Related papers: Learning from many trajectories
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.…
Many machine learning algorithms are based on the assumption that training examples are drawn independently. However, this assumption does not hold anymore when learning from a networked sample because two or more training examples may…
Learning from temporally-correlated data is a core facet of modern machine learning. Yet our understanding of sequential learning remains incomplete, particularly in the multi-trajectory setting where data consists of many independent…
Suppose that we observe a short time series where each time-t-specific data-structure consists of many slightly dependent data indexed by a and that we want to estimate a feature of the law of the experiment that depends neither on t nor on…
Meta-learning is a tool that allows us to build sample-efficient learning systems. Here we show that, once meta-trained, LSTM Meta-Learners aren't just faster learners than their sample-inefficient deep learning (DL) and reinforcement…
Standard supervised learning breaks down under data distribution shift. However, the principle of independent causal mechanisms (ICM, Peters et al. (2017)) can turn this weakness into an opportunity: one can take advantage of distribution…
Learning rate schedules are ubiquitously used to speed up and improve optimisation. Many different policies have been introduced on an empirical basis, and theoretical analyses have been developed for convex settings. However, in many…
We study a special case of the problem of statistical learning without the i.i.d. assumption. Specifically, we suppose a learning method is presented with a sequence of data points, and required to make a prediction (e.g., a classification)…
The identification of a linear system model from data has wide applications in control theory. The existing work that provides finite sample guarantees for linear system identification typically uses data from a single long system…
A fundamental challenge in learning to control an unknown dynamical system is to reduce model uncertainty by making measurements while maintaining safety. In this work, we formulate a mathematical definition of what it means to safely learn…
Recent advances in natural language processing highlight two key factors for improving reasoning in large language models (LLMs): (i) allocating more test-time compute tends to help on harder problems but often introduces redundancy in the…
We introduce algorithms for learning nonlinear dynamical systems of the form $x_{t+1}=\sigma(\Theta^{\star}x_t)+\varepsilon_t$, where $\Theta^{\star}$ is a weight matrix, $\sigma$ is a nonlinear link function, and $\varepsilon_t$ is a…
Empirical process theory for i.i.d. observations has emerged as a ubiquitous tool for understanding the generalization properties of various statistical problems. However, in many applications where the data exhibit temporal dependencies…
Implementing an autonomous vehicle that is able to output feasible, smooth and efficient trajectories is a long-standing challenge. Several approaches have been considered, roughly falling under two categories: rule-based and learning-based…
The ability of a brain or a neural network to efficiently learn depends crucially on both the task structure and the learning rule. Previous works have analyzed the dynamical equations describing learning in the relatively simplified…
We study the problem of learning a mixture of multiple linear dynamical systems (LDSs) from unlabeled short sample trajectories, each generated by one of the LDS models. Despite the wide applicability of mixture models for time-series data,…
Identifying a linear system model from data has wide applications in control theory. The existing work on finite sample analysis for linear system identification typically uses data from a single system trajectory under i.i.d random inputs,…
Given a single trajectory of a dynamical system, we analyze the performance of the nonparametric least squares estimator (LSE). More precisely, we give nonasymptotic expected $l^2$-distance bounds between the LSE and the true regression…
Classic supervised learning involves algorithms trained on $n$ labeled examples to produce a hypothesis $h \in \mathcal{H}$ aimed at performing well on unseen examples. Meta-learning extends this by training across $n$ tasks, with $m$…
Training autonomous agents that can learn new tasks from only a handful of demonstrations is a long-standing problem in machine learning. Recently, transformers have been shown to learn new language or vision tasks without any weight…