## 2 Materials and Methods
### Reinforcement Learning in Continuous Environments
The agent continuously learns by observing states, selecting actions, and receiving rewards, improving its policy to accomplish tasks autonomously. Deep reinforcement learning (DRL) is a subset of machine learning that combines reinforcement learning (RL) with deep neural networks. In RL, an agent learns to make decisions by performing actions in an environment to maximize a cumulative reward [20]. The agent receives feedback from the environment in the form of rewards or penalties and updates its policy to improve future performance. Deep Q-learning (DQN) is one of the earliest DRL algorithms, which combines Q-learning with deep neural networks to handle high-dimensional state spaces. The integration of DRL into industrial robot arm teaching involves several key steps:

* Environment Simulation: A realistic simulation environment is essential for training DRL agents. This environment must accurately model the physical characteristics and constraints of the robot and its operating space. * Reward Function Design: The reward function guides the learning process by defining what constitutes successful behavior. Designing an appropriate reward function is critical and often involves balancing multiple objectives such as speed, accuracy, and safety. * State and Action Space Definition: The state space represents the observable variables that describe the environment, such as joint angles and end-effector positions. The action space defines the set of possible actions the robot can take, such as joint movements or gripper operations. * Training and Optimization: Training a DRL agent involves running numerous simulations where the agent explores the environment and updates its policy based on the received rewards. This process requires significant computational resources and time. The use of DRL in teaching industrial robot arms offers several significant advantages. This approach enables robots to learn from their environment and adapt to new tasks and conditions autonomously, reducing the need for human intervention. It also enables them to handle complex tasks that are difficult to program manually, such as tasks requiring fine manipulation or dynamic adjustment to varying conditions [21]. Once trained, DRL-based systems can perform tasks more efficiently and with higher precision than manually programmed robots, and the same DRL framework can be applied to different robots and tasks, making it highly scalable and versatile. Deep reinforcement learning holds significant promise for revolutionizing the teaching strategies of industrial robot arms. By enabling autonomous learning and adaptation, DRL can address many limitations of traditional programming methods, offering greater flexibility, efficiency, and scalability. However, realizing this potential requires addressing challenges related to data requirements, computational complexity, safety, and sim-to-real transfer. Through continued research and development, DRL can become a cornerstone of intelligent, autonomous robotic systems in industrial applications. Generally, DRL algorithms offer greater flexibility and capability in handling a wide range of tasks, especially in environments with complex dynamics and high-dimensional state-action spaces as shown in Table 4. They often require extensive training data, computational resources, and careful hyperparameter tuning to achieve stable and effective performance. DMP algorithms provide a structured and interpretable way to encode and reproduce complex movements, making them particularly suitable for tasks requiring smooth and precise control. Their main limitations lie in the need for manual tuning and potential difficulty in handling highly variable or discontinuous tasks without significant modifications [22; 23; 24]. The choice between DRL and DMP algorithms, or a combination thereof, depends on the specific requirements of the robotic task at hand, the complexity of the environment, and the desired balance between learning flexibility and control precision.