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A canonical formalism and constraint analysis for discrete systems subject to a variational action principle are devised. The formalism is equivalent to the covariant formulation, encompasses global and local discrete time evolution moves…

Recently, adaptive control systems with relaxed persistent excitation (PE) conditions have been proposed to guarantee true parameter convergence and improve the transient response. However, in some cases, sufficient control performance and…

The goal of machine learning is to provide solutions which are trained by data or by experience coming from the environment. Many training algorithms exist and some brilliant successes were achieved. But even in structured environments for…

Model learning has gained increasing interest in recent years. It derives behavioural models from test data of black-box systems. The main advantage offered by such techniques is that they enable model-based analysis without access to the…

We consider the problem of learning the dynamics of autonomous linear systems (i.e., systems that are not affected by external control inputs) from observations of multiple trajectories of those systems, with finite sample guarantees.…

We consider recent work of Haber and Ruthotto 2017 and Chang et al. 2018, where deep learning neural networks have been interpreted as discretisations of an optimal control problem subject to an ordinary differential equation constraint. We…

Continuous-depth neural networks can be viewed as deep limits of discrete neural networks whose dynamics resemble a discretization of an ordinary differential equation (ODE). Although important steps have been taken to realize the…

This work initiates a general study of learning and generalization without the i.i.d. assumption, starting from first principles. While the traditional approach to statistical learning theory typically relies on standard assumptions from…

In order to autonomously learn wide repertoires of complex skills, robots must be able to learn from their own autonomously collected data, without human supervision. One learning signal that is always available for autonomously collected…

When deploying autonomous agents in unstructured environments over sustained periods of time, adaptability and robustness oftentimes outweigh optimality as a primary consideration. In other words, safety and survivability constraints play a…

Supervised learning, characterized by both discriminative and generative learning, seeks to predict the values of single (or sometimes multiple) predefined target attributes based on a predefined set of predictor attributes. For…

This paper presents a data-integrated framework for learning the dynamics of fractional-order nonlinear systems in both discrete-time and continuous-time settings. The proposed framework consists of two main steps. In the first step,…

Temporal difference (TD) learning with linear function approximation (linear TD) is a classic and powerful prediction algorithm in reinforcement learning. While it is well-understood that linear TD converges almost surely to a unique point,…

Automatic differentiation plays a prominent role in scientific computing and in modern machine learning, often in the context of powerful programming systems. The relation of the various embodiments of automatic differentiation to the…

In the classical herding model, asymptotic learning refers to situations where individuals eventually take the correct action regardless of their private information. Classical results identify classes of information structures for which…

We develop a continuous-time reinforcement learning framework for a class of singular stochastic control problems without entropy regularization. The optimal singular control is characterized as the optimal singular control law, which is a…

In singular models, the optimal set of parameters forms an analytic set with singularities and classical statistical inference cannot be applied to such models. This is significant for deep learning as neural networks are singular and thus…

Many autonomous systems, such as robots and self-driving cars, involve real-time decision making in complex environments, and require prediction of future outcomes from limited data. Moreover, their decisions are increasingly required to be…

A supervised learning problem is to find a function in a hypothesis function space given values on isolated data points. Inspired by the frequency principle in neural networks, we propose a Fourier-domain variational formulation for…

While neural models show remarkable accuracy on individual predictions, their internal beliefs can be inconsistent across examples. In this paper, we formalize such inconsistency as a generalization of prediction error. We propose a…