Ivan Dario Jimenez Rodriguez

Yujia Huang, Ivan Dario Jimenez Rodriguez, Huan Zhang et al.

Forward invariance is a long-studied property in control theory that is used to certify that a dynamical system stays within some pre-specified set of states for all time, and also admits robustness guarantees (e.g., the certificate holds under perturbations). We propose a general framework for training and provably certifying robust forward invariance in Neural ODEs. We apply this framework to provide certified safety in robust continuous control. To our knowledge, this is the first instance of training Neural ODE policies with such non-vacuous certified guarantees. In addition, we explore the generality of our framework by using it to certify adversarial robustness for image classification.

Ivan Dario Jimenez Rodriguez, Aaron D. Ames, Yisong Yue

We propose a method for training ordinary differential equations by using a control-theoretic Lyapunov condition for stability. Our approach, called LyaNet, is based on a novel Lyapunov loss formulation that encourages the inference dynamics to converge quickly to the correct prediction. Theoretically, we show that minimizing Lyapunov loss guarantees exponential convergence to the correct solution and enables a novel robustness guarantee. We also provide practical algorithms, including one that avoids the cost of backpropagating through a solver or using the adjoint method. Relative to standard Neural ODE training, we empirically find that LyaNet can offer improved prediction performance, faster convergence of inference dynamics, and improved adversarial robustness. Our code available at https://github.com/ivandariojr/LyapunovLearning .

Andrew Silva, Taylor Killian, Ivan Dario Jimenez Rodriguez et al.

Decision trees are ubiquitous in machine learning for their ease of use and interpretability. Yet, these models are not typically employed in reinforcement learning as they cannot be updated online via stochastic gradient descent. We overcome this limitation by allowing for a gradient update over the entire tree that improves sample complexity affords interpretable policy extraction. First, we include theoretical motivation on the need for policy-gradient learning by examining the properties of gradient descent over differentiable decision trees. Second, we demonstrate that our approach equals or outperforms a neural network on all domains and can learn discrete decision trees online with average rewards up to 7x higher than a batch-trained decision tree. Third, we conduct a user study to quantify the interpretability of a decision tree, rule list, and a neural network with statistically significant results ($p < 0.001$).

Brandon Amos, Ivan Dario Jimenez Rodriguez, Jacob Sacks et al.

We present foundations for using Model Predictive Control (MPC) as a differentiable policy class for reinforcement learning in continuous state and action spaces. This provides one way of leveraging and combining the advantages of model-free and model-based approaches. Specifically, we differentiate through MPC by using the KKT conditions of the convex approximation at a fixed point of the controller. Using this strategy, we are able to learn the cost and dynamics of a controller via end-to-end learning. Our experiments focus on imitation learning in the pendulum and cartpole domains, where we learn the cost and dynamics terms of an MPC policy class. We show that our MPC policies are significantly more data-efficient than a generic neural network and that our method is superior to traditional system identification in a setting where the expert is unrealizable.