# Hyperparameter Trajectory Inference with Conditional Lagrangian Optimal Transport

arXiv: https://arxiv.org/abs/2603.01771 · HTML: https://mlsanity.com/paper/2603.01771/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Deep RL algorithms and representations, one of 15 directions in Deep reinforcement learning methods.
- Builds on 34 of its 60 references that are in the map.
- First posted on arXiv 2 Mar 2026.

## Placed in

- Deep reinforcement learning methods / [Deep RL algorithms and representations](https://mlsanity.com/deeprl/deep-rl-algorithms-and-representations/)

## Builds on (most cited first, 30 of 34)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [Building Normalizing Flows with Stochastic Interpolants](https://mlsanity.com/paper/2209.15571/) (2022)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [Flow Matching Guide and Code](https://mlsanity.com/paper/2412.06264/) (2024)
- [Multisample Flow Matching: Straightening Flows with Minibatch Couplings](https://mlsanity.com/paper/2304.14772/) (2023)
- [A Multi-Horizon Quantile Recurrent Forecaster](https://mlsanity.com/paper/1711.11053/) (2017)
- [Optimal transport mapping via input convex neural networks](https://mlsanity.com/paper/1908.10962/) (2019)
- [Flow Q-Learning](https://mlsanity.com/paper/2502.02538/) (2025)
- [TrajectoryNet: A Dynamic Optimal Transport Network for Modeling Cellular Dynamics](https://mlsanity.com/paper/2002.04461/) (2020)
- [Large-Scale Optimal Transport and Mapping Estimation](https://mlsanity.com/paper/1711.02283/) (2017)
- [Guided Flows for Generative Modeling and Decision Making](https://mlsanity.com/paper/2311.13443/) (2023)
- [Do Neural Optimal Transport Solvers Work? A Continuous Wasserstein-2 Benchmark](https://mlsanity.com/paper/2106.01954/) (2021)
- [Diffusion Models for Reinforcement Learning: A Survey](https://mlsanity.com/paper/2311.01223/) (2023)
- [Metric Flow Matching for Smooth Interpolations on the Data Manifold](https://mlsanity.com/paper/2405.14780/) (2024)
- [Multi-Objective Multi-Agent Decision Making: A Utility-based Analysis and Survey](https://mlsanity.com/paper/1909.02964/) (2019)
- [Scalable Unbalanced Optimal Transport using Generative Adversarial Networks](https://mlsanity.com/paper/1810.11447/) (2018)
- [Neural Optimal Transport with General Cost Functionals](https://mlsanity.com/paper/2205.15403/) (2022)
- [2-Wasserstein Approximation via Restricted Convex Potentials with Application to Improved Training for GANs](https://mlsanity.com/paper/1902.07197/) (2019)
- [Towards a mathematical theory of trajectory inference](https://mlsanity.com/paper/2102.09204/) (2021)
- [On amortizing convex conjugates for optimal transport](https://mlsanity.com/paper/2210.12153/) (2022)
- [A Geometric Perspective on Variational Autoencoders](https://mlsanity.com/paper/2209.07370/) (2022)
- [Pulling back information geometry](https://mlsanity.com/paper/2106.05367/) (2021)

## Abstract (arXiv)

Neural networks (NNs) often have critical behavioural trade-offs that are set at design time with hyperparameters-such as reward weights in reinforcement learning or quantile targets in regression. Post-deployment, however, user preferences can evolve, making initial settings undesirable, necessitating potentially expensive retraining. To circumvent this, we introduce the task of Hyperparameter Trajectory Inference (HTI): to learn, from observed data, how a NN's conditional output distribution changes with its hyperparameters, and construct a surrogate model that approximates the NN at unobserved hyperparameter settings. HTI requires extending existing trajectory inference approaches to incorporate conditions, exacerbating the challenge of ensuring inferred paths are feasible. We propose an approach based on conditional Lagrangian optimal transport, jointly learning the Lagrangian function governing hyperparameter-induced dynamics along with the associated optimal transport maps and geodesics between observed marginals, which form the surrogate model. We incorporate inductive biases based on the manifold hypothesis and least-action principles into the learned Lagrangian, improving surrogate model feasibility. We empirically demonstrate that our approach reconstructs NN outputs across various hyperparameter spectra better than other alternatives.