Malte Heinrich

Julian D. Schiller, Malte Heinrich, Victor G. Lopez et al.

Training recurrent neural networks (RNNs) with standard backpropagation through time (BPTT) can be challenging, especially in the presence of long input sequences. A practical alternative to reduce computational and memory overhead is to perform BPTT repeatedly over shorter segments of the training data set, corresponding to truncated BPTT. In this paper, we examine the training of RNNs when using such a truncated learning approach for time series tasks. Specifically, we establish theoretical bounds on the accuracy and performance loss when optimizing over subsequences instead of the full data sequence. This reveals that the burn-in phase of the RNN is an important tuning knob in its training, with significant impact on the performance guarantees. We validate our theoretical results through experiments on standard benchmarks from the fields of system identification and time series forecasting. In all experiments, we observe a strong influence of the burn-in phase on the training process, and proper tuning can lead to a reduction of the prediction error on the training and test data of more than 60% in some cases.

Victor G. Lopez, Malte Heinrich, Matthias A. Müller

In the reinforcement learning literature, strong theoretical guarantees have been obtained for algorithms applicable to LTI systems. However, in the nonlinear case only weaker results have been obtained for algorithms that mostly rely on the use of function approximation strategies like, for example, neural networks. In this paper, we study the applicability of a known output-feedback Q-learning algorithm to the class of nonlinear systems that admit a Koopman linear embedding. This algorithm uses only input-output data, and no knowledge of either the system model or the Koopman lifting functions is required. Moreover, no function approximation techniques are used, and the same theoretical guarantees as for LTI systems are preserved. Furthermore, we analyze the performance of the algorithm when the Koopman linear embedding is only an approximation of the real nonlinear system. A simulation example verifies the applicability of this method.