Echo State Networks (ESNs) are time-series processing models working under the Echo State Property (ESP) principle. The ESP is a notion of stability that imposes an asymptotic fading of the memory of the input. On the other hand, the resulting inherent architectural bias of ESNs may lead to an excessive loss of information, which in turn harms the performance in certain tasks with long short-term memory requirements. With the goal of bringing together the fading memory property and the ability to retain as much memory as possible, in this paper we introduce a new ESN architecture, called the Edge of Stability Echo State Network (ES$^2$N). The introduced ES$^2$N model is based on defining the reservoir layer as a convex combination of a nonlinear reservoir (as in the standard ESN), and a linear reservoir that implements an orthogonal transformation. We provide a thorough mathematical analysis of the introduced model, proving that the whole eigenspectrum of the Jacobian of the ES$^2$N map can be contained in an annular neighbourhood of a complex circle of controllable radius, and exploit this property to demonstrate that the ES$^2$N's forward dynamics evolves close to the edge-of-chaos regime by design. Remarkably, our experimental analysis shows that the newly introduced reservoir model is able to reach the theoretical maximum short-term memory capacity. At the same time, in comparison to standard ESN, ES$^2$N is shown to offer an excellent trade-off between memory and nonlinearity, as well as a significant improvement of performance in autoregressive nonlinear modeling.

Safe reinforcement learning has been a promising approach for optimizing the policy of an agent that operates in safety-critical applications. In this paper, we propose an algorithm, SNO-MDP, that explores and optimizes Markov decision processes under unknown safety constraints. Specifically, we take a stepwise approach for optimizing safety and cumulative reward. In our method, the agent first learns safety constraints by expanding the safe region, and then optimizes the cumulative reward in the certified safe region. We provide theoretical guarantees on both the satisfaction of the safety constraint and the near-optimality of the cumulative reward under proper regularity assumptions. In our experiments, we demonstrate the effectiveness of SNO-MDP through two experiments: one uses a synthetic data in a new, openly-available environment named GP-SAFETY-GYM, and the other simulates Mars surface exploration by using real observation data.

The action programming language GOLOG has been found useful for the control of autonomous agents such as mobile robots. In scenarios like these, tasks are often open-ended so that the respective control programs are non-terminating. Before deploying such programs on a robot, it is often desirable to verify that they meet certain requirements. For this purpose, Claßen and Lakemeyer recently introduced algorithms for the verification of temporal properties of GOLOG programs. However, given the expressiveness of GOLOG, their verification procedures are not guaranteed to terminate. In this paper, we show how decidability can be obtained by suitably restricting the underlying base logic, the effect axioms for primitive actions, and the use of actions within GOLOG programs. Moreover, we show that dropping any of these restrictions immediately leads to undecidability of the verification problem.