A Classic Introduction to Reinforcement Learning: In-depth Analysis and Practice of the Inverted Pendulum Control Problem

The inverted pendulum problem is the "Hello World" of the reinforcement learning field, containing core challenges of control theory and serving as an important milestone for beginners to understand the essence of reinforcement learning. Based on ZhuYouHanXue's AI course assignment project, this article provides an in-depth analysis of the physical nature of the inverted pendulum control problem, the construction of a reinforcement learning framework, algorithm implementation, and practical value, offering beginners a complete learning path from theory to code.

Project Background

This project originates from an introductory AI course assignment, fully demonstrating the transformation from reinforcement learning theory to runnable code, and providing beginners with a case that combines theory and practice.

Physical Nature

The inverted pendulum system consists of a moving cart and an articulated pole. The control goal is to counteract the pole's tilting torque through the horizontal movement of the cart. This is a typical underactuated system where the number of control input degrees of freedom is less than the system's degrees of freedom (cart position/velocity, pole angle/angular velocity).

Framework Establishment

• State space: cart position, velocity; pole angle, angular velocity
• Action space: discrete (move left/right) or continuous (force/acceleration)
• Reward function: positive reward for upright position, negative reward or termination of the episode for tilting

Algorithm Selection

• Discrete actions: Q-Learning, DQN
• Continuous actions: REINFORCE, Actor-Critic, DDPG, PPO (prioritizing stability and sample efficiency)

Environment Interaction

Use OpenAI Gym/Gymnasium's CartPole/Pendulum environment, which encapsulates physical simulation and interaction loops, allowing focus on algorithm implementation.

Role of Neural Networks

When the state space is continuous or large, neural networks are used as function approximators:

• DQN: Input state, output action Q-values
• Policy gradient: Output action distribution parameters Training updates weights by minimizing Bellman error or maximizing expected return.

Training Challenges

• Exploration-exploitation trade-off
• Sample efficiency issues
• Stability of continuous control (requires optimizing hyperparameters such as learning rate and target network update frequency)

Project visualization includes:

• Training curves: Return changes over the number of episodes
• Test animations: Verify the correctness of the strategy
• Quantitative metrics: Pole upright duration, cart position range A successful strategy needs to keep the pole upright for a long time and maintain a reasonable cart position.

Practical Applications

The inverted pendulum structure is widely present in real-world scenarios: rocket landing attitude control, bipedal robot walking, drone hovering, etc.

Classic Value

In the AI era dominated by large models, the inverted pendulum carries the core principles of reinforcement learning. Mastering the basics is a necessary path to becoming an excellent AI engineer.

Learning Value

Through project implementation, deeply understand core concepts such as Bellman equations, policy iteration, and value function approximation.

Expansion Directions

• Try complex algorithms like SAC/TD3
• Handle noisy observations and partially observable environments
• Extend to complex systems like multi-link pendulums