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Thomas Schön

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8 papers

1 author row

NeurIPS Conference 2025 Conference Paper

Kernel Learning with Adversarial Features: Numerical Efficiency and Adaptive Regularization

Antonio Ribeiro
David Vävinggren
Dave Zachariah
Thomas Schön
Francis Bach

Adversarial training has emerged as a key technique to enhance model robustness against adversarial input perturbations. Many of the existing methods rely on computationally expensive min-max problems that limit their application in practice. We propose a novel formulation of adversarial training in reproducing kernel Hilbert spaces, shifting from input to feature-space perturbations. This reformulation enables the exact solution of inner maximization and efficient optimization. It also provides a regularized estimator that naturally adapts to the noise level and the smoothness of the underlying function. We establish conditions under which the feature-perturbed formulation is a relaxation of the original problem and propose an efficient optimization algorithm based on iterative kernel ridge regression. We provide generalization bounds that help to understand the properties of the method. We also extend the formulation to multiple kernel learning. Empirical evaluation shows good performance in both clean and adversarial settings.

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NeurIPS Conference 2023 Conference Paper

Regularization properties of adversarially-trained linear regression

Antonio Ribeiro
Dave Zachariah
Francis Bach
Thomas Schön

State-of-the-art machine learning models can be vulnerable to very small input perturbations that are adversarially constructed. Adversarial training is an effective approach to defend against it. Formulated as a min-max problem, it searches for the best solution when the training data were corrupted by the worst-case attacks. Linear models are among the simple models where vulnerabilities can be observed and are the focus of our study. In this case, adversarial training leads to a convex optimization problem which can be formulated as the minimization of a finite sum. We provide a comparative analysis between the solution of adversarial training in linear regression and other regularization methods. Our main findings are that: (A) Adversarial training yields the minimum-norm interpolating solution in the overparameterized regime (more parameters than data), as long as the maximum disturbance radius is smaller than a threshold. And, conversely, the minimum-norm interpolator is the solution to adversarial training with a given radius. (B) Adversarial training can be equivalent to parameter shrinking methods (ridge regression and Lasso). This happens in the underparametrized region, for an appropriate choice of adversarial radius and zero-mean symmetrically distributed covariates. (C) For $\ell_\infty$-adversarial training---as in square-root Lasso---the choice of adversarial radius for optimal bounds does not depend on the additive noise variance. We confirm our theoretical findings with numerical examples.

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NeurIPS Conference 2019 Conference Paper

Robust exploration in linear quadratic reinforcement learning

Jack Umenberger
Mina Ferizbegovic
Thomas Schön
Håkan Hjalmarsson

Learning to make decisions in an uncertain and dynamic environment is a task of fundamental performance in a number of domains. This paper concerns the problem of learning control policies for an unknown linear dynamical system so as to minimize a quadratic cost function. We present a method, based on convex optimization, that accomplishes this task ‘robustly’, i. e. , the worst-case cost, accounting for system uncertainty given the observed data, is minimized. The method balances exploitation and exploration, exciting the system in such a way so as to reduce uncertainty in the model parameters to which the worst-case cost is most sensitive. Numerical simulations and application to a hardware-in-the-loop servo-mechanism are used to demonstrate the approach, with appreciable performance and robustness gains over alternative methods observed in both.

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NeurIPS Conference 2018 Conference Paper

Learning convex bounds for linear quadratic control policy synthesis

Jack Umenberger
Thomas Schön

Learning to make decisions from observed data in dynamic environments remains a problem of fundamental importance in a numbers of fields, from artificial intelligence and robotics, to medicine and finance. This paper concerns the problem of learning control policies for unknown linear dynamical systems so as to maximize a quadratic reward function. We present a method to optimize the expected value of the reward over the posterior distribution of the unknown system parameters, given data. The algorithm involves sequential convex programing, and enjoys reliable local convergence and robust stability guarantees. Numerical simulations and stabilization of a real-world inverted pendulum are used to demonstrate the approach, with strong performance and robustness properties observed in both.

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NeurIPS Conference 2017 Conference Paper

Linearly constrained Gaussian processes

Carl Jidling
Niklas Wahlström
Adrian Wills
Thomas Schön

We consider a modification of the covariance function in Gaussian processes to correctly account for known linear constraints. By modelling the target function as a transformation of an underlying function, the constraints are explicitly incorporated in the model such that they are guaranteed to be fulfilled by any sample drawn or prediction made. We also propose a constructive procedure for designing the transformation operator and illustrate the result on both simulated and real-data examples.

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NeurIPS Conference 2014 Conference Paper

Sequential Monte Carlo for Graphical Models

Christian Andersson Naesseth
Fredrik Lindsten
Thomas Schön

We propose a new framework for how to use sequential Monte Carlo (SMC) algorithms for inference in probabilistic graphical models (PGM). Via a sequential decomposition of the PGM we find a sequence of auxiliary distributions defined on a monotonically increasing sequence of probability spaces. By targeting these auxiliary distributions using SMC we are able to approximate the full joint distribution defined by the PGM. One of the key merits of the SMC sampler is that it provides an unbiased estimate of the partition function of the model. We also show how it can be used within a particle Markov chain Monte Carlo framework in order to construct high-dimensional block-sampling algorithms for general PGMs.

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NeurIPS Conference 2013 Conference Paper

Bayesian Inference and Learning in Gaussian Process State-Space Models with Particle MCMC

Roger Frigola
Fredrik Lindsten
Thomas Schön
Carl Edward Rasmussen

State-space models are successfully used in many areas of science, engineering and economics to model time series and dynamical systems. We present a fully Bayesian approach to inference and learning in nonlinear nonparametric state-space models. We place a Gaussian process prior over the transition dynamics, resulting in a flexible model able to capture complex dynamical phenomena. However, to enable efficient inference, we marginalize over the dynamics of the model and instead infer directly the joint smoothing distribution through the use of specially tailored Particle Markov Chain Monte Carlo samplers. Once an approximation of the smoothing distribution is computed, the state transition predictive distribution can be formulated analytically. We make use of sparse Gaussian process models to greatly reduce the computational complexity of the approach.

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NeurIPS Conference 2012 Conference Paper

Ancestor Sampling for Particle Gibbs

Fredrik Lindsten
Thomas Schön
Michael Jordan

We present a novel method in the family of particle MCMC methods that we refer to as particle Gibbs with ancestor sampling (PG-AS). Similarly to the existing PG with backward simulation (PG-BS) procedure, we use backward sampling to (considerably) improve the mixing of the PG kernel. Instead of using separate forward and backward sweeps as in PG-BS, however, we achieve the same effect in a single forward sweep. We apply the PG-AS framework to the challenging class of non-Markovian state-space models. We develop a truncation strategy of these models that is applicable in principle to any backward-simulation-based method, but which is particularly well suited to the PG-AS framework. In particular, as we show in a simulation study, PG-AS can yield an order-of-magnitude improved accuracy relative to PG-BS due to its robustness to the truncation error. Several application examples are discussed, including Rao-Blackwellized particle smoothing and inference in degenerate state-space models.

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