# Safe Continuous Control with Constrained Model-Based Policy Optimization

arXiv: https://arxiv.org/abs/2104.06922 · HTML: https://mlsanity.com/paper/2104.06922/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 31 references that are in the map.
- First posted on arXiv 14 Apr 2021.

## Builds on (most cited first, 18 of 18)

- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Trust Region Policy Optimization](https://mlsanity.com/paper/1502.05477/) (2015)
- [Addressing Function Approximation Error in Actor-Critic Methods](https://mlsanity.com/paper/1802.09477/) (2018)
- [High-Dimensional Continuous Control Using Generalized Advantage Estimation](https://mlsanity.com/paper/1506.02438/) (2015)
- [Constrained Policy Optimization](https://mlsanity.com/paper/1705.10528/) (2017)
- [Deep Reinforcement Learning in a Handful of Trials using Probabilistic Dynamics Models](https://mlsanity.com/paper/1805.12114/) (2018)
- [When to Trust Your Model: Model-Based Policy Optimization](https://mlsanity.com/paper/1906.08253/) (2019)
- [Learning Dexterous In-Hand Manipulation](https://mlsanity.com/paper/1808.00177/) (2018)
- [Safe Model-based Reinforcement Learning with Stability Guarantees](https://mlsanity.com/paper/1705.08551/) (2017)
- [Risk-Constrained Reinforcement Learning with Percentile Risk Criteria](https://mlsanity.com/paper/1512.01629/) (2015)
- [Emergent Tool Use From Multi-Agent Autocurricula](https://mlsanity.com/paper/1909.07528/) (2019)
- [A Lyapunov-based Approach to Safe Reinforcement Learning](https://mlsanity.com/paper/1805.07708/) (2018)
- [Safe Exploration in Continuous Action Spaces](https://mlsanity.com/paper/1801.08757/) (2018)
- [Model-Ensemble Trust-Region Policy Optimization](https://mlsanity.com/paper/1802.10592/) (2018)
- [Projection-Based Constrained Policy Optimization](https://mlsanity.com/paper/2010.03152/) (2020)
- [Deep Reinforcement Learning and the Deadly Triad](https://mlsanity.com/paper/1812.02648/) (2018)
- [Learning-based Model Predictive Control for Safe Exploration](https://mlsanity.com/paper/1803.08287/) (2018)

## Built on by (most cited first, 17 of 17)

- [A Review of Safe Reinforcement Learning: Methods, Theory and Applications](https://mlsanity.com/paper/2205.10330/) (2022)
- [Safe Reinforcement Learning by Imagining the Near Future](https://mlsanity.com/paper/2202.07789/) (2022)
- [Constrained Policy Optimization via Bayesian World Models](https://mlsanity.com/paper/2201.09802/) (2022)
- [Learning Barrier Certificates: Towards Safe Reinforcement Learning with Zero Training-time Violations](https://mlsanity.com/paper/2108.01846/) (2021)
- [Multi-Agent Constrained Policy Optimisation](https://mlsanity.com/paper/2110.02793/) (2021)
- [When to Ask for Help: Proactive Interventions in Autonomous Reinforcement Learning](https://mlsanity.com/paper/2210.10765/) (2022)
- [CUP: A Conservative Update Policy Algorithm for Safe Reinforcement Learning](https://mlsanity.com/paper/2202.07565/) (2022)
- [Safe Model-Based Reinforcement Learning with an Uncertainty-Aware Reachability Certificate](https://mlsanity.com/paper/2210.07553/) (2022)
- [Safe Reinforcement Learning From Pixels Using a Stochastic Latent Representation](https://mlsanity.com/paper/2210.01801/) (2022)
- [SPiDR: A Simple Approach for Zero-Shot Safety in Sim-to-Real Transfer](https://mlsanity.com/paper/2509.18648/) (2025)
- [Reinforcement Learning by Guided Safe Exploration](https://mlsanity.com/paper/2307.14316/) (2023)
- [PIGDreamer: Privileged Information Guided World Models for Safe Partially Observable Reinforcement Learning](https://mlsanity.com/paper/2508.02159/) (2025)
- [Value Functions are Control Barrier Functions: Verification of Safe Policies using Control Theory](https://mlsanity.com/paper/2306.04026/) (2023)
- [Approximate Shielding of Atari Agents for Safe Exploration](https://mlsanity.com/paper/2304.11104/) (2023)
- [Q-learning-based Model-free Safety Filter](https://mlsanity.com/paper/2411.19809/) (2024)
- [Safe and Near-Optimal Control with Online Dynamics Learning](https://mlsanity.com/paper/2509.16650/) (2025)
- [Constrained Meta Agnostic Reinforcement Learning](https://mlsanity.com/paper/2406.14047/) (2024)

## Abstract (arXiv)

The applicability of reinforcement learning (RL) algorithms in real-world domains often requires adherence to safety constraints, a need difficult to address given the asymptotic nature of the classic RL optimization objective. In contrast to the traditional RL objective, safe exploration considers the maximization of expected returns under safety constraints expressed in expected cost returns. We introduce a model-based safe exploration algorithm for constrained high-dimensional control to address the often prohibitively high sample complexity of model-free safe exploration algorithms. Further, we provide theoretical and empirical analyses regarding the implications of model-usage on constrained policy optimization problems and introduce a practical algorithm that accelerates policy search with model-generated data. The need for accurate estimates of a policy's constraint satisfaction is in conflict with accumulating model-errors. We address this issue by quantifying model-uncertainty as the expected Kullback-Leibler divergence between predictions of an ensemble of probabilistic dynamics models and constrain this error-measure, resulting in an adaptive resampling scheme and dynamically limited rollout horizons. We evaluate this approach on several simulated constrained robot locomotion tasks with high-dimensional action- and state-spaces. Our empirical studies find that our algorithm reaches model-free performances with a 10-20 fold reduction of training samples while maintaining approximate constraint satisfaction levels of model-free methods.