EPFL AI Center, TML Lab and ELLIS Lausanne Unit

Lorenzo Rosasco considers learning from a single finite trajectory of a dynamical system, focusing on discrete-time autonomous stochastic systems that define time-homogeneous ergodic Markov processes. He first studies estimation of the optimal one-step prediction function by nonlinear least squares and develops an analysis with high-probability guarantees with respect to the invariant measure, showing how non-independent, non-identically distributed trajectory data changes classical supervised learning analysis; the analysis extends to higher-order processes and finite state spaces. He then refines it using weaker notions of ergodicity and assumptions linking the geometry of the chain to the prediction task, and shows how the approach extends to learning Koopman operators, which can be used to control nonlinear dynamical systems, including a model predictive control approach for switching dynamical systems.