Energy-Efficient Resource Allocation in O-RAN Using Soft Actor-Critic

The control of quadrotors is inherently difficult due to their underactuated nature and highly coupled nonlinear dynamics. Although traditional control strategies often depend on model linearization, Deep Reinforcement Learning (DRL) has emerged as a robust, model-free approach suitable for handling complex aerodynamics and environmental uncertainties. Despite this potential, the identification of the most effective learning agent for specific flight regimes remains unresolved. This study conducts a comprehensive comparative assessment of three prominent algorithms: Proximal Policy Optimization (PPO), Soft Actor-Critic (SAC), and Deep Deterministic Policy Gradient (DDPG). Through rigorous simulation, we evaluate these algorithms based on convergence speed, sample efficiency, and steady-state tracking accuracy. Our findings reveal a distinct trade-off: while SAC exhibits faster convergence in early training phases, PPO ensures superior stability and reduced variance during aggressive maneuvering in the steady state. Additionally, the resilience of these policies to sensor noise and parametric uncertainty is investigated. By elucidating the performance disparities between on-policy and off-policy algorithms, this work establishes a practical framework for selecting DRL architectures for autonomous quadrotor deployment.

The hybrid flow shop scheduling problem (HFSP) has been extensively studied due to its wide applications in modern manufacturing systems. However, existing research primarily focuses on machine-centric scheduling while neglecting the critical role of human resources, whose varying skill levels impact processing efficiency and whose availability constraints complicate scheduling decisions. Therefore, this paper investigates the HFSP with human resource constraints (HFSP-HRC), which requires the joint optimization of job sequencing, machine allocation, and worker assignment to obtain efficient scheduling solutions. We propose a deep reinforcement learning (DRL) method integrated with a meta-path-based heterogeneous graph neural network (MP-HGNN) to solve this problem. It innovatively captures complex interdependencies among operations, machines, and workers through machine-centric and worker-centric meta-paths, overcoming limitations of existing methods that fail to model heterogeneous resource competition relationships. The integration enables high-order semantic feature fusion for enhanced scheduling robustness. Combined with the proximal policy optimization (PPO) algorithm, the framework realizes end-to-end learning from raw scheduling states to optimal decisions. Experiments across four different problem scales demonstrate that the proposed method significantly outperforms baseline heuristic rules and DRL method in makespan, with particularly outstanding performance on large-scale instances.

Traditional control approaches heavily rely on hard-coded expert knowledge, complicating the development of optimal control solutions as system complexity increases. Deep Reinforcement Learning (DRL) offers a self-learning control solution, proving advantageous in scenarios where crafting expert-based solutions becomes intricate. This study investigates the potential of DRL for supervisory control in a unique and complex heating system within a large-scale university building. The DRL framework aims to minimize energy costs while ensuring occupant comfort. However, the trial-and-error learning approach of DRL raises concerns about the trustworthiness of executed actions, hindering practical implementation. To address this, the study incorporates action masking, enabling the integration of hard constraints into DRL to enhance user trust. Maskable Proximal Policy Optimization (MPPO) is evaluated alongside standard Proximal Policy Optimization (PPO) and Soft Actor–Critic (SAC). Simulation results reveal that MPPO achieves comparable energy savings (8% relative to the baseline control) with fewer comfort violations than other methods. Therefore, it is selected among the candidate algorithms and experimentally implemented in the university building over one week. Experimental findings demonstrate that MPPO reduces energy costs while maintaining occupant comfort, resulting in a 36% saving compared to a historical day with similar weather conditions. These results underscore the proactive decision-making capability of DRL, establishing its viability for autonomous control in complex energy systems.

An adaptive PID controller for path following of autonomous underwater vehicle based on Soft Actor–Critic

By addressing the drawbacks of static optimization techniques, this research seeks to improve the dynamic energy management of thermoelectric generators (TEGs). Finding the best deep reinforcement learning (DRL) algorithm to maximize energy distribution, prolong battery life, and boost system efficiency in the face of the variable conditions present in waste heat recovery systems is the goal. The TEG system was modeled using the Markov decision process and implemented in a computer-simulated environment. Three advanced DRL algorithms were used: soft actor-critic (SAC), proximal policy optimization (PPO), and deep Q-networks (DQN); which were trained to act as intelligent controllers. The performance of each algorithm was systematically evaluated and compared using key metrics, including average cumulative reward, battery health, system efficiency, and a novel metric termed the energy fulfillment rate, which measures the ability to meet demand while storing surplus energy. The comparative analysis revealed a critical trade-off between maximizing performance and ensuring hardware longevity. The SAC algorithm demonstrated the best overall performance, achieving the highest average reward (− 7.03) and energy fulfillment rate (22.84%). However, the A2C, DDPG, and PPO algorithms all achieved a perfect average battery health of 100.00%, highlighting their superior capability for preserving system longevity, albeit with slightly lower rewards. The DQN algorithm consistently showed the least effective performance across all metrics, particularly in maintaining battery health (60.73%). The SAC algorithm is the most suitable of the methods tested for dynamically managing TEG systems. Its underlying principle of maximization of entropy enables a better exploration of control strategies, leading to a better balance between immediate energy dispatch and long-term storage goals. The findings confirm the significant potential of DRL to create efficient and adaptive controllers for renewable energy applications, although further validation of physical hardware is required to confirm real-world viability.Supplementary InformationThe online version contains supplementary material available at 10.1038/s41598-025-27210-7.

In this paper, we propose a novel deep reinforcement learning (DRL) method for optimal path planning for mobile robots using dynamic programming (DP)-based data collection. The proposed method can overcome the slow learning process and improve training data quality inherently in DRL algorithms. The main idea of our approach is as follows. First, we mapped the dynamic programming method to typical optimal path planning problems for mobile robots, and created a new efficient DP-based method to find an exact, analytical, optimal solution for the path planning problem. Then, we used high-quality training data gathered using the DP method for DRL, which greatly improves training data quality and learning efficiency. Next, we established a two-stage reinforcement learning method where, prior to the DRL, we employed extreme learning machines (ELM) to initialize the parameters of actor and critic neural networks to a near-optimal solution in order to significantly improve the learning performance. Finally, we illustrated our method using some typical path planning tasks. The experimental results show that our DRL method can converge much easier and faster than other methods. The resulting action neural network is able to successfully guide robots from any start position in the environment to the goal position while following the optimal path and avoiding collision with obstacles.

With the continuous progress of UAV technology and the rapid development of mobile edge computing (MEC), the UAV-assisted MEC system has shown great application potential in special fields such as disaster rescue and emergency response. However, traditional deep reinforcement learning (DRL) decision-making methods suffer from limitations such as difficulty in balancing multiple objectives and training convergence when making mixed action space decisions for UAV path planning and task offloading. This article innovatively proposes a hybrid decision framework based on the improved Dynamic Adaptive Genetic Optimization Algorithm (DAGOA) and soft actor–critic with hierarchical action decomposition, an uncertainty-quantified critic ensemble, and adaptive entropy temperature, where DAGOA performs an effective search and optimization in discrete action space, while SAC can perform fine control and adjustment in continuous action space. By combining the above algorithms, the joint optimization of drone path planning and task offloading can be achieved, improving the overall performance of the system. The experimental results show that the framework offers significant advantages in improving system performance, reducing energy consumption, and enhancing task completion efficiency. When the system adopts a hybrid decision framework, the reward score increases by a maximum of 153.53% compared to pure deep reinforcement learning algorithms for decision-making. Moreover, it can achieve an average improvement of 61.09% on the basis of various reinforcement learning algorithms such as proposed SAC, proximal policy optimization (PPO), deep deterministic policy gradient (DDPG), and twin delayed deep deterministic policy gradient (TD3).

The object of the study is a mobile walking robot with two or more movable articulated limbs. The concept of a "critical condition" is introduced, in which the mechanism balances on the verge of falling (but does not fall) or there is a possibility of damage to mechanical components due to the generation of unacceptable joint angles. The subject of the study is a general algorithm for the elimination of critical conditions, which provides the possibility of training an agent based on a deep reinforcement learning algorithm directly on a real robot, without the risk of damaging its mechanisms and interrupting the process of interaction with the environment to restore a stable state. The purpose of this work is to develop a general algorithm for the elimination of critical conditions in the context of adaptive control of a walking robot based on deep learning algorithms with reinforcement. A comparison was made between the proposed and standard methods of applying deep OP on a real robot. The experiments were conducted on 6,000 episodes, with a dimension of 300 steps each. The following quality metrics were selected for evaluation: the percentage of episodes without an actual fall, the percentage of fully completed episodes, and the maximum episode length. The algorithm is based on the concept of "critical condition" and uses the following principles and methods: the "trial and error" method, the feedback principle, holding the projection of the center of gravity point in the area of the polygon formed by the points of contact of the limbs with the work surface, which ensures the balancing of the structure and allows you to determine the boundary areas in which the robot is still stable. The scientific novelty of the work lies in the proposed approach, which allows an intelligent agent to control a physical robot "directly", without pre-configuration in a simulation environment with subsequent transfer implementation. The proposed algorithm is not aimed at improving the agent's performance, but is intended to provide greater autonomy in the learning process of the robot, directly in the hardware. The basic idea is to immediately respond to a critical condition in the form of the fastest sequential return to a certain number of steps back along the decision-making trajectory, ensuring that the agent remains in a stable and safe state at all times. The method of proximal policy optimization (PPO) was used as a method of deep reinforcement learning. As a result of the comparative analysis, the proposed algorithm demonstrated a hundredfold increase in the stability of the mechanism.

Reinforcement learning and deep reinforcement learning, as a research hotspot in the field of machine learning, have been widely used in our daily life. In this field, game is playing an extremely important role in the developing of reinforcement learning algorithms. Based on the Tennis environment built by Unity ML Agents, this paper used three algorithms, Proximal Policy Optimization (PPO), Multi-Agent Deep Deterministic Policy Gradients (MADDPG) and Soft Actor-Critic (SAC), combined with PyTorch framework, solved the continuous control problem of this environment. Meanwhile, a group of optimal parameters are obtained through multiple trainings, so that Agents can achieve a perfect effect of solving the continuous control problem in Tennis environment. At the end, this paper compared and analyzed the difference among these three algorithms, summarized the application and properties of each algorithm. For different parameters of the algorithm, this paper also maked a comparison and explained the reasons for some special cases as well which can be used for the future work.

Magnetic levitation (Maglev) technology is widely adopted for transportation, photolithography, clean room, and material-handling applications, owing to its vibration- and friction-free, untethered motion. The magnetic movers are actuated using the stator coil array, which functions as mobile maglev robots (MLRs) with precision position and orientation motion control. Therefore, this article studies the MLRs for intelligent manufacturing, such as material handling and collaboration with manufacturing components, by integrating them with deep reinforcement learning (DRL) policy controllers. Linear DRL policies are developed and compared between Soft Actor-Critic (SAC) and Proximal Policy Optimization (PPO) for the horizontal motion control, which takes 455 μs to compute the actuating forces for real-time operations. During policy training, random magnitude horizontal step responses are ticked every 500 ms to explore and exploit the dynamic capacity of the MLRs. The PPO policies are finalized based on the discovered deterministic nature of the maglev environment. Furthermore, the symmetry of the MLR configuration is utilized for policy training, with a threshold boundary included to enable MLRs to translate smoothly across the horizontal operating range. The trained policies exhibit aggressive oscillations and persistent offsets relative to references, respectively. To alleviate the fitting problem, distance-based soft state machines are introduced to integrate the DRL policy with the basic controller. The state machine parameters are empirically tuned using various location step responses. This feature enables the dynamic responses of the DRL policy to be combined with the precision responses at references. The soft state machines are also trained as auxiliary policy actions and evaluated using full operating-range trajectory tracking and long-stroke step responses alongside the policy and the basic controller. The DRL policy controllers outperform the basic controllers, with improved rise and settling times in step responses, while showing enhanced performance in tracking trajectories. Finally, the policy robustness is empirically evaluated.

Improving the interpretability of deep reinforcement learning in urban drainage system operation

A latent space method with maximum entropy deep reinforcement learning for data assimilation

Uneven food distribution across various regions in Indonesia often results in supply-demand imbalances, leading to price surges, stock shortages, and overall market instability. This challenge is compounded by the limitations of conventional distribution systems, which are ill-equipped to respond to rapidly changing market dynamics. In response, this study introduces a novel, AI-driven approach by implementing Deep Reinforcement Learning (DRL) to optimize food distribution policies using real-world data. Specifically, we perform a comparative evaluation of four emerging DRL models—Double Deep Q-Network (Double DQN), Dueling DQN, Proximal Policy Optimization (PPO), and Advantage Actor-Critic (A2C)—to determine their effectiveness in learning adaptive distribution strategies from national food logistics data provided by Indonesia’s Central Bureau of Statistics (BPS). Each model was trained within a custom simulation environment based on the Markov Decision Process (MDP) framework and evaluated using five core performance metrics: cumulative reward, average reward, success rate, sample efficiency, and best reward. The results reveal that A2C consistently outperformed the other models, delivering the highest average reward and most stable training performance, while PPO demonstrated strong efficiency and success rate. These findings underscore the potential of policy-gradient methods—particularly A2C—as robust and intelligent solutions for dynamic food logistics management. This research offers one of the first comparative benchmarks of DRL methods in the food distribution domain and highlights their applicability for future integration into national AI-powered logistics systems.

With the improvement in the intelligence level of UAVs and the development of cluster control technology, the intelligent decision-making method of UAV cluster confrontation will become the key technology of UAV combat in the future. The UAV cluster confrontation learning environment is of complex characteristics of high dimension, non-linearity, incomplete information, continuous action space, and so on. Recently, artificial intelligence technology represented by deep learning and reinforcement learning has made a great breakthrough. Deep reinforcement learning has shown a great ability to solve intelligent decision-making problems in complex environments. In this paper, enlightened by the multi-agent centralized training distributed execution framework and the idea of maximum policy entropy, we propose a deep reinforcement learning method of the multi-agent soft actor-critic (MASAC) with incomplete information. A game model for UAV cluster confrontation based on multi-agent deep reinforcement learning is established, and a continuous space multiple UAV combat environment is constructed. Simulation experiments are performed on the asymmetric confrontation of UAV clusters with red and blue teams. The experimental results show that MASAC outperforms the existing popular multi-agent deep reinforcement learning methods, making the game players converge to a higher return equilibrium point of the game. Moreover, the convergence of MASAC is investigated and analyzed extensively, and the results show that MASAC is of good convergence and stability, ensuring the practicability of MASAC in intelligent decision-making regarding UAV cluster confrontation.

Since the sample data after one exploration process can only be used to update network parameters once in on-policy deep reinforcement learning (DRL), a high sample efficiency is necessary to accelerate the training process of on-policy DRL. In the proposed method, a submartingale criterion is proposed on the basis of the equivalence relationship between the optimal policy and martingale, and then an advanced value iteration (AVI) method is proposed to conduct value iteration with a high accuracy. Based on this foundation, an anti-martingale (AM) reinforcement learning framework is established to efficiently select the sample data that is conducive to policy optimization. In succession, an AM proximal policy optimization (AMPPO) method, which combines the AM framework with proximal policy optimization (PPO), is proposed to reasonably accelerate the updating process of state value that satisfies the submartingale criterion. Experimental results on the Mujoco platform show that AMPPO can achieve better performance than several state-of-the-art comparative DRL methods.