# Robust Value Iteration for Continuous Control Tasks

arXiv: https://arxiv.org/abs/2105.12189 · HTML: https://mlsanity.com/paper/2105.12189/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 64 references that are in the map.
- First posted on arXiv 25 May 2021.

## Builds on (most cited first, 30 of 31)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Continuous control with deep reinforcement learning](https://mlsanity.com/paper/1509.02971/) (2015)
- [Trust Region Policy Optimization](https://mlsanity.com/paper/1502.05477/) (2015)
- [Learning Dexterous In-Hand Manipulation](https://mlsanity.com/paper/1808.00177/) (2018)
- [Robust Adversarial Reinforcement Learning](https://mlsanity.com/paper/1703.02702/) (2017)
- [Safe Model-based Reinforcement Learning with Stability Guarantees](https://mlsanity.com/paper/1705.08551/) (2017)
- [Closing the Sim-to-Real Loop: Adapting Simulation Randomization with Real World Experience](https://mlsanity.com/paper/1810.05687/) (2018)
- [Adversarial Policies: Attacking Deep Reinforcement Learning](https://mlsanity.com/paper/1905.10615/) (2019)
- [Hamilton-Jacobi Reachability: A Brief Overview and Recent Advances](https://mlsanity.com/paper/1709.07523/) (2017)
- [Action Robust Reinforcement Learning and Applications in Continuous Control](https://mlsanity.com/paper/1901.09184/) (2019)
- [Risk-Sensitive and Robust Decision-Making: a CVaR Optimization Approach](https://mlsanity.com/paper/1506.02188/) (2015)
- [Model-Based Value Estimation for Efficient Model-Free Reinforcement Learning](https://mlsanity.com/paper/1803.00101/) (2018)
- [Robust Deep Reinforcement Learning with Adversarial Attacks](https://mlsanity.com/paper/1712.03632/) (2017)
- [Neural Lyapunov Control](https://mlsanity.com/paper/2005.00611/) (2020)
- [Conservative Safety Critics for Exploration](https://mlsanity.com/paper/2010.14497/) (2020)
- [Learning Stable Deep Dynamics Models](https://mlsanity.com/paper/2001.06116/) (2020)
- [The Lyapunov Neural Network: Adaptive Stability Certification for Safe Learning of Dynamical Systems](https://mlsanity.com/paper/1808.00924/) (2018)
- [BayesSim: adaptive domain randomization via probabilistic inference for robotics simulators](https://mlsanity.com/paper/1906.01728/) (2019)
- [Dynamics Randomization Revisited:A Case Study for Quadrupedal Locomotion](https://mlsanity.com/paper/2011.02404/) (2020)
- [MushroomRL: Simplifying Reinforcement Learning Research](https://mlsanity.com/paper/2001.01102/) (2020)
- [Data-efficient Domain Randomization with Bayesian Optimization](https://mlsanity.com/paper/2003.02471/) (2020)
- [Hamilton-Jacobi Deep Q-Learning for Deterministic Continuous-Time Systems with Lipschitz Continuous Controls](https://mlsanity.com/paper/2010.14087/) (2020)
- [Safe Optimal Control Using Stochastic Barrier Functions and Deep Forward-Backward SDEs](https://mlsanity.com/paper/2009.01196/) (2020)
- [Value Iteration in Continuous Actions, States and Time](https://mlsanity.com/paper/2105.04682/) (2021)
- [Scaling Up Robust MDPs by Reinforcement Learning](https://mlsanity.com/paper/1306.6189/) (2013)
- [Supervision via Competition: Robot Adversaries for Learning Tasks](https://mlsanity.com/paper/1610.01685/) (2016)
- [Learning Deep Stochastic Optimal Control Policies using Forward-Backward SDEs](https://mlsanity.com/paper/1902.03986/) (2019)
- [ADAPT: Zero-Shot Adaptive Policy Transfer for Stochastic Dynamical Systems](https://mlsanity.com/paper/1707.04674/) (2017)

## Built on by (most cited first, 8 of 8)

- [Robot Learning from Randomized Simulations: A Review](https://mlsanity.com/paper/2111.00956/) (2021)
- [Vision-Guided Quadrupedal Locomotion in the Wild with Multi-Modal Delay Randomization](https://mlsanity.com/paper/2109.14549/) (2021)
- [Continuous-Time Fitted Value Iteration for Robust Policies](https://mlsanity.com/paper/2110.01954/) (2021)
- [Toward Evaluating Robustness of Reinforcement Learning with Adversarial Policy](https://mlsanity.com/paper/2305.02605/) (2023)
- [Adversarially Robust Stability Certificates can be Sample-Efficient](https://mlsanity.com/paper/2112.10690/) (2021)
- [Twice Regularized Markov Decision Processes: The Equivalence between Robustness and Regularization](https://mlsanity.com/paper/2303.06654/) (2023)
- [Is Bellman Equation Enough for Learning Control?](https://mlsanity.com/paper/2503.02171/) (2025)
- [Entropy Regularization Improves Policy Robustness in Continuous-Time Reinforcement Learning](https://mlsanity.com/paper/2607.03168/) (2026)

## Abstract (arXiv)

When transferring a control policy from simulation to a physical system, the policy needs to be robust to variations in the dynamics to perform well. Commonly, the optimal policy overfits to the approximate model and the corresponding state-distribution, often resulting in failure to trasnfer underlying distributional shifts. In this paper, we present Robust Fitted Value Iteration, which uses dynamic programming to compute the optimal value function on the compact state domain and incorporates adversarial perturbations of the system dynamics. The adversarial perturbations encourage a optimal policy that is robust to changes in the dynamics. Utilizing the continuous-time perspective of reinforcement learning, we derive the optimal perturbations for the states, actions, observations and model parameters in closed-form. Notably, the resulting algorithm does not require discretization of states or actions. Therefore, the optimal adversarial perturbations can be efficiently incorporated in the min-max value function update. We apply the resulting algorithm to the physical Furuta pendulum and cartpole. By changing the masses of the systems we evaluate the quantitative and qualitative performance across different model parameters. We show that robust value iteration is more robust compared to deep reinforcement learning algorithm and the non-robust version of the algorithm. Videos of the experiments are shown at https://sites.google.com/view/rfvi