Paweł Wachel

Dominik Baumann, Krzysztof Kowalczyk, Koen Tiels et al.

Safety is an essential asset when learning control policies for physical systems, as violating safety constraints during training can lead to expensive hardware damage. In response to this need, the field of safe learning has emerged with algorithms that can provide probabilistic safety guarantees without knowledge of the underlying system dynamics. Those algorithms often rely on Gaussian process inference. Unfortunately, Gaussian process inference scales cubically with the number of data points, limiting applicability to high-dimensional and embedded systems. In this paper, we propose a safe learning algorithm that provides probabilistic safety guarantees but leverages the Nadaraya-Watson estimator instead of Gaussian processes. For the Nadaraya-Watson estimator, we can reach logarithmic scaling with the number of data points. We provide theoretical guarantees for the estimates, embed them into a safe learning algorithm, and show numerical experiments on a simulated seven-degrees-of-freedom robot manipulator.

Krzysztof Kowalczyk, Paweł Wachel, Cristian R. Rojas

This paper addresses a kernel-based learning problem for a network of agents locally observing a latent multidimensional, nonlinear phenomenon in a noisy environment. We propose a learning algorithm that requires only mild a priori knowledge about the phenomenon under investigation and delivers a model with corresponding non-asymptotic high probability error bounds. Both non-asymptotic analysis of the method and numerical simulation results are presented and discussed in the paper.

Krzysztof Zając, Wojciech Sopot, Paweł Wachel

We consider applications of neural networks in nonlinear system identification and formulate a hypothesis that adjusting general network structure by incorporating frequency information or other known orthogonal transform, should result in an efficient neural network retaining its universal properties. We show that such a structure is a universal approximator and that using any orthogonal transform in a proposed way implies regularization during training by adjusting the learning rate of each parameter individually. We empirically show in particular, that such a structure, using the Fourier transform, outperforms equivalent models without orthogonality support.

Paweł Wachel, Krzysztof Kowalczyk, Cristian R. Rojas

We study the problem of diffusion-based network learning of a nonlinear phenomenon, $m$, from local agents' measurements collected in a noisy environment. For a decentralized network and information spreading merely between directly neighboring nodes, we propose a non-parametric learning algorithm, that avoids raw data exchange and requires only mild \textit{a priori} knowledge about $m$. Non-asymptotic estimation error bounds are derived for the proposed method. Its potential applications are illustrated through simulation experiments.