# In-Distribution Barrier Functions: Self-Supervised Policy Filters that Avoid Out-of-Distribution States

arXiv: https://arxiv.org/abs/2301.12012 · HTML: https://mlsanity.com/paper/2301.12012/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 47 references that are in the map.
- First posted on arXiv 27 Jan 2023.

## Builds on (most cited first, 30 of 32)

- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [FaceNet: A Unified Embedding for Face Recognition and Clustering](https://mlsanity.com/paper/1503.03832/) (2015)
- [Learning Latent Dynamics for Planning from Pixels](https://mlsanity.com/paper/1811.04551/) (2018)
- [Stabilizing Off-Policy Q-Learning via Bootstrapping Error Reduction](https://mlsanity.com/paper/1906.00949/) (2019)
- [Deep Reinforcement Learning in a Handful of Trials using Probabilistic Dynamics Models](https://mlsanity.com/paper/1805.12114/) (2018)
- [Behavior Regularized Offline Reinforcement Learning](https://mlsanity.com/paper/1911.11361/) (2019)
- [Control Barrier Function Based Quadratic Programs for Safety Critical Systems](https://mlsanity.com/paper/1609.06408/) (2016)
- [Embed to Control: A Locally Linear Latent Dynamics Model for Control from Raw Images](https://mlsanity.com/paper/1506.07365/) (2015)
- [Visual Foresight: Model-Based Deep Reinforcement Learning for Vision-Based Robotic Control](https://mlsanity.com/paper/1812.00568/) (2018)
- [Neural Lyapunov Control](https://mlsanity.com/paper/2005.00611/) (2020)
- [Safe Nonlinear Control Using Robust Neural Lyapunov-Barrier Functions](https://mlsanity.com/paper/2109.06697/) (2021)
- [Learning Control Barrier Functions from Expert Demonstrations](https://mlsanity.com/paper/2004.03315/) (2020)
- [Self-supervised Deep Reinforcement Learning with Generalized Computation Graphs for Robot Navigation](https://mlsanity.com/paper/1709.10489/) (2017)
- [Robust Control Barrier-Value Functions for Safety-Critical Control](https://mlsanity.com/paper/2104.02808/) (2021)
- [Synthesis of Control Barrier Functions Using a Supervised Machine Learning Approach](https://mlsanity.com/paper/2003.04950/) (2020)
- [Neural Certificates for Safe Control Policies](https://mlsanity.com/paper/2006.08465/) (2020)
- [Guaranteeing Safety of Learned Perception Modules via Measurement-Robust Control Barrier Functions](https://mlsanity.com/paper/2010.16001/) (2020)
- [Nonlinear state-space identification using deep encoder networks](https://mlsanity.com/paper/2012.07697/) (2020)
- [Lyapunov Density Models: Constraining Distribution Shift in Learning-Based Control](https://mlsanity.com/paper/2206.10524/) (2022)
- [Learning Barrier Functions with Memory for Robust Safe Navigation](https://mlsanity.com/paper/2011.01899/) (2020)
- [Control Barrier Functions for Unknown Nonlinear Systems using Gaussian Processes](https://mlsanity.com/paper/2010.05818/) (2020)
- [Learning Robust Output Control Barrier Functions from Safe Expert Demonstrations](https://mlsanity.com/paper/2111.09971/) (2021)
- [Control Barriers in Bayesian Learning of System Dynamics](https://mlsanity.com/paper/2012.14964/) (2020)
- [SABLAS: Learning Safe Control for Black-box Dynamical Systems](https://mlsanity.com/paper/2201.01918/) (2022)
- [Robustness to Out-of-Distribution Inputs via Task-Aware Generative Uncertainty](https://mlsanity.com/paper/1812.10687/) (2018)
- [Towards Robust Data-Driven Control Synthesis for Nonlinear Systems with Actuation Uncertainty](https://mlsanity.com/paper/2011.10730/) (2020)
- [Convex synthesis and verification of control-Lyapunov and barrier functions with input constraints](https://mlsanity.com/paper/2210.00629/) (2022)
- [Pointwise Feasibility of Gaussian Process-based Safety-Critical Control under Model Uncertainty](https://mlsanity.com/paper/2106.07108/) (2021)
- [LS3: Latent Space Safe Sets for Long-Horizon Visuomotor Control of Sparse Reward Iterative Tasks](https://mlsanity.com/paper/2107.04775/) (2021)

## Built on by (most cited first, 16 of 16)

- [Can We Detect Failures Without Failure Data? Uncertainty-Aware Runtime Failure Detection for Imitation Learning Policies](https://mlsanity.com/paper/2503.08558/) (2025)
- [Generalizing Safety Beyond Collision-Avoidance via Latent-Space Reachability Analysis](https://mlsanity.com/paper/2502.00935/) (2025)
- [Uncertainty-aware Latent Safety Filters for Avoiding Out-of-Distribution Failures](https://mlsanity.com/paper/2505.00779/) (2025)
- [EVORA: Deep Evidential Traversability Learning for Risk-Aware Off-Road Autonomy](https://mlsanity.com/paper/2311.06234/) (2023)
- [Safety Filters for Black-Box Dynamical Systems by Learning Discriminating Hyperplanes](https://mlsanity.com/paper/2402.05279/) (2024)
- [State-Wise Safe Reinforcement Learning With Pixel Observations](https://mlsanity.com/paper/2311.02227/) (2023)
- [Learning Conservative Neural Control Barrier Functions from Offline Data](https://mlsanity.com/paper/2505.00908/) (2025)
- [V-OCBF: Learning Safety Filters from Offline Data via Value-Guided Offline Control Barrier Functions](https://mlsanity.com/paper/2512.10822/) (2025)
- [Pixels to Proofs: Probabilistically-Safe Latent World Model Control via Parallel Conformal Robust MPC](https://mlsanity.com/paper/2606.15594/) (2026)
- [Learning Ensembles of Vision-based Safety Control Filters](https://mlsanity.com/paper/2412.02029/) (2024)
- [Pre-Trained Vision Models as Perception Backbones for Safety Filters in Autonomous Driving](https://mlsanity.com/paper/2410.22585/) (2024)
- [Learning Neural Control Barrier Functions from Expert Demonstrations using Inverse Constraint Learning](https://mlsanity.com/paper/2510.21560/) (2025)
- [RISE: Robust Imitation through Stochastic Encoding](https://mlsanity.com/paper/2503.12243/) (2025)
- [Solving Parameter-Robust Avoid Problems with Unknown Feasibility using Reinforcement Learning](https://mlsanity.com/paper/2602.15817/) (2026)
- [Discriminative Barrier Functions for Safe Adversarial Imitation Learning from Observation](https://mlsanity.com/paper/2607.13938/) (2026)
- [Latent Safety Filters: When a Lossy Encoder Admits a Transferable Certificate](https://mlsanity.com/paper/2610.04297/) (2026)

## Abstract (arXiv)

Learning-based control approaches have shown great promise in performing complex tasks directly from high-dimensional perception data for real robotic systems. Nonetheless, the learned controllers can behave unexpectedly if the trajectories of the system divert from the training data distribution, which can compromise safety. In this work, we propose a control filter that wraps any reference policy and effectively encourages the system to stay in-distribution with respect to offline-collected safe demonstrations. Our methodology is inspired by Control Barrier Functions (CBFs), which are model-based tools from the nonlinear control literature that can be used to construct minimally invasive safe policy filters. While existing methods based on CBFs require a known low-dimensional state representation, our proposed approach is directly applicable to systems that rely solely on high-dimensional visual observations by learning in a latent state-space. We demonstrate that our method is effective for two different visuomotor control tasks in simulation environments, including both top-down and egocentric view settings.