Research | Ferdinand Genans

Fast and Large-Scale Unbalanced Optimal Transport via its Semi-Dual and Adaptive Gradient Methods

COLT 2026 · 2026 F. Genans 📄 Paper

In Unbalanced Optimal Transport (UOT), we investigate the entropically regularized semi-dual objective. We prove the convergence rates of SGD and ASGD in both stochastic and semi-discrete settings. For the discrete case, we introduce a smoothness-adaptive Nesterov accelerated gradient descent scheme. We establish its global convergence rate and demonstrate an enhanced local convergence of O(log(1/δ)/√ε) to achieve δ-accuracy.

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Decreasing Entropic Regularization Averaged Gradient for Semi-Discrete Optimal Transport

NeurIPS 2025 · 2025 F. Genans, A. Godichon-Baggioni, F.-X. Vialard, O. Wintenberger 📄 Paper

We introduce DRAG, a stochastic algorithm for semi-discrete Optimal Transport that decreases entropic regularization during training. This yields unbiased estimates and faster convergence than fixed-regularization methods, with both theory and experiments confirming its efficiency.

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Stochastic Optimization in Semi-Discrete Optimal Transport: Convergence Analysis and Minimax Rate

NeurIPS 2025 — Spotlight · 2025 F. Genans, A. Godichon-Baggioni, F.-X. Vialard, O. Wintenberger 📄 Paper

We prove that Stochastic Gradient Descent can efficiently approximate the OT map in the semi-discrete setting, even in an online fashion, establishing the first minimax convergence guarantees for a broad class of cost functions and non-compact measures in this setting.

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Increasing Missingness to Reduce Bias: Richardson-SGD with Missing Data

Preprint — under review at NeurIPS 2026 · 2026 F. Genans, E. Scornet 📄 Paper

A Richardson-extrapolation-based SGD scheme for learning with missing data, which paradoxically increases missingness during training to reduce the bias of the final estimator.

Figure for Increasing Missingness to Reduce Bias: Richardson-SGD with Missing Data

Geometry-Aware Optimal Transport: Fast Intrinsic Dimension and Wasserstein Distance Estimation

Preprint — under review at NeurIPS 2026 · 2026 F. Genans, O. Wintenberger 📄 Paper

We introduce a fast estimator for the one-sample Wasserstein discretization error that avoids the need for an OT solver. Building on this, we propose a resolution-dependent intrinsic dimension estimator for probability measures. Finally, we derive a new OT Richardson extrapolation estimator for the OT distance utilizing this intrinsic dimension.