• Safe Reinforcement Learning (RL) as Deep Deterministic Policy Gradient is used. • Deep Deterministic Policy Gradient (DDPG) is combined with metaheuristic SMA. • The approach mitigates the drawbacks of DDPG-based safe RL optimal control. • SMA initializes the parameters of the neural network-based controller. • State safety constraints are incorporated into the search process of SMA. This paper presents a novel optimal control approach resulting from the combination between the safe Reinforcement Learning (RL) framework represented by a Deep Deterministic Policy Gradient (DDPG) algorithm and a Slime Mould Algorithm (SMA) as a representative nature-inspired optimization algorithm. The main drawbacks of the traditional DDPG-based safe RL optimal control approach are the possible instability of the control system caused by randomly generated initial values of the controller parameters and the lack of state safety guarantees in the first iterations of the learning process due to (i) and (ii): (i) the safety constraints are considered only in the DDPG-based training process of the controller, which is usually implemented as a neural network (NN); (ii) the initial values of the weights and the biases of the NN-based controller are initialized with randomly generated values. The proposed approach mitigates these drawbacks by initializing the parameters of the NN-based controller using SMA. The fitness function of the SMA-based initialization process is designed to incorporate state safety constraints into the search process, resulting in an initial NN-based controller with embedded state safety constraints. The proposed approach is compared to the classical one using real-time experimental results and performance indices popular for optimal reference tracking control problems and based on a state safety score.

Multiple poll forecasting solutions, based on statistics and economic indices, have been proposed over time, but, as we better understand diffusion phenomena, we know that temporal characteristics provide even more uncertainty. As such, current literature is not yet able to define truly reliable models for the evolution of political opinion, marketing preferences, or social unrest. Inspired by micro-scale opinion dynamics, we develop an original time-aware (TA) methodology which is able to improve the prediction of opinion distribution, by modeling opinion as a function which spikes up when opinion is expressed, and slowly dampens down otherwise. After a parametric analysis, we validate our TA method on survey data from the US presidential elections of 2012 and 2016. By comparing our time-aware method (TA) with classic survey averaging (SA), and cumulative vote counting (CC), we find our method is substantially closer to the real election outcomes. On average, we measure that SA is 6.3% off, CC is 5.6% off, while TA is only 1.5% off from the final registered election outcomes; this difference translates into an ≈ 75% prediction improvement of our TA method. As our work falls in line with studies on the microscopic temporal dynamics of social networks, we find evidence of how macroscopic prediction can be improved using time-awareness.