Related papers: Distributionally Robust PAC-Bayesian Control

Current PAC-Bayes generalisation bounds are restricted to scalar metrics of performance, such as the loss or error rate. However, one ideally wants more information-rich certificates that control the entire distribution of possible…

We are motivated by the problem of providing strong generalization guarantees in the context of meta-learning. Existing generalization bounds are either challenging to evaluate or provide vacuous guarantees in even relatively simple…

This paper presents an approach for learning vision-based planners that provably generalize to novel environments (i.e., environments unseen during training). We leverage the Probably Approximately Correct (PAC)-Bayes framework to obtain an…

We study control of constrained linear systems with only partial statistical information about the uncertainty affecting the system dynamics and the sensor measurements. Specifically, given a finite collection of disturbance realizations…

We address the challenge of sequential data-driven decision-making under context distributional uncertainty. This problem arises in numerous real-world scenarios where the learner optimizes black-box objective functions in the presence of…

PAC-Bayesian bounds are known to be tight and informative when studying the generalization ability of randomized classifiers. However, they require a loose and costly derandomization step when applied to some families of deterministic…

We provide two main contributions in PAC-Bayesian theory for domain adaptation where the objective is to learn, from a source distribution, a well-performing majority vote on a different, but related, target distribution. Firstly, we…

We introduce a new framework for studying meta-learning methods using PAC-Bayesian theory. Its main advantage over previous work is that it allows for more flexibility in how the transfer of knowledge between tasks is realized. For previous…

Safety is a critical issue in learning-based robotic and autonomous systems as learned information about their environments is often unreliable and inaccurate. In this paper, we propose a risk-aware motion control tool that is robust…

In this paper, we derive a PAC-Bayes bound on the generalisation gap, in a supervised time-series setting for a special class of discrete-time non-linear dynamical systems. This class includes stable recurrent neural networks (RNN), and the…

We present a novel data-driven distributionally robust Model Predictive Control formulation for unknown discrete-time linear time-invariant systems affected by unknown and possibly unbounded additive uncertainties. We use off-line collected…

Empirically, the PAC-Bayesian analysis is known to produce tight risk bounds for practical machine learning algorithms. However, in its naive form, it can only deal with stochastic predictors while such predictors are rarely used and…

The limit of infinite width allows for substantial simplifications in the analytical study of over-parameterised neural networks. With a suitable random initialisation, an extremely large network exhibits an approximately Gaussian…

Gaussian Processes (GPs) are a generic modelling tool for supervised learning. While they have been successfully applied on large datasets, their use in safety-critical applications is hindered by the lack of good performance guarantees. To…

The Sliced-Wasserstein distance (SW) is a computationally efficient and theoretically grounded alternative to the Wasserstein distance. Yet, the literature on its statistical properties -- or, more accurately, its generalization properties…

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…

We propose a distributionally robust data-driven predictive control framework for stochastic linear time-invariant systems with unknown dynamics and disturbance distributions. We use an offline trajectory to fit the subspace predictive…

While PAC-Bayes is now an established learning framework for light-tailed losses (\emph{e.g.}, subgaussian or subexponential), its extension to the case of heavy-tailed losses remains largely uncharted and has attracted a growing interest…

Wasserstein distributionally robust control (DRC) recently emerges as a principled paradigm for handling uncertainty in stochastic dynamical systems. However, it constructs data-driven ambiguity sets via uniform distribution shifts before…

Training machine learning and statistical models often involves optimizing a data-driven risk criterion. The risk is usually computed with respect to the empirical data distribution, but this may result in poor and unstable out-of-sample…