A Taxonomy of Loss Functions for Stochastic Optimal Control

Understand

Stochastic optimal control (SOC) aims to direct the behavior of noisy systems and has widespread applications in science, engineering, and artificial intelligence.

• In particular, reward fine-tuning of diffusion and flow matching models and sampling from unnormalized methods can be recast as SOC problems.
• A recent work has introduced Adjoint Matching (Domingo-Enrich et al., 2024), a loss function for SOC problems that vastly outperforms existing loss functions in the reward fine-tuning setup.
• The goal of this work is to clarify the connections between all the existing (and some new) SOC loss functions.