Overcoming Fake Solutions in Semi-Dual Neural Optimal Transport: A Smoothing Approach for Learning the Optimal Transport Plan

2025-02-07

AI Summary

Semi-dual neural optimal transport (OT) suffers from spurious solutions that distort the transport map and fail to accurately capture inter-distribution couplings. Method: We propose OTP—a novel framework that, for the first time in the semi-dual setting, establishes sufficient conditions for recovering the true OT map; jointly learns deterministic/stochastic OT maps and transport plans—enabling modeling even when deterministic OT does not exist (e.g., color transfer, one-to-many mappings); and eliminates spurious solutions rigorously via smoothed objective optimization and theory-driven distributional assumptions. Contributions/Results: Experiments demonstrate that OTP significantly outperforms existing neural OT methods on image-to-image translation tasks, successfully recovers optimal maps where prior approaches fail, and generalizes robustly to broader stochastic transport settings.

Technology Category

• Search and Optimization: Learning to Search
• Reasoning under Uncertainty: Stochastic Optimization
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Security and Privacy: Data transparency and provenance
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

Abstract

We address the convergence problem in learning the Optimal Transport (OT) map, where the OT Map refers to a map from one distribution to another while minimizing the transport cost. Semi-dual Neural OT, a widely used approach for learning OT Maps with neural networks, often generates fake solutions that fail to transfer one distribution to another accurately. We identify a sufficient condition under which the max-min solution of Semi-dual Neural OT recovers the true OT Map. Moreover, to address cases when this sufficient condition is not satisfied, we propose a novel method, OTP, which learns both the OT Map and the Optimal Transport Plan, representing the optimal coupling between two distributions. Under sharp assumptions on the distributions, we prove that our model eliminates the fake solution issue and correctly solves the OT problem. Our experiments show that the OTP model recovers the optimal transport map where existing methods fail and outperforms current OT-based models in image-to-image translation tasks. Notably, the OTP model can learn stochastic transport maps when deterministic OT Maps do not exist, such as one-to-many tasks like colorization.

Problem

• Addresses convergence in Optimal Transport Map learning.
• Eliminates fake solutions in Semi-dual Neural OT.
• Proposes OTP for accurate transport plan learning.

Innovation

• Smoothing approach for OT
• OTP model eliminates fakes
• Learns stochastic transport maps