# DR-PETS: Learning-Based Control With Planning in Adversarial Environments

arXiv: https://arxiv.org/abs/2503.20660 · HTML: https://mlsanity.com/paper/2503.20660/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 21 references that are in the map.
- First posted on arXiv 26 Mar 2025.

## Builds on (most cited first, 15 of 15)

- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Deep Reinforcement Learning in a Handful of Trials using Probabilistic Dynamics Models](https://mlsanity.com/paper/1805.12114/) (2018)
- [Cautious Model Predictive Control using Gaussian Process Regression](https://mlsanity.com/paper/1705.10702/) (2017)
- [Distributionally Robust Model-Based Offline Reinforcement Learning with Near-Optimal Sample Complexity](https://mlsanity.com/paper/2208.05767/) (2022)
- [Finite-Sample Guarantees for Wasserstein Distributionally Robust Optimization: Breaking the Curse of Dimensionality](https://mlsanity.com/paper/2009.04382/) (2020)
- [Distributional Robustness and Regularization in Reinforcement Learning](https://mlsanity.com/paper/2003.02894/) (2020)
- [Variational Inference MPC for Bayesian Model-based Reinforcement Learning](https://mlsanity.com/paper/1907.04202/) (2019)
- [Distributionally Robust Counterpart in Markov Decision Processes](https://mlsanity.com/paper/1501.07418/) (2015)
- [Optimal Transport Perturbations for Safe Reinforcement Learning with Robustness Guarantees](https://mlsanity.com/paper/2301.13375/) (2023)
- [Probabilistic design of optimal sequential decision-making algorithms in learning and control](https://mlsanity.com/paper/2201.05212/) (2022)
- [Control-Tutored Reinforcement Learning: Towards the Integration of Data-Driven and Model-Based Control](https://mlsanity.com/paper/2112.06018/) (2021)
- [Data-driven distributionally robust MPC for constrained stochastic systems](https://mlsanity.com/paper/2103.03006/) (2021)
- [Minimax Q-learning Control for Linear Systems Using the Wasserstein Metric](https://mlsanity.com/paper/2010.06794/) (2020)
- [Ambiguity Tube MPC](https://mlsanity.com/paper/2206.09085/) (2022)
- [Stochastic MPC with Distributionally Robust Chance Constraints](https://mlsanity.com/paper/2005.00313/) (2020)

## Built on by (most cited first, 1 of 1)

- [Self-Adaptive Learning and Model Predictive Control for Tracking Unknown Dynamics with No Regret](https://mlsanity.com/paper/2607.26370/) (2026)

## Abstract (arXiv)

Ensuring robustness against epistemic, possibly adversarial, perturbations is essential for reliable real-world decision-making. While the Probabilistic Ensembles with Trajectory Sampling (PETS) algorithm inherently handles uncertainty via ensemble-based probabilistic models, it lacks guarantees against structured adversarial or worst-case uncertainty distributions. To address this, we propose DR-PETS, a distributionally robust extension of PETS that certifies robustness against adversarial perturbations. We formalize uncertainty via a p-Wasserstein ambiguity set, enabling worst-case-aware planning through a min-max optimization framework. While PETS passively accounts for stochasticity, DR-PETS actively optimizes robustness via a tractable convex approximation integrated into PETS planning loop. Experiments on pendulum stabilization and cart-pole balancing show that DR-PETS certifies robustness against adversarial parameter perturbations, achieving consistent performance in worst-case scenarios where PETS deteriorates.