From open learners to open games
This is an incremental theoretical contribution linking abstract categories in machine learning and game theory, with potential for further exploration.
The paper tackles the problem of connecting two mathematical frameworks, open learners and open games, by proving a faithful symmetric monoidal functor maps supervised neural networks to open games, where parameters are controlled by players and gradient descent dynamics are encoded.
The categories of open learners (due to Fong, Spivak and Tuyéras) and open games (due to the present author, Ghani, Winschel and Zahn) bear a very striking and unexpected similarity. The purpose of this short note is to prove that there is a faithful symmetric monoidal functor from the former to the latter, which means that any supervised neural network (without feedback or other complicating features) can be seen as an open game in a canonical way. Roughly, each parameter is controlled by a different player, and the game's best response relation encodes the dynamics of gradient descent. We suggest paths for further work exploiting the link.