Erik Börve

Jonathan Dong, Erik Börve, Mushegh Rafayelyan et al.

Reservoir Computing is a class of Recurrent Neural Networks with internal weights fixed at random. Stability relates to the sensitivity of the network state to perturbations. It is an important property in Reservoir Computing as it directly impacts performance. In practice, it is desirable to stay in a stable regime, where the effect of perturbations does not explode exponentially, but also close to the chaotic frontier where reservoir dynamics are rich. Open questions remain today regarding input regularization and discontinuous activation functions. In this work, we use the recurrent kernel limit to draw new insights on stability in reservoir computing. This limit corresponds to large reservoir sizes, and it already becomes relevant for reservoirs with a few hundred neurons. We obtain a quantitative characterization of the frontier between stability and chaos, which can greatly benefit hyperparameter tuning. In a broader sense, our results contribute to understanding the complex dynamics of Recurrent Neural Networks.

Erik Börve, Nikolce Murgovski, Morteza Haghir Chehreghani et al.

We investigate interactive trajectory planning subject to uncertainty in the decisions of surrounding agents. To control the ego-agent, we aim to first learn the decision distribution and solve a Stochastic Model Predictive Control (SMPC) problem. To account for errors in the learned distribution, we show that it is possible to utilize Probably Approximately Correct (PAC) learning in combination with Distributionally Robust (DR) optimization to obtain a solution which accounts for the errors induced by the learning model. The results indicate that our PAC learning-based DR-MPC framework provides a method to interpolate between a robust MPC and an omnipotent SMPC, based on the available number of samples.