Fine-Tuning Generative Models for Extreme Events via CVaR-Penalized Wasserstein Gradient Flows

2026-08-11

AI Summary

This work addresses the challenge that generative models often fail to accurately capture heavy-tailed distributions and extreme events when tail priors are unavailable. To overcome this limitation, the authors propose CVaR-GPA, an algorithm that, for the first time, incorporates Conditional Value-at-Risk (CVaR) penalties into Wasserstein gradient flows. This approach constructs a bounded yet non-Lipschitz velocity field, enabling sample-level refinement of generator outputs without requiring access to the generator’s internal architecture. Leveraging the Rockafellar–Uryasev representation, the method derives a density-free first-order variational subgradient for CVaR and combines it with a kinetic stopping criterion and Lipschitz-regularized KL divergence for efficient optimization. Experiments demonstrate that CVaR-GPA significantly outperforms baseline methods on both synthetic and real high-dimensional financial datasets, improving generation accuracy across both global and tail regions.

Abstract

We propose CVaR-penalized Generative Particle Algorithm (CVaR-GPA), a robust, tail-agnostic algorithm for fine-tuning generative models to learn heavy-tailed distributions and capture extreme events, requiring no prior knowledge or estimation of the target's tail characteristics. The method is the Wasserstein gradient flow of the Lipschitz-regularized Kullback-Leibler (KL) divergence penalized by a Conditional Value-at-Risk (CVaR) discrepancy term: the Lipschitz-regularized KL divergence enables robust learning under minimal assumptions on the target distribution, while the CVaR penalty restores the velocity that otherwise vanishes prematurely in the under-sampled tails. The penalized flow admits a bounded but non-Lipschitz velocity field. This departs from the Lipschitz transport maps of standard generators, which preserve the tail behavior of a light-tailed source, and enables transport toward heavier-tailed targets. To define this flow on empirical measures, we derive the first-variation subgradients of CVaR from its Rockafellar-Uryasev representation, valid precisely where the classical density-based formula fails. The particle algorithm CVaR-GPA fine-tunes the output samples of any pre-trained model, without access to its architecture, and runs on an adaptive time horizon set by a kinetic-energy stopping criterion rather than a preset depth. On synthetic isotropic and anisotropic Student-$t$ target distributions, Neal's funnel distribution, and the real-world high-dimensional Fama-French 25 portfolio dataset, CVaR-GPA dramatically improves global and tail accuracy on heavy-tailed targets over the pre-trained baseline.

Problem

• heavy-tailed distributions
• extreme events
• generative models
• fine-tuning
• tail behavior

Innovation

• CVaR-penalized Wasserstein gradient flow
• heavy-tailed distribution modeling
• generative model fine-tuning
• tail-agnostic extreme event learning
• non-Lipschitz transport velocity