Variational Regularized Unbalanced Optimal Transport: Single Network, Least Action

• URL: http://arxiv.org/abs/2505.11823v1
• Date: Sat, 17 May 2025 04:16:14 GMT
• Title: Variational Regularized Unbalanced Optimal Transport: Single Network, Least Action
• Authors: Yuhao Sun, Zhenyi Zhang, Zihan Wang, Tiejun Li, Peijie Zhou,
• Abstract summary: We propose Variational RUOT (Var-RUOT), a new framework to solve the RUOT problem.<n>Var-RUOT can find solutions with lower action while exhibiting faster convergence and improved training stability.
• Score: 9.229946487941056
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Recovering the dynamics from a few snapshots of a high-dimensional system is a challenging task in statistical physics and machine learning, with important applications in computational biology. Many algorithms have been developed to tackle this problem, based on frameworks such as optimal transport and the Schr\"odinger bridge. A notable recent framework is Regularized Unbalanced Optimal Transport (RUOT), which integrates both stochastic dynamics and unnormalized distributions. However, since many existing methods do not explicitly enforce optimality conditions, their solutions often struggle to satisfy the principle of least action and meet challenges to converge in a stable and reliable way. To address these issues, we propose Variational RUOT (Var-RUOT), a new framework to solve the RUOT problem. By incorporating the optimal necessary conditions for the RUOT problem into both the parameterization of the search space and the loss function design, Var-RUOT only needs to learn a scalar field to solve the RUOT problem and can search for solutions with lower action. We also examined the challenge of selecting a growth penalty function in the widely used Wasserstein-Fisher-Rao metric and proposed a solution that better aligns with biological priors in Var-RUOT. We validated the effectiveness of Var-RUOT on both simulated data and real single-cell datasets. Compared with existing algorithms, Var-RUOT can find solutions with lower action while exhibiting faster convergence and improved training stability.

Related papers

• Can Large Language Models Solve Robot Routing? [13.672207504142456]
  Large Language Models (LLMs) can replace the entire pipeline from tasks described in natural language to the generation of robot routes. We construct a dataset with 80 unique robot routing problems across 8 variants in both single and multi-robot settings. Our findings reveal that both self-ging and self-verification enhance success rates without significantly lowering the optimality gap.
  arXiv  Detail & Related papers  (2024-03-16T03:54:38Z)
• Solving Robust MDPs through No-Regret Dynamics [1.3597551064547502]
  Reinforcement Learning is a powerful framework for training agents to navigate different situations. We show how an algorithm can be used to improve policy training methods.
  arXiv  Detail & Related papers  (2023-05-30T13:52:16Z)
• Light Unbalanced Optimal Transport [69.18220206873772]
  We propose a novel theoretically-justified, lightweight, unbalanced EOT solver.<n>Our advancement consists of developing a novel view on the optimization of the UEOT problem yielding tractable and a non-minimax optimization objective.<n>We show that our solver provides a universal approximation of UEOT solutions and obtains its generalization bounds.
  arXiv  Detail & Related papers  (2023-03-14T15:44:40Z)
• Entropic Neural Optimal Transport via Diffusion Processes [105.34822201378763]
  We propose a novel neural algorithm for the fundamental problem of computing the entropic optimal transport (EOT) plan between continuous probability distributions. Our algorithm is based on the saddle point reformulation of the dynamic version of EOT which is known as the Schr"odinger Bridge problem. In contrast to the prior methods for large-scale EOT, our algorithm is end-to-end and consists of a single learning step.
  arXiv  Detail & Related papers  (2022-11-02T14:35:13Z)
• Message Passing Neural PDE Solvers [60.77761603258397]
  We build a neural message passing solver, replacing allally designed components in the graph with backprop-optimized neural function approximators. We show that neural message passing solvers representationally contain some classical methods, such as finite differences, finite volumes, and WENO schemes. We validate our method on various fluid-like flow problems, demonstrating fast, stable, and accurate performance across different domain topologies, equation parameters, discretizations, etc., in 1D and 2D.
  arXiv  Detail & Related papers  (2022-02-07T17:47:46Z)
• RoMA: Robust Model Adaptation for Offline Model-based Optimization [115.02677045518692]
  We consider the problem of searching an input maximizing a black-box objective function given a static dataset of input-output queries. A popular approach to solving this problem is maintaining a proxy model that approximates the true objective function. Here, the main challenge is how to avoid adversarially optimized inputs during the search.
  arXiv  Detail & Related papers  (2021-10-27T05:37:12Z)
• Combining Deep Learning and Optimization for Security-Constrained Optimal Power Flow [94.24763814458686]
  Security-constrained optimal power flow (SCOPF) is fundamental in power systems. Modeling of APR within the SCOPF problem results in complex large-scale mixed-integer programs. This paper proposes a novel approach that combines deep learning and robust optimization techniques.
  arXiv  Detail & Related papers  (2020-07-14T12:38:21Z)
• An Online Method for A Class of Distributionally Robust Optimization with Non-Convex Objectives [54.29001037565384]
  We propose a practical online method for solving a class of online distributionally robust optimization (DRO) problems. Our studies demonstrate important applications in machine learning for improving the robustness of networks.
  arXiv  Detail & Related papers  (2020-06-17T20:19:25Z)
• Unsupervised Deep Learning for Optimizing Wireless Systems with Instantaneous and Statistic Constraints [29.823814915538463]
  We establish a unified framework of using unsupervised deep learning to solve both kinds of problems with both instantaneous and statistic constraints. We show that unsupervised learning outperforms supervised learning in terms of violation probability and approximation accuracy of the optimal policy.
  arXiv  Detail & Related papers  (2020-05-30T13:37:14Z)
• Scalable Autonomous Vehicle Safety Validation through Dynamic Programming and Scene Decomposition [37.61747231296097]
  We present a new safety validation approach that attempts to estimate the distribution over failures of an autonomous policy using approximate dynamic programming. In both experiments, we observed an increase in the number of failures discovered compared to baseline approaches.
  arXiv  Detail & Related papers  (2020-04-14T21:03:50Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.