Related papers: (Un)supervised Learning of Maximal Lyapunov Functi…
Despite Neural Ordinary Differential Equations (Neural ODEs) exhibiting intrinsic robustness, existing methods often impose Lyapunov stability for formal guarantees. However, these methods still face a fundamental accuracy-robustness…
In this paper, we study the construction of Lyapunov functions based on first order approximations. In a first part, the study of local exponential stability property of a transverse invariant manifold is considered. This part is mainly a…
We investigate properties of neural networks that use both ReLU and $x^2$ as activation functions and build upon previous results to show that both analytic functions and functions in Sobolev spaces can be approximated by such networks of…
We study two time-scale linear stochastic approximation algorithms, which can be used to model well-known reinforcement learning algorithms such as GTD, GTD2, and TDC. We present finite-time performance bounds for the case where the…
The inherent approximation ability of neural networks plays an essential role in adaptive neural control, where the prerequisite for existence of the compact set is crucial in the control designs. Instead of using practical system state, in…
Learning-based neural network (NN) control policies have shown impressive empirical performance. However, obtaining stability guarantees and estimates of the region of attraction of these learned neural controllers is challenging due to the…
Reinforcement learning (RL) is promising for complicated stochastic nonlinear control problems. Without using a mathematical model, an optimal controller can be learned from data evaluated by certain performance criteria through…
We build on the dynamical systems approach to deep learning, where deep residual networks are idealized as continuous-time dynamical systems, from the approximation perspective. In particular, we establish general sufficient conditions for…
Despite a variety of available techniques the issue of the proper regularization parameter choice for inverse problems still remains one of the biggest challenges. The main difficulty lies in constructing a rule, allowing to compute the…
In this paper, we study the dynamics of temporal difference learning with neural network-based value function approximation over a general state space, namely, \emph{Neural TD learning}. We consider two practically used algorithms,…
This paper presents a general framework for exploiting the representational capacity of neural networks to approximate complex, nonlinear reward functions in the context of solving the inverse reinforcement learning (IRL) problem. We show…
We study continuous action reinforcement learning problems in which it is crucial that the agent interacts with the environment only through safe policies, i.e.,~policies that do not take the agent to undesirable situations. We formulate…
Despite their spectacular progress, language models still struggle on complex reasoning tasks, such as advanced mathematics. We consider a long-standing open problem in mathematics: discovering a Lyapunov function that ensures the global…
We propose a novel framework for the Lyapunov analysis of an important class of hybrid systems, inspired by the theory of symbolic dynamics and earlier results on the restricted class of switched systems. This new framework allows us to…
This paper presents an algorithm for computing inner estimates of the regions of attraction of limit cycles of a nonlinear hybrid system. The basic procedure is: (1) compute the dynamics of the system transverse to the limit cycle; (2) from…
We present a technique for learning control Lyapunov-like functions, which are used in turn to synthesize controllers for nonlinear dynamical systems that can stabilize the system, or satisfy specifications such as remaining inside a safe…
We provide algorithms for computing a Lyapunov function for a class of systems where the state trajectories are constrained to evolve within a closed convex set. The dynamical systems that we consider comprise a differential equation which…
Meta-learning algorithms use past experience to learn to quickly solve new tasks. In the context of reinforcement learning, meta-learning algorithms acquire reinforcement learning procedures to solve new problems more efficiently by…
Learning controllers merely based on a performance metric has been proven effective in many physical and non-physical tasks in both control theory and reinforcement learning. However, in practice, the controller must guarantee some notion…
The continuous dynamical system approach to deep learning is explored in order to devise alternative frameworks for training algorithms. Training is recast as a control problem and this allows us to formulate necessary optimality conditions…