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We consider the problem of continuous-time policy evaluation. This consists in learning through observations the value function associated with an uncontrolled continuous-time stochastic dynamic and a reward function. We propose two…

The discovery of structure from time series data is a key problem in fields of study working with complex systems. Most identifiability results and learning algorithms assume the underlying dynamics to be discrete in time. Comparatively…

Many learning algorithms are formulated in terms of finding model parameters which minimize a data-fitting loss function plus a regularizer. When the regularizer involves the l0 pseudo-norm, the resulting regularization path consists of a…

There is an increasing need of continual learning in dynamic systems, such as the self-driving vehicle, the surveillance drone, and the robotic system. Such a system requires learning from the data stream, training the model to preserve…

Unsupervised learning of time series data, also known as temporal clustering, is a challenging problem in machine learning. Here we propose a novel algorithm, Deep Temporal Clustering (DTC), to naturally integrate dimensionality reduction…

Training dynamic models, such as neural ODEs, on long trajectories is a hard problem that requires using various tricks, such as trajectory splitting, to make model training work in practice. These methods are often heuristics with poor…

Quantile optimal treatment regimes (OTRs) aim to assign treatments that maximize a specified quantile of patients' outcomes. Compared to treatment regimes that target the mean outcomes, quantile OTRs offer fairer regimes when a lower…

Neural Ordinary Differential Equations (ODEs) represent a significant advancement at the intersection of machine learning and dynamical systems, offering a continuous-time analog to discrete neural networks. Despite their promise, deploying…

The neural network-based approach to solving partial differential equations has attracted considerable attention due to its simplicity and flexibility in representing the solution of the partial differential equation. In training a neural…

Traditional test-time training (TTT) methods, while addressing domain shifts, often assume a consistent class set, limiting their applicability in real-world scenarios characterized by infinite variety. Open-World Test-Time Training (OWTTT)…

Temporal difference (TD) learning is a fundamental algorithm for estimating value functions in reinforcement learning. Recent finite-time analyses of TD with linear function approximation quantify its theoretical convergence rate. However,…

Machine learning models are prone to making incorrect predictions on inputs that are far from the training distribution. This hinders their deployment in safety-critical applications such as autonomous vehicles and healthcare. The detection…

Deep sequence models have achieved notable success in time-series analysis, such as interpolation and forecasting. Recent advances move beyond discrete-time architectures like Recurrent Neural Networks (RNNs) toward continuous-time…

A key appeal of the recently proposed Neural Ordinary Differential Equation (ODE) framework is that it seems to provide a continuous-time extension of discrete residual neural networks. As we show herein, though, trained Neural ODE models…

For a large class of dynamical systems, the optimally time-dependent (OTD) modes, a set of deformable orthonormal tangent vectors that track directions of instabilities along any trajectory, are known to depend "pointwise" on the state of…

We establish a time-stepping learning algorithm and apply it to predict the solution of the partial differential equation of motion in micromagnetism as a dynamical system depending on the external field as parameter. The data-driven…

We consider the neural ODE perspective of supervised learning and study the impact of the final time $T$ (which may indicate the depth of a corresponding ResNet) in training. For the classical $L^2$--regularized empirical risk minimization…

Multistage stochastic programming deals with operational and planning problems that involve a sequence of decisions over time while responding to realizations that are uncertain. Algorithms designed to address multistage stochastic linear…

In contrast to humans and animals who naturally execute seamless motions, learning and smoothly executing sequences of actions remains a challenge in robotics. This paper introduces a novel skill-agnostic framework that learns to sequence…

We introduce the Optimizing a Discrete Loss (ODIL) framework for the numerical solution of Partial Differential Equations (PDE) using machine learning tools. The framework formulates numerical methods as a minimization of discrete residuals…