Notice: The reproducibility variables underlying each score are classified using an automated LLM-based pipeline, validated against a manually labeled dataset. LLM-based classification introduces uncertainty and potential bias; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in Coakley et alK. L. Coakley, T. Snelleman, H. Hoos, and O. E. Gundersen, "The embrace of open science: An analysis of a decade of AI research and 56 800 conference papers," Under Review, 2026..
Safely Learning Controlled Stochastic Dynamics
Authors: Luc Brogat-Motte, Alessandro Rudi, Riccardo Bonalli
NeurIPS 2025 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Experimental evaluations demonstrate the practical effectiveness of our method in terms of safety, estimation accuracy, and computational efficiency. Specifically, we evaluate it on a benchmark two-dimensional stochastic dynamical system evolving in a bounded, safety-critical environment under stochastic perturbations (see Figure 1). An open-source Python implementation is provided (available at github.com/lmotte/dynamics-safe-learn). ... 6 Numerical experiments We evaluate our method on a representative smooth nonlinear stochastic system. |
| Researcher Affiliation | Academia | Luc Brogat-Motte Laboratoire des Signaux et Systèmes, CNRS, Centrale Supélec Université Paris-Saclay, Gif-sur-Yvette, France Istituto Italiano di Tecnologia, Genoa, Italy EMAIL Alessandro Rudi SDA Bocconi, Bocconi University, Milan, Italy EMAIL Riccardo Bonalli Laboratoire des Signaux et Systèmes, CNRS, Centrale Supélec Université Paris-Saclay, Gif-sur-Yvette, France EMAIL |
| Pseudocode | Yes | A step-by-step breakdown of the overall method is provided in Appendix B, with algorithm tables for each module and their computational complexities. ... Algorithm 1: Density Estimation({xj}Q j=1, ρR) ... Algorithm 2: Compute Probabilities(ˆpθi,ti, g, h, Q , mode) ... Algorithm 3: Fit Kernel Maps({(θi, ti)}N i=1, ˆP( ), ˆS, ˆR, k, λ) ... Algorithm 4: Efficient sampling algorithm |
| Open Source Code | Yes | Experimental validation. We empirically demonstrate the performance of the approach in terms of safety, estimation accuracy, and computational efficiency. Specifically, we evaluate it on a benchmark two-dimensional stochastic dynamical system evolving in a bounded, safety-critical environment under stochastic perturbations (see Figure 1). An open-source Python implementation is provided (available at github.com/lmotte/dynamics-safe-learn). |
| Open Datasets | No | We consider the problem of safely learning the dynamics of controlled continuous-time stochastic systems from discrete-time observations of trajectory data. ... Figure 1: Illustration of a complex, smooth dynamical system under deterministic conditions (left) and stochastic conditions with unknown disturbances (right). Shown are 100 simulated trajectories under three different controls. ... 6 Numerical experiments We evaluate our method on a representative smooth nonlinear stochastic system. Specifically, the experiments aim to assess the following: (i) satisfaction of safety and reset constraints, (ii) efficiency of exploration under different safety thresholds, (iii) prediction accuracy for dynamics, safety, and reset maps, (iv) computational cost and scalability. System and environment. We consider a 2D second-order dynamical system whose acceleration is directly controlled by the input. |
| Dataset Splits | No | The paper uses a simulated environment where data is generated dynamically through exploration. While it mentions 'validation controls' and 'test controls', it does not provide specific splits (e.g., percentages or counts) for a pre-existing static dataset. Section B.3 states: 'Typically, hyperparameters are tuned using validation data. Parameters for density estimation (γkde, λkde) can be optimized after data collection by maximizing log-likelihood. In contrast, the parameters governing safety and reset exploration (γcollect, λcollect, βcollect) must be set beforehand, as they directly impact safe exploration. When prior knowledge is limited, we recommend initially conservative settings high γ, low λ, high β, and large kernel bandwidth R and gradually relaxing them based on data-driven insights. In our experiments, γkde and λkde were visually tuned using validation controls (2π/3, π/3), ( 2π/3, π/3), and (0, π/3).' Section C.1 mentions 'three test controls ((-0.81 1.20), (-1.07 0.92), (-1.13 1.18))'. |
| Hardware Specification | Yes | B.4 Computational considerations To provide practical insight into computational requirements, we report measured execution times from experiments on a standard machine (Apple M3 Pro, 18GB RAM). |
| Software Dependencies | No | B.1 System estimation ... This section details the implementation of the method described in Section 4, available on Git Hub (lmotte/dynamics-safe-learn) as an open-source Python library. We detail all computational steps, including vectorized implementations using Python libraries such as Num Py for efficiency. ... While Python and NumPy are mentioned, specific version numbers for these or any other libraries are not provided. |
| Experiment Setup | Yes | 6 Numerical experiments ... System and environment. We consider a 2D second-order dynamical system whose acceleration is directly controlled by the input. The system evolves according to the controlled SDE d X(t) = V (t)dt, d V (t) = u(t, X(t), V (t))dt + a(X(t))d Wt. ... The initial state follows N(0, σ0IR2) with σ0 = 0.1, and the maximal time horizon is Tmax = 20. The system evolves within the bounded safe region ( 10, 10)2, and each trajectory must end in the reset region defined as a disk of radius 2.5 centered at the origin. ... Control space. Controls are parameterized as sequences of m fixed accelerations of magnitude v... We set v = 2.0, κ = 0.5, m = 2, Texplo = 6, and nsteps = 500. ... Method s hyperparameters. Our method depends on several hyperparameters that govern safety thresholds (ε, ξ), confidence levels (βs, βr), kernel smoothness (λ, γ), and bandwidth R, with distinct values for estimating dynamics and constraints. We test (ε, ξ) {0.1, 0.3, 0.5, }, with 1000 iterations and initial safe control ( π/3, π/3). Candidate selection for uncertainty maximization is restricted to a local subset for efficiency (Appendix B, Algorithm 4). |