# Saddle Flow Dynamics: Observable Certificates and Separable Regularization

arXiv: https://arxiv.org/abs/2009.14714 · HTML: https://mlsanity.com/paper/2009.14714/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Sep 2020.

## Built on by (most cited first, 2 of 2)

- [Dissipative Gradient Descent Ascent Method: A Control Theory Inspired Algorithm for Min-max Optimization](https://mlsanity.com/paper/2403.09090/) (2024)
- [Constrained Reinforcement Learning via Dissipative Saddle Flow Dynamics](https://mlsanity.com/paper/2212.01505/) (2022)

## Abstract (arXiv)

This paper proposes a certificate, rooted in observability, for asymptotic convergence of saddle flow dynamics of convex-concave functions to a saddle point. This observable certificate directly bridges the gap between the invariant set and the equilibrium set in a LaSalle argument, and generalizes conventional conditions such as strict convexity-concavity and proximal regularization. We further build upon this certificate to propose a separable regularization method for saddle flow dynamics that makes minimal requirements on convexity-concavity and yet still guarantees asymptotic convergence to a saddle point. Our results generalize to saddle flow dynamics with projections on the vector field and have an immediate application as a distributed solution to linear programs.