AI and the World's Hard Problems · Theoretical computer science · arXiv · 2026-10-23
An Optimal Control Approach To Transformer Training
The study treats Transformer training as an optimal control problem that respects structural constraints, including input-independent execution and positional dependence. The authors lift the model to a fully observed Markov decision process over probability measures, prove that globally optimal policies exist, and propose a triply quantized training procedure that quantizes the state, measure and action spaces. They show that any optimal policy for the quantized model is near-optimal for the original training problem, offering a theoretical alternative to gradient-based training that requires no smoothness or convexity.