Abstract

Mathematicians and software developers use the word "function" very differently, and yet, sometimes, things that are in practice implemented using the software developer's "function", are mathematically formalized using the mathematician's "function". This mismatch can lead to inaccurate formalisms. We consider a special case of this meta-problem. Various kinds of agents might, in actual practice, make use of private memory, reading and writing to a memory-bank invisible to the ambient environment. In some sense, we humans do this when we silently subvocalize thoughts about the actions we are taking (at least when the environment we're in is too primitive to probe the contents of our brains). Mathematical function formalizations of agents often ignore this ability. We show that in a general agent-environment framework (of which reinforcement learning is a special case), in a technical sense, such private memories do not enable qualitatively different agent behavior.