits of naturally occurring protein assemblies often fit together with substantial shape complementarity to generate architectures optimal for function in a manner not achievable by current design approaches. We describe a "top-down" reinforcement learning-based design approach that solves this problem using Monte Carlo tree search to sample protein conformers in the context of an overall architecture and specified functional constraints. Cryo-electron microscopy structures of the designed disk-shaped nanopores and ultracompact icosahedra are very close to the computational models. The icosohedra enable very-high-density display of immunogens and signaling molecules, which potentiates vaccine response and angiogenesis induction. Our approach enables the top-down design of complex protein nanomaterials with desired system properties and demonstrates the power of reinforcement learning in protein design.