A Taxonomy of Loss Functions for Stochastic Optimal Control

Fuente: arXiv
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Main Author: Domingo-Enrich, Carles
Format: Preprint
Published: 2024
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author Domingo-Enrich, Carles
author_facet Domingo-Enrich, Carles
contents 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. Namely, we show that SOC loss functions can be grouped into classes that share the same gradient in expectation, which means that their optimization landscape is the same; they only differ in their gradient variance. We perform simple SOC experiments to understand the strengths and weaknesses of different loss functions.
format Preprint
id arxiv_https___arxiv_org_abs_2410_00345
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle A Taxonomy of Loss Functions for Stochastic Optimal Control
Domingo-Enrich, Carles
Machine Learning
Optimization and Control
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. Namely, we show that SOC loss functions can be grouped into classes that share the same gradient in expectation, which means that their optimization landscape is the same; they only differ in their gradient variance. We perform simple SOC experiments to understand the strengths and weaknesses of different loss functions.
title A Taxonomy of Loss Functions for Stochastic Optimal Control
topic Machine Learning
Optimization and Control
url https://arxiv.org/abs/2410.00345