Safe reinforcement learning (RL) is a promising approach for many real-world decision-making problems where ensuring safety is a critical necessity.

Abstract-- We consider the problem of repetitive scenario design where one has to solve repeatedly a scenario design problem and can adjust the sample size (number of scenarios) to obtain a desired level of risk (constraint violation probability). We propose an approach to learn on the fly the optimal sample size based on observed data consisting in previous scenario solutions and their risk level. Our approach consists in learning a function that represents the pdf (probability density function) of the risk as a function of the sample size. Once this function is known, retrieving the optimal sample size is straightforward. We prove the soundness and convergence of our approach to obtain the optimal sample size for the class of fixed-complexity scenario problems, which generalizes fully-supported convex scenario programs that have been studied extensively in the scenario optimization literature. We also demonstrate the practical efficiency of our approach on a series of challenging repetitive scenario design problems, including non-fixed-complexity problems, nonconvex constraints and time-varying distributions.

In Wireless Networked Control Systems (WNCSs), control and communication systems must be co-designed due to their strong interdependence. This paper presents a novel optimization theory-based safe deep reinforcement learning (DRL) framework for ultra-reliable WNCSs, ensuring constraint satisfaction while optimizing performance, for the first time in the literature. The approach minimizes power consumption under key constraints, including Peak Age of Information (PAoI) violation probability, transmit power, and schedulability in the finite blocklength regime. PAoI violation probability is uniquely derived by combining stochastic maximum allowable transfer interval (MATI) and maximum allowable packet delay (MAD) constraints in a multi-sensor network. The framework consists of two stages: optimization theory and safe DRL. The first stage derives optimality conditions to establish mathematical relationships among variables, simplifying and decomposing the problem. The second stage employs a safe DRL model where a teacher-student framework guides the DRL agent (student). The control mechanism (teacher) evaluates compliance with system constraints and suggests the nearest feasible action when needed. Extensive simulations show that the proposed framework outperforms rule-based and other optimization theory based DRL benchmarks, achieving faster convergence, higher rewards, and greater stability.

We study chance constrained optimization problems $\min_x f(x)$ s.t. $P(\left\{ \theta: g(x,\theta)\le 0 \right\})\ge 1-\epsilon$ where $\epsilon\in (0,1)$ is the violation probability, when the distribution $P$ is not known to the decision maker (DM). When the DM has access to a set of distributions $\mathcal{U}$ such that $P$ is contained in $\mathcal{U}$, then the problem is known as the ambiguous chance-constrained problem \cite{erdougan2006ambiguous}. We study ambiguous chance-constrained problem for the case when $\mathcal{U}$ is of the form $\left\{\mu:\frac{\mu (y)}{\nu(y)}\leq C, \forall y\in\Theta, \mu(y)\ge 0\right\}$, where $\nu$ is a ``reference distribution.'' We show that in this case the original problem can be ``well-approximated'' by a sampled problem in which $N$ i.i.d. samples of $\theta$ are drawn from $\nu$, and the original constraint is replaced with $g(x,\theta_i)\le 0,~i=1,2,\ldots,N$. We also derive the sample complexity associated with this approximation, i.e., for $\epsilon,\delta>0$ the number of samples which must be drawn from $\nu$ so that with a probability greater than $1-\delta$ (over the randomness of $\nu$), the solution obtained by solving the sampled program yields an $\epsilon$-feasible solution for the original chance constrained problem.

Deep neural networks (DNNs) are emerging as a potential solution to solve NP-hard wireless resource allocation problems. However, in the presence of intricate constraints, e.g., users' quality-of-service (QoS) constraints, guaranteeing constraint satisfaction becomes a fundamental challenge. In this paper, we propose a novel unsupervised learning framework to solve the classical power control problem in a multi-user interference channel, where the objective is to maximize the network sumrate under users' minimum data rate or QoS requirements and power budget constraints. Utilizing a differentiable projection function, two novel deep learning (DL) solutions are pursued. The first is called Deep Implicit Projection Network (DIPNet), and the second is called Deep Explicit Projection Network (DEPNet). DIPNet utilizes a differentiable convex optimization layer to implicitly define a projection function. On the other hand, DEPNet uses an explicitly-defined projection function, which has an iterative nature and relies on a differentiable correction process. DIPNet requires convex constraints; whereas, the DEPNet does not require convexity and has a reduced computational complexity. To enhance the sum-rate performance of the proposed models even further, Frank-Wolfe algorithm (FW) has been applied to the output of the proposed models. Extensive simulations depict that the proposed DNN solutions not only improve the achievable data rate but also achieve zero constraint violation probability, compared to the existing DNNs. The proposed solutions outperform the classic optimization methods in terms of computation time complexity.

Prediction has recently been considered as a promising approach to meet low-latency and high-reliability requirements in long-distance haptic communications. However, most of the existing methods did not take features of tasks and the relationship between prediction and communication into account. In this paper, we propose a task-oriented prediction and communication co-design framework, where the reliability of the system depends on prediction errors and packet losses in communications. The goal is to minimize the required radio resources subject to the low-latency and high-reliability requirements of various tasks. Specifically, we consider the just noticeable difference (JND) as a performance metric for the haptic communication system. We collect experiment data from a real-world teleoperation testbed and use time-series generative adversarial networks (TimeGAN) to generate a large amount of synthetic data. This allows us to obtain the relationship between the JND threshold, prediction horizon, and the overall reliability including communication reliability and prediction reliability. We take 5G New Radio as an example to demonstrate the proposed framework and optimize bandwidth allocation and data rates of devices. Our numerical and experimental results show that the proposed framework can reduce wireless resource consumption up to 77.80% compared with a task-agnostic benchmark.

Nowadays, the PQ flexibility from the distributed energy resources (DERs) in the high voltage (HV) grids plays a more critical and significant role in grid congestion management in TSO grids. This work proposed a multi-stage deep reinforcement learning approach to estimate the PQ flexibility (PQ area) at the TSO-DSO interfaces and identifies the DER PQ setpoints for each operating point in a way, that DERs in the meshed HV grid can be coordinated to offer flexibility for the transmission grid. In the estimation process, we consider the steady-state grid limits and the robustness in the resulting voltage profile against uncertainties and the N-1 security criterion regarding thermal line loading, essential for real-life grid operational planning applications. Using deep reinforcement learning (DRL) for PQ flexibility estimation is the first of its kind. Furthermore, our approach of considering N-1 security criterion for meshed grids and robustness against uncertainty directly in the optimization tasks offers a new perspective besides the common relaxation schema in finding a solution with mathematical optimal power flow (OPF). Finally, significant improvements in the computational efficiency in estimation PQ area are the highlights of the proposed method.

In this paper, we aim to improve the Quality-of-Service (QoS) of Ultra-Reliability and Low-Latency Communications (URLLC) in interference-limited wireless networks. To obtain time diversity within the channel coherence time, we first put forward a random repetition scheme that randomizes the interference power. Then, we optimize the number of reserved slots and the number of repetitions for each packet to minimize the QoS violation probability, defined as the percentage of users that cannot achieve URLLC. We build a cascaded Random Edge Graph Neural Network (REGNN) to represent the repetition scheme and develop a model-free unsupervised learning method to train it. We analyze the QoS violation probability using stochastic geometry in a symmetric scenario and apply a modelbased Exhaustive Search (ES) method to find the optimal solution. Simulation results show that in the symmetric scenario, the QoS violation probabilities achieved by the model-free learning method and the model-based ES method are nearly the same. In more general scenarios, the cascaded REGNN generalizes very well in wireless networks with different scales, network topologies, cell densities, and frequency reuse factors. It outperforms the model-based ES method in the presence of the model mismatch. Yuhong Liu, Changyang She, Wibowo Hardjawana and Branka Vucetic are with School of Electrical and Information Engineering, The University of Sydney, Sydney, Australia. Yi Zhong is with School of Electronic Information and Communications, Huazhong University of Science and Technology, Wuhan, P. R. China.

In this paper, we develop a distributionally robust chance-constrained formulation of the Optimal Power Flow problem (OPF) whereby the system operator can leverage contextual information. For this purpose, we exploit an ambiguity set based on probability trimmings and optimal transport through which the dispatch solution is protected against the incomplete knowledge of the relationship between the OPF uncertainties and the context that is conveyed by a sample of their joint probability distribution. We provide an exact reformulation of the proposed distributionally robust chance-constrained OPF problem under the popular conditional-value-at-risk approximation. By way of numerical experiments run on a modified IEEE-118 bus network with wind uncertainty, we show how the power system can substantially benefit from taking into account the well-known statistical dependence between the point forecast of wind power outputs and its associated prediction error. Furthermore, the experiments conducted also reveal that the distributional robustness conferred on the OPF solution by our probability-trimmings-based approach is superior to that bestowed by alternative approaches in terms of expected cost and system reliability.