Related papers: Stability revisited: new generalisation bounds for…
Evaluating the predictive performance of a statistical model is commonly done using cross-validation. Among the various methods, leave-one-out cross-validation (LOOCV) is frequently used. Originally designed for exchangeable observations,…
Stability certification and identifying a safe and stabilizing initial set are two important concerns in ensuring operational safety, stability, and robustness of dynamical systems. With the advent of machine-learning tools, these issues…
Hypothesis transfer learning (HTL) contrasts domain adaptation by allowing for a previous task leverage, named the source, into a new one, the target, without requiring access to the source data. Indeed, HTL relies only on a hypothesis…
Many machine learning problems can be formulated as minimax problems such as Generative Adversarial Networks (GANs), AUC maximization and robust estimation, to mention but a few. A substantial amount of studies are devoted to studying the…
We present a data-driven framework based on Lyapunov theory to provide stability guarantees for a family of hybrid systems. In particular, we are interested in the asymptotic stability of switching linear systems whose switching sequence is…
PAC-Bayes is a popular and efficient framework for obtaining generalization guarantees in situations involving uncountable hypothesis spaces. Unfortunately, in its classical formulation, it only provides guarantees on the expected risk of a…
Global asymptotic stability of rational difference equations is an area of research that has been well studied. In contrast to the many current methods for proving global asymptotic stability, we propose an algorithmic approach. The…
We study the properties and stability of networks with arbitrary Laplacian coupling. Classic approaches to studying networked systems require unrealistic assumptions, including homogeneous node dynamics, one-dimensional and undirected…
We study reinforcement learning (RL) with linear function approximation. Existing algorithms for this problem only have high-probability regret and/or Probably Approximately Correct (PAC) sample complexity guarantees, which cannot guarantee…
This paper presents the first sufficient conditions that guarantee the stability and almost sure convergence of multi-timescale stochastic approximation (SA) iterates. It extends the existing results on one-timescale and two-timescale SA…
We introduce a data-driven approach to analyze the performance of continuous optimization algorithms using generalization guarantees from statistical learning theory. We study classical and learned optimizers to solve families of parametric…
Long-horizon execution in Large Language Models (LLMs) remains unstable even when high-level strategies are provided. Evaluating on controlled algorithmic puzzles, we demonstrate that while decomposition is essential for stability, extreme…
Control policies from imitation learning can often fail to generalize to novel environments due to imperfect demonstrations or the inability of imitation learning algorithms to accurately infer the expert's policies. In this paper, we…
Bagging is an important technique for stabilizing machine learning models. In this paper, we derive a finite-sample guarantee on the stability of bagging for any model. Our result places no assumptions on the distribution of the data, on…
We propose the first general PAC-Bayesian generalization bounds for adversarial robustness, that estimate, at test time, how much a model will be invariant to imperceptible perturbations in the input. Instead of deriving a worst-case…
This dissertation investigates how reinforcement learning (RL) methods can be designed to be safe, sample-efficient, and robust. Framed through the unifying perspective of contextual-bandit RL, the work addresses two major application…
Updating machine learning models with new information usually improves their predictive performance, yet, in many applications, it is also desirable to avoid changing the model predictions too much. This property is called stability. In…
Deep neural networks generalize well despite being heavily overparameterized, in apparent contradiction with classical learning theory based on uniform convergence over fixed hypothesis spaces. Uniform bounds over the entire parameter space…
In this note we identify a class of underactuated mechanical systems whose desired constant equilibrium position can be globally stabilised with the ubiquitous PID controller. The class is characterised via some easily verifiable conditions…
The stability analysis of model predictive control schemes without terminal constraints and/or costs has attracted considerable attention during the last years. We pursue a recently proposed approach which can be used to determine a…