Master the Hill Climbing Algorithm and Balance a Cart Pole

Master the Hill Climbing Algorithm and Balance a Cart Pole

Table of Contents:

1. Introduction
2. What is the Hill Climbing Algorithm?
3. Applying the Hill Climbing Algorithm to the Cartpole Environment
4. The Cartpole Environment
5. The Function for Balancing the Pole
6. The Initial Test Run
7. Sampling a New Trial Weight Matrix
8. Updating the Model
9. Running The Simulation with Hill Climbing Algorithm
10. Pros and Cons of Hill Climbing Algorithm
11. Conclusion

Introduction

In this article, we will explore the hill climbing algorithm and its application to the Cartpole environment in OpenAI Gym. We will first understand what the hill climbing algorithm is all about and then dive into the specifics of applying it to the Cartpole environment. This algorithm is a powerful technique used for solving optimization problems, and we will see how it can be used to maximize the balance of a pole on a cart. By the end of this article, You will have a clear understanding of how the hill climbing algorithm works and how it can be implemented in the Cartpole environment.

What is the Hill Climbing Algorithm?

The hill climbing algorithm is a technique used for solving optimization problems, where the objective is to maximize or minimize the output of a given function. It starts with an initial solution and then iteratively tweaks the solution in an arbitrary manner, evaluating the modified solution against the previous one. If the modified solution performs better, it becomes the new best solution, and the process is repeated. However, if the modified solution performs worse, it is discarded and a different modification is attempted. This trial and error approach continues until an optimal solution is reached.

Applying the Hill Climbing Algorithm to the Cartpole Environment

The Cartpole environment is a control problem where the objective is to push a cart either left or right to keep a pole balanced upright. The goal is to keep the pole balanced within an angle of 12 degrees on either side of the vertical for 200 time steps. At each time step, the Current state of the cart's position and velocity, as well as the pole's angle and angular velocity, are provided. We need to determine the best action (left or right) to take in order to keep the pole balanced.

To solve this problem using the hill climbing algorithm, we need to develop a function that takes the current state as input and outputs the best action to maximize the overall reward. The current state is represented as a vector of the cart's position, velocity, pole's angle, and angular velocity. Our function will output a vector with predicted values for each possible action, and we will select the action with the highest value.

To transform the input state vector into an output vector of predicted values, we can multiply the input state with a weight matrix. Initially, we start with a random weight matrix and evaluate its performance in the environment. Based on the total reward obtained, we save it as the initial best observed reward and the corresponding weights. We then sample a new trial weight matrix by adding a random noise matrix to the best weights and evaluate its performance again. Depending on the trial reward, we update our weights accordingly and repeat the process with the new weights.

The Cartpole Environment

The Cartpole environment in OpenAI Gym is a classic control problem. The goal is to balance a pole on a cart by applying the right amount of force (pushing) to the cart in either direction. The environment provides information about the cart's position, velocity, pole's angle, and angular velocity at each time step. Our task is to use this information to determine the best action (push left or right) to keep the pole balanced within the specified constraints.

The Function for Balancing the Pole

To solve the Cartpole environment using the hill climbing algorithm, we need a function that takes the current state as input and outputs the best action to keep the pole balanced. The function will transform the input state vector into an output vector of predicted values for each possible action. The action with the highest value will be selected as the best action to take in that given state.

The Initial Test Run

Before we start fine-tuning our function, we need an initial test run in the environment. We will use a random weight matrix and evaluate its performance in terms of balancing the pole. Based on the total reward obtained in this test run, we will save it as the initial best observed reward and the corresponding best weights.

Sampling a New Trial Weight Matrix

Once we have the initial best weights, we can sample a new trial weight matrix by adding a random noise matrix to the best weights. This random noise matrix introduces variation in the weights to explore different possibilities. Each trial weight matrix represents a different modification of the best weights.

Updating the Model

After obtaining the trial weight matrix, we test the function's performance in the environment again and compare the trial reward with the best observed reward. If the trial reward is greater, we save it as the new best reward, update our best weights, and adjust the magnitude of the next random noise matrix for finer variation. However, if the trial reward is worse, we increase the magnitude of the next random noise matrix to explore different modifications further.

Running the Simulation with Hill Climbing Algorithm

Once we have the process of updating the model in place, we can run the simulation with the hill climbing algorithm. In each time step of the simulation, we calculate the action to take based on the current state using the updated model. We train the model for a fixed number of episodes and update it based on the observed rewards. Over time, the model is expected to improve its performance in balancing the pole, maximizing the overall reward.

Pros and Cons of Hill Climbing Algorithm

Pros:

• Simple and straightforward algorithm to implement.
• Can find solutions to optimization problems quickly.

Cons:

• Relies on trial and error approach, which can be time-consuming and inefficient.
• May get stuck at local optima and fail to reach the global optimum in some cases.

Conclusion

In this article, we have explored the hill climbing algorithm and its application to the Cartpole environment in OpenAI Gym. We have discussed the basics of the hill climbing algorithm and how it can be used to solve the optimization problem of balancing a pole on a cart. By implementing the hill climbing algorithm, we have seen how the model can improve its performance over time and maximize the overall reward. The hill climbing algorithm serves as a useful technique for solving optimization problems and can be further enhanced by incorporating neural networks and other advanced methods in the future.

Highlights

• The hill climbing algorithm is a technique used for solving optimization problems by iteratively tweaking the initial solution.
• The Cartpole environment in OpenAI Gym is a control problem where the objective is to balance a pole on a cart.
• The hill climbing algorithm can be applied to the Cartpole environment by developing a function that outputs the best action to keep the pole balanced.
• The function transforms the input state vector into an output vector of predicted values, and the action with the highest value is selected.
• The hill climbing algorithm improves the weights of the function by trial and error, updating them based on the observed rewards.
• The algorithm has pros such as simplicity and quick solution finding, but it also has cons like trial and error reliance and local optima issues.

FAQ:

Q: How does the hill climbing algorithm work? A: The hill climbing algorithm starts with an initial solution and iteratively modifies it in an arbitrary way. If the modified solution performs better, it becomes the new best solution and the process is repeated. However, if the modified solution performs worse, it is discarded and a different modification is attempted. This trial and error approach continues until an optimal solution is found.

Q: What is the Cartpole environment in OpenAI Gym? A: The Cartpole environment is a classic control problem where the goal is to balance a pole on a cart. The environment provides information about the cart's position, velocity, pole's angle, and angular velocity at each time step. The task is to determine the best action (push left or right) to keep the pole balanced within specified constraints.

Q: How is the function for balancing the pole developed? A: The function takes the current state as input and outputs the best action to keep the pole balanced. It transforms the input state vector into an output vector of predicted values for each possible action. The action with the highest value is selected as the best action to take in that given state.

Q: How is the model updated in the hill climbing algorithm? A: The model is updated by evaluating its performance in the environment and comparing the observed reward with the best observed reward. If the observed reward is greater, the weights of the model are updated. The magnitude of the random noise matrix used for exploring different modifications is also adjusted based on the performance.

Q: What are the pros and cons of the hill climbing algorithm? A: The pros of the hill climbing algorithm include simplicity and quick solution finding. However, it has cons such as reliance on trial and error, which can be time-consuming, and the potential to get stuck at local optima and fail to reach the global optimum in some cases.