# Predictive Safety Curricula for Robust Legged Locomotion

arXiv: https://arxiv.org/abs/2609.37070 · HTML: https://mlsanity.com/paper/2609.37070/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 25 of its 31 references that are in the map.
- First posted on arXiv 29 Sep 2026.

## Builds on (most cited first, 25 of 25)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Constrained Policy Optimization](https://mlsanity.com/paper/1705.10528/) (2017)
- [A Distributional Perspective on Reinforcement Learning](https://mlsanity.com/paper/1707.06887/) (2017)
- [Learning Quadrupedal Locomotion over Challenging Terrain](https://mlsanity.com/paper/2010.11251/) (2020)
- [Learning to Walk in Minutes Using Massively Parallel Deep Reinforcement Learning](https://mlsanity.com/paper/2109.11978/) (2021)
- [Distributional Reinforcement Learning with Quantile Regression](https://mlsanity.com/paper/1710.10044/) (2017)
- [Learning robust perceptive locomotion for quadrupedal robots in the wild](https://mlsanity.com/paper/2201.08117/) (2022)
- [Curriculum Learning for Reinforcement Learning Domains: A Framework and Survey](https://mlsanity.com/paper/2003.04960/) (2020)
- [Implicit Quantile Networks for Distributional Reinforcement Learning](https://mlsanity.com/paper/1806.06923/) (2018)
- [Prioritized Level Replay](https://mlsanity.com/paper/2010.03934/) (2020)
- [Recovery RL: Safe Reinforcement Learning with Learned Recovery Zones](https://mlsanity.com/paper/2010.15920/) (2020)
- [Evolving Curricula with Regret-Based Environment Design](https://mlsanity.com/paper/2203.01302/) (2022)
- [Active Domain Randomization](https://mlsanity.com/paper/1904.04762/) (2019)
- [Automatic Curriculum Learning For Deep RL: A Short Survey](https://mlsanity.com/paper/2003.04664/) (2020)
- [Teacher algorithms for curriculum learning of Deep RL in continuously parameterized environments](https://mlsanity.com/paper/1910.07224/) (2019)
- [Safe Reinforcement Learning via Curriculum Induction](https://mlsanity.com/paper/2006.12136/) (2020)
- [Agile But Safe: Learning Collision-Free High-Speed Legged Locomotion](https://mlsanity.com/paper/2401.17583/) (2024)
- [RSL-RL: A Learning Library for Robotics Research](https://mlsanity.com/paper/2509.10771/) (2025)
- [Efficient Risk-Averse Reinforcement Learning](https://mlsanity.com/paper/2205.05138/) (2022)
- [Robust Quadrupedal Locomotion via Risk-Averse Policy Learning](https://mlsanity.com/paper/2308.09405/) (2023)
- [Learning Risk-Aware Quadrupedal Locomotion using Distributional Reinforcement Learning](https://mlsanity.com/paper/2309.14246/) (2023)
- [Adversarial Environment Design via Regret-Guided Diffusion Models](https://mlsanity.com/paper/2410.19715/) (2024)
- [HACL: History-Aware Curriculum Learning for Fast Locomotion](https://mlsanity.com/paper/2505.18429/) (2025)
- [Scaling Rough Terrain Locomotion with Automatic Curriculum Reinforcement Learning](https://mlsanity.com/paper/2601.17428/) (2026)
- [Trajectory-Level Automatic Curriculum Learning for Legged Locomotion on Unstructured Terrain](https://mlsanity.com/paper/2608.16164/) (2026)

## Abstract (arXiv)

Rare but consequential failures can persist in learned locomotion policies for legged robots even when average task performance is high, in part because standard curricula primarily adapt task difficulty rather than the distribution of safety-critical experience. We introduce Predictive Safety Curricula (PSC), a framework for allocating locomotion training experience using learned predictions of future safety cost. PSC trains a distributional safety critic from policy rollouts and uses its predictions to prioritize both terrain contexts and previously encountered randomized events. The resulting curriculum modifies the training distribution while leaving the task reward and policy-optimization loss unchanged. We evaluate PSC in controlled rough-terrain locomotion and in production locomotion systems. PSC improves reliability relative to standard terrain progression, advantage-based replay, and learning-progress curricula, with the largest gains on difficult terrain and under degraded observations. The same allocation principle transfers to two production locomotion stacks. On ANYmal-D hardware, PSC reduces shank-collision incidence by 63% relative to the learning-progress curriculum across three matched training seeds, with a reduction in every seed. On a production stair-climbing platform, PSC eliminates observed shank collisions in the evaluated hardware trials. These results show that learned predictions of future safety cost can provide an effective signal for allocating training experience toward rare failure modes and improving locomotion reliability.