Victor D. Dorobantu

Victor Dorobantu, Charlotte Borcherds, Yisong Yue

We propose conformal generative modeling, a framework for generative modeling on 2D surfaces approximated by discrete triangle meshes. Our approach leverages advances in discrete conformal geometry to develop a map from a source triangle mesh to a target triangle mesh of a simple manifold such as a sphere. After accounting for errors due to the mesh discretization, we can use any generative modeling approach developed for simple manifolds as a plug-and-play subroutine. We demonstrate our framework on multiple complicated manifolds and multiple generative modeling subroutines, where we show that our approach can learn good estimates of distributions on meshes from samples, and can also learn simultaneously from multiple distinct meshes of the same underlying manifold.

Victor D. Dorobantu, Kamyar Azizzadenesheli, Yisong Yue

We study policy optimization problems for deterministic Markov decision processes (MDPs) with metric state and action spaces, which we refer to as Metric Policy Optimization Problems (MPOPs). Our goal is to establish theoretical results on the well-posedness of MPOPs that can characterize practically relevant continuous control systems. To do so, we define a special class of MPOPs called Compactly Restrictable MPOPs (CR-MPOPs), which are flexible enough to capture the complex behavior of robotic systems but specific enough to admit solutions using dynamic programming methods such as value iteration. We show how to arrive at CR-MPOPs using forward-invariance. We further show that our theoretical results on CR-MPOPs can be used to characterize feedback linearizable control affine systems.

Andrew J. Taylor, Victor D. Dorobantu, Sarah Dean et al.

Modern nonlinear control theory seeks to endow systems with properties such as stability and safety, and has been deployed successfully across various domains. Despite this success, model uncertainty remains a significant challenge in ensuring that model-based controllers transfer to real world systems. This paper develops a data-driven approach to robust control synthesis in the presence of model uncertainty using Control Certificate Functions (CCFs), resulting in a convex optimization based controller for achieving properties like stability and safety. An important benefit of our framework is nuanced data-dependent guarantees, which in principle can yield sample-efficient data collection approaches that need not fully determine the input-to-state relationship. This work serves as a starting point for addressing important questions at the intersection of nonlinear control theory and non-parametric learning, both theoretical and in application. We validate the proposed method in simulation with an inverted pendulum in multiple experimental configurations.

Victor Dorobantu, Per Andre Stromhaug, Jess Renteria

The vanishing and exploding gradient problems are well-studied obstacles that make it difficult for recurrent neural networks to learn long-term time dependencies. We propose a reparameterization of standard recurrent neural networks to update linear transformations in a provably norm-preserving way through Givens rotations. Additionally, we use the absolute value function as an element-wise non-linearity to preserve the norm of backpropagated signals over the entire network. We show that this reparameterization reduces the number of parameters and maintains the same algorithmic complexity as a standard recurrent neural network, while outperforming standard recurrent neural networks with orthogonal initializations and Long Short-Term Memory networks on the copy problem.