Diffusion-DFL: Decision-focused Diffusion Models for Stochastic Optimization

Area of Science:

• Machine Learning
• Optimization
• Artificial Intelligence

Background:

• Traditional decision-focused learning (DFL) relies on deterministic predictions, which fail to capture real-world environmental stochasticity.
• Existing methods are limited in handling uncertainty inherent in complex systems.

Purpose of the Study:

• To develop the first diffusion-based decision-focused learning (DFL) approach.
• To address the limitations of deterministic predictions in DFL by incorporating distributional uncertainty.

Main Methods:

• Formulated diffusion DFL using the reparameterization trick for end-to-end training.
• Proposed a lightweight score function estimator to mitigate memory and compute intensity during diffusion sampling.
• Optimized decisions by solving stochastic optimization problems with samples from a trained diffusion model.

Main Results:

• The proposed diffusion DFL approach consistently outperformed strong baselines in decision quality.
• The lightweight score function estimator proved effective in avoiding computationally intensive backpropagation through diffusion sampling.
• Demonstrated the efficacy of diffusion models in representing parameter distributions for improved decision-making.

Conclusions:

• Diffusion-based DFL offers a robust framework for decision-making under uncertainty.
• The developed methods provide a more computationally efficient and effective way to integrate diffusion models into DFL.
• This work advances the field of DFL by enabling the handling of complex stochastic environments.