CMPS140: Artificial Intelligence - Project 3: Reinforcement Learning
Introduction
In this project, you will implement value iteration and q-learning. You will test your agents first on Gridworld (from class), then apply them to a simulated robot controller (Crawler) and Pac-Man.
The code for this project consists of several Python files, some of which you will need to read and understand in order to complete the assignment, and some you can glance over.
In this project, you will implement value iteration and q-learning. You will test your agents first on Gridworld (from class), then apply them to a simulated robot controller (Crawler) and Pac-Man.
The code for this project consists of several Python files, some of which you will need to read and understand in order to complete the assignment, and some you can glance over.
Submission
You will fill in portions of pacai.student.valueIterationAgents, pacai.student.qlearningAgents, and pacai.student.analysis during this assignment. You should only submit these two files.
This assignment should be submitted with the filename solution.zip HERE. Please use the command line zip tool to make sure your submission gets zipped correctly:
zip -j solution.zip pacai/student/analysis.py pacai/student/qlearningAgents.py pacai/student/valueIterationAgent.pyFor these submissions, unzip should directly yield the source files and not a directory named "solution", "pN", or "pacai". Note that this is counter to standard conventions when sending a zip file to a human, but easier for the autograder.
After submitting, the autograder will grade your submission and report the result back to you. Do not close the tab or you will not be able to see your score. You can submit as many times as you want. However, if we find you continually making tiny changes instead of testing locally, then we will deduct points. Any attempt to trick the autograder is considered cheating.
You will fill in portions of pacai.student.valueIterationAgents, pacai.student.qlearningAgents, and pacai.student.analysis during this assignment. You should only submit these two files.
This assignment should be submitted with the filename solution.zip HERE. Please use the command line zip tool to make sure your submission gets zipped correctly:
zip -j solution.zip pacai/student/analysis.py pacai/student/qlearningAgents.py pacai/student/valueIterationAgent.pyFor these submissions, unzip should directly yield the source files and not a directory named "solution", "pN", or "pacai". Note that this is counter to standard conventions when sending a zip file to a human, but easier for the autograder.
After submitting, the autograder will grade your submission and report the result back to you. Do not close the tab or you will not be able to see your score. You can submit as many times as you want. However, if we find you continually making tiny changes instead of testing locally, then we will deduct points. Any attempt to trick the autograder is considered cheating.
Evaluation
Your code will be autograded for technical correctness. Please do not change the names of any provided functions or classes within the code, or you will wreak havoc on the autograder (and points will be deducted!). However, you are allowed to add any new classes or function that you need. The correctness of your implementation -- not the autograder's output -- will be the final judge of your score. If necessary, we will review and grade assignments individually to ensure that you receive due credit for your work. This assignment is graded out of 30 points. 25 points will be for correctness as determined by the autograder and the point system given below for each problem. 5 points will be for style, which the autograder will also check. You can run the style checker using the run_style.sh script in the project root.
Your code will be autograded for technical correctness. Please do not change the names of any provided functions or classes within the code, or you will wreak havoc on the autograder (and points will be deducted!). However, you are allowed to add any new classes or function that you need. The correctness of your implementation -- not the autograder's output -- will be the final judge of your score. If necessary, we will review and grade assignments individually to ensure that you receive due credit for your work. This assignment is graded out of 30 points. 25 points will be for correctness as determined by the autograder and the point system given below for each problem. 5 points will be for style, which the autograder will also check. You can run the style checker using the run_style.sh script in the project root.
Running Code on Your Local Machine
In order to run the Pac-Man code on your local machine, you must have Tk, python >= 3.5, and pip installed. Finally you want to install Pacai's package requirements listed in the requirements.txt file in the project's root directory:
pip3 install --user -r requirements.txtFor the next set of instructions, simply follow the steps listed below depending on your OS.
In order to run the Pac-Man code on your local machine, you must have Tk, python >= 3.5, and pip installed. Finally you want to install Pacai's package requirements listed in the requirements.txt file in the project's root directory:
pip3 install --user -r requirements.txtFor the next set of instructions, simply follow the steps listed below depending on your OS.
Linux
Install the Python binding for the Tk package, usually called something like python3-tk. On Ubuntu you can use the following command:
sudo apt-get install python3-tk
Install the Python binding for the Tk package, usually called something like python3-tk. On Ubuntu you can use the following command:
sudo apt-get install python3-tkMac OS X
The required additional components (Tk and Python3 Tk bindings) are typically bundled with the Python3 package.
The required additional components (Tk and Python3 Tk bindings) are typically bundled with the Python3 package.
Windows
There are two separate methods for getting Pacai to work on Windows. One is using the Windows Subsystem for Linux (WSL) and the other is using Git Bash. We will first talk about the WSL.
There are two separate methods for getting Pacai to work on Windows. One is using the Windows Subsystem for Linux (WSL) and the other is using Git Bash. We will first talk about the WSL.
Windows Subsystem for Linux (WSL)
1. First, make sure you have the WSL installed on your local machine. You can follow this installation guide. You are allowed to pick any distribution, however we will be providing specific instructions for Ubuntu. Other distributions will have similar steps.
2. Next, you want to make sure you have an X server running. This allows the WSL to launch graphical applications. We recommend using VcXsrv and following this installation guide. Make sure your X server is running whenever you want to run Pacai with graphics.
3. Now launch your WSL. You can do this by typing "Windows Subsystem for Linux" in your start menu and clicking on the icon.
4. Next, you must configure your bash inside the WSL to use the X server from step #2. To do this, use the following commands:
echo "export DISPLAY=localhost:0.0" >> ~/.bashrc
source ~/.bashrcThis sets your DISPLAY environmental variable in your bashrc and then reloads your bashrc.
5. Let's make sure you have all the required packages:
sudo apt-get update
sudo apt-get install python3 python3-pip python3-tk x11-apps7. In order to test that you have the graphics set up correctly, you can use the xeyes command:
xeyes8. Finally, clone the Pacai repository and install Pacai's package requirements:
pip3 install --user -r requirements.txt
1. First, make sure you have the WSL installed on your local machine. You can follow this installation guide. You are allowed to pick any distribution, however we will be providing specific instructions for Ubuntu. Other distributions will have similar steps.
2. Next, you want to make sure you have an X server running. This allows the WSL to launch graphical applications. We recommend using VcXsrv and following this installation guide. Make sure your X server is running whenever you want to run Pacai with graphics.
3. Now launch your WSL. You can do this by typing "Windows Subsystem for Linux" in your start menu and clicking on the icon.
4. Next, you must configure your bash inside the WSL to use the X server from step #2. To do this, use the following commands:
echo "export DISPLAY=localhost:0.0" >> ~/.bashrc
source ~/.bashrcThis sets your DISPLAY environmental variable in your bashrc and then reloads your bashrc.
5. Let's make sure you have all the required packages:
sudo apt-get update
sudo apt-get install python3 python3-pip python3-tk x11-apps7. In order to test that you have the graphics set up correctly, you can use the xeyes command:
xeyes8. Finally, clone the Pacai repository and install Pacai's package requirements:
pip3 install --user -r requirements.txtGit Bash
1. Install Git Bash, you can follow this installation guide.
2. Now launch your Git Bash. You can do this by typing "Git Bash" in your start menu and clicking on the icon.
3. If you are using a newer version of Windows, there may be a conflict with the version of Python 3 installed from the Windows Store. This conflict will cause a permission denied error when running Python 3 in Git Bash. To avoid this error, you will want to disable the Windows Store version of Python. To do this, type "manage app execution aliases" into your start menu and click on the icon. Within the app execution aliases, disable both python.exe and python3.exe.
4. You may also want to create an alias for python3. All the commands in the instructions use python3, but Git Bash just refers to the executable as python. To create the alias, you can use the following commands:
echo "alias python3=python" >> ~/.bash_profile
source ~/.bash_profile5. Finally, clone the Pacai repository and install Pacai's package requirements:
pip3 install --user -r requirements.txt
1. Install Git Bash, you can follow this installation guide.
2. Now launch your Git Bash. You can do this by typing "Git Bash" in your start menu and clicking on the icon.
3. If you are using a newer version of Windows, there may be a conflict with the version of Python 3 installed from the Windows Store. This conflict will cause a permission denied error when running Python 3 in Git Bash. To avoid this error, you will want to disable the Windows Store version of Python. To do this, type "manage app execution aliases" into your start menu and click on the icon. Within the app execution aliases, disable both python.exe and python3.exe.
4. You may also want to create an alias for python3. All the commands in the instructions use python3, but Git Bash just refers to the executable as python. To create the alias, you can use the following commands:
echo "alias python3=python" >> ~/.bash_profile
source ~/.bash_profile5. Finally, clone the Pacai repository and install Pacai's package requirements:
pip3 install --user -r requirements.txtCode
All the code for this (and later projects) is available in this repository: https://github.com/linqs/pacman. The only files you should edit are located in the pacai.student package. You should not use any third-party libraries, but the Python Standard Library is fair-game. If a bug is found in the code (non-student) code, then the class will be alerted and you will have to pull the changes from this repository.
Any commands provided throughout these instructions are to be executed from the project root directory (the one with the README.md and LICENSE.md files).
- States
- pacai.core.gamestate.AbstractGamestate
- pacai.bin.pacman.PacmanGameState
- Other Binaries
- pacai.bin.crawler
- pacai.bin.gridworld
- Utilities
- pacai.util.probability.flipCoin
All the code for this (and later projects) is available in this repository: https://github.com/linqs/pacman. The only files you should edit are located in the pacai.student package. You should not use any third-party libraries, but the Python Standard Library is fair-game. If a bug is found in the code (non-student) code, then the class will be alerted and you will have to pull the changes from this repository.
Any commands provided throughout these instructions are to be executed from the project root directory (the one with the README.md and LICENSE.md files).
- States
- pacai.core.gamestate.AbstractGamestate
- pacai.bin.pacman.PacmanGameState
- Other Binaries
- pacai.bin.crawler
- pacai.bin.gridworld
- Utilities
- pacai.util.probability.flipCoin
MDPs
To get started, run Gridworld in manual control mode, which uses the arrow keys:
python3 -m pacai.bin.gridworld --manualYou will see the two-exit layout from class. The blue dot is the agent. Note that when you press up, the agent only actually moves north 80% of the time. Such is the life of a Gridworld agent!
You can control many aspects of the simulation. A full list of options is available by running:
python3 -m pacai.bin.gridworld --helpThe default agent moves randomly
python3 -m pacai.bin.gridworld --grid MazeGridYou should see the random agent bounce around the grid until it happens upon an exit. Not the finest hour for an AI agent.
Note: The Gridworld MDP is such that you first must enter a pre-terminal state (the double boxes shown in the GUI) and then take the special 'exit' action before the episode actually ends. In this case, the true terminal state is called TERMINAL_STATE, which is not shown in the GUI. If you run an episode manually, your total return may be less than you expected, due to the discount rate (--discount to change; 0.9 by default).
Look at the console output that accompanies the graphical output. You should see information about each transition the agent experiences. You can turn this off by using --quiet or augment it using --debug. You can also run in text-only mode using --text-graphics.
As in Pac-Man, positions are represented by (x, y) Cartesian coordinates. Thus any arrays are indexed by [x][y] with 'north' being the direction of increasing y, etc. By default, most transitions will receive a reward of zero, though you can change this with the living reward option (--living-reward).
To get started, run Gridworld in manual control mode, which uses the arrow keys:
python3 -m pacai.bin.gridworld --manualYou will see the two-exit layout from class. The blue dot is the agent. Note that when you press up, the agent only actually moves north 80% of the time. Such is the life of a Gridworld agent!
You can control many aspects of the simulation. A full list of options is available by running:
python3 -m pacai.bin.gridworld --helpThe default agent moves randomly
python3 -m pacai.bin.gridworld --grid MazeGridYou should see the random agent bounce around the grid until it happens upon an exit. Not the finest hour for an AI agent.
Note: The Gridworld MDP is such that you first must enter a pre-terminal state (the double boxes shown in the GUI) and then take the special 'exit' action before the episode actually ends. In this case, the true terminal state is called TERMINAL_STATE, which is not shown in the GUI. If you run an episode manually, your total return may be less than you expected, due to the discount rate (--discount to change; 0.9 by default).
Look at the console output that accompanies the graphical output. You should see information about each transition the agent experiences. You can turn this off by using --quiet or augment it using --debug. You can also run in text-only mode using --text-graphics.
As in Pac-Man, positions are represented by (x, y) Cartesian coordinates. Thus any arrays are indexed by [x][y] with 'north' being the direction of increasing y, etc. By default, most transitions will receive a reward of zero, though you can change this with the living reward option (--living-reward).
Question 1 (6 points)
Write a value iteration agent in pacai.student.valueIterationAgent.ValueIterationAgent. Your value iteration agent is an offline planner, not a reinforcement agent. This means the relevant training option is the number of iterations of value iteration it should run (option --iterations) in its initial planning phase. A ValueIterationAgent takes an MDP on construction and runs value iteration for the specified number of iterations.
Value iteration computes k-step estimates of the optimal values, Vk. In addition to running value iteration, implement the following methods for ValueIterationAgent using Vk.
- getValue(state) returns the value of a state.
- getPolicy(state) returns the best action according to computed values.
- getQValue(state, action) returns the q-value of the (state, action) pair.
These quantities are all displayed in the GUI: values are numbers in squares, q-values are numbers in square quarters, and policies are arrows out from each square.
Important: Use the "batch" version of value iteration where each vector Vk is computed from a fixed vector Vk-1 (like in lecture), not the "online" version where one single weight vector is updated in place. The difference is discussed in Sutton & Barto starting in 4th paragraph of section 4.1.
Note: A policy synthesized from values of depth k (which reflect the next k rewards) will actually reflect the next k+1 rewards (i.e. you return πk+1). Similarly, the q-values will also reflect one more reward than the values (i.e. you return Qk+1). You may assume that 100 iterations is enough for convergence in the questions below.
The following command loads your ValueIterationAgent, which will compute a policy and execute it 10 times. Press a key to cycle through values, q-values, and the simulation. You should find that the value of the start state (V(start)) and the empirical resulting average reward are quite close.
python3 -m pacai.bin.gridworld --agent value --iterations 100 --episodes 10Hint: On the default BookGrid, running value iteration for 5 iterations should give you this output:
python3 -m pacai.bin.gridworld --agent value --iterations 5
Your value iteration agent will be graded on a new grid. We will check your values, q-values, and policies after fixed numbers of iterations and at convergence (e.g. after 100 iterations).
Write a value iteration agent in pacai.student.valueIterationAgent.ValueIterationAgent. Your value iteration agent is an offline planner, not a reinforcement agent. This means the relevant training option is the number of iterations of value iteration it should run (option --iterations) in its initial planning phase. A ValueIterationAgent takes an MDP on construction and runs value iteration for the specified number of iterations.
Value iteration computes k-step estimates of the optimal values, Vk. In addition to running value iteration, implement the following methods for ValueIterationAgent using Vk.
- getValue(state) returns the value of a state.
- getPolicy(state) returns the best action according to computed values.
- getQValue(state, action) returns the q-value of the (state, action) pair.
These quantities are all displayed in the GUI: values are numbers in squares, q-values are numbers in square quarters, and policies are arrows out from each square.
Important: Use the "batch" version of value iteration where each vector Vk is computed from a fixed vector Vk-1 (like in lecture), not the "online" version where one single weight vector is updated in place. The difference is discussed in Sutton & Barto starting in 4th paragraph of section 4.1.
Note: A policy synthesized from values of depth k (which reflect the next k rewards) will actually reflect the next k+1 rewards (i.e. you return πk+1). Similarly, the q-values will also reflect one more reward than the values (i.e. you return Qk+1). You may assume that 100 iterations is enough for convergence in the questions below.
The following command loads your ValueIterationAgent, which will compute a policy and execute it 10 times. Press a key to cycle through values, q-values, and the simulation. You should find that the value of the start state (V(start)) and the empirical resulting average reward are quite close.
python3 -m pacai.bin.gridworld --agent value --iterations 100 --episodes 10Hint: On the default BookGrid, running value iteration for 5 iterations should give you this output:
python3 -m pacai.bin.gridworld --agent value --iterations 5
Your value iteration agent will be graded on a new grid. We will check your values, q-values, and policies after fixed numbers of iterations and at convergence (e.g. after 100 iterations).
Question 2 (1 point)
On BridgeGrid with the default discount of 0.9 and the default noise of 0.2, the optimal policy does not cross the bridge. Change only ONE of the discount and noise parameters so that the optimal policy causes the agent to attempt to cross the bridge. Put your answer in pacai.student.analysis.question2. Note: noise refers to how often an agent ends up in an unintended successor state when they perform an action. The default corresponds to:
python3 -m pacai.bin.gridworld --agent value --iterations 100 --grid BridgeGrid --discount 0.9 --noise 0.2
On BridgeGrid with the default discount of 0.9 and the default noise of 0.2, the optimal policy does not cross the bridge. Change only ONE of the discount and noise parameters so that the optimal policy causes the agent to attempt to cross the bridge. Put your answer in pacai.student.analysis.question2. Note: noise refers to how often an agent ends up in an unintended successor state when they perform an action. The default corresponds to:
python3 -m pacai.bin.gridworld --agent value --iterations 100 --grid BridgeGrid --discount 0.9 --noise 0.2
Question 3 (5 points)
Consider the DiscountGrid layout, shown below. This grid has two terminal states with positive payoff (shown in green), a close exit with payoff +1 and a distant exit with payoff +10. The bottom row of the grid consists of terminal states with negative payoff (shown in red). Each state in this "cliff" region has payoff -10. The starting state is the yellow square. We distinguish between two types of paths: (1) paths that "risk the cliff" and travel near the bottom row of the grid. These paths are shorter but risk earning a large negative payoff. These paths are represented by the red arrow in the figure below. (2) paths that "avoid the cliff" and travel along the top edge of the grid. These paths are longer but are less likely to incur huge negative payoffs. These paths are represented by the green arrow in the figure below.
Give an assignment of parameter values for discount, noise, and living-reward which produce the following optimal policy types or state that the policy is impossible by returning the constant NOT_POSSIBLE. The default corresponds to:
python3 -m pacai.bin.gridworld --agent value --iterations 100 --grid DiscountGrid --discount 0.9 --noise 0.2 --living-reward 0.0- Prefer the close exit (+1), risking the cliff (-10)
- Prefer the close exit (+1), but avoiding the cliff (-10)
- Prefer the distant exit (+10), risking the cliff (-10)
- Prefer the distant exit (+10), avoiding the cliff (-10)
- Avoid both exits (also avoiding the cliff)
Now code analysis.question3a through analysis.question3e by returning a 3-item tuple of discount, noise, living reward. If no answer is possible, return the constant NOT_POSSIBLE.
Note: You can check your policies in the GUI. For example, using a correct answer to 3(a), the arrow in (0, 1) should point east, the arrow in (1, 1) should also point east, and the arrow in (2, 1) should point north.
Consider the DiscountGrid layout, shown below. This grid has two terminal states with positive payoff (shown in green), a close exit with payoff +1 and a distant exit with payoff +10. The bottom row of the grid consists of terminal states with negative payoff (shown in red). Each state in this "cliff" region has payoff -10. The starting state is the yellow square. We distinguish between two types of paths: (1) paths that "risk the cliff" and travel near the bottom row of the grid. These paths are shorter but risk earning a large negative payoff. These paths are represented by the red arrow in the figure below. (2) paths that "avoid the cliff" and travel along the top edge of the grid. These paths are longer but are less likely to incur huge negative payoffs. These paths are represented by the green arrow in the figure below.
Give an assignment of parameter values for discount, noise, and living-reward which produce the following optimal policy types or state that the policy is impossible by returning the constant NOT_POSSIBLE. The default corresponds to:
python3 -m pacai.bin.gridworld --agent value --iterations 100 --grid DiscountGrid --discount 0.9 --noise 0.2 --living-reward 0.0- Prefer the close exit (+1), risking the cliff (-10)
- Prefer the close exit (+1), but avoiding the cliff (-10)
- Prefer the distant exit (+10), risking the cliff (-10)
- Prefer the distant exit (+10), avoiding the cliff (-10)
- Avoid both exits (also avoiding the cliff)
Now code analysis.question3a through analysis.question3e by returning a 3-item tuple of discount, noise, living reward. If no answer is possible, return the constant NOT_POSSIBLE.
Note: You can check your policies in the GUI. For example, using a correct answer to 3(a), the arrow in (0, 1) should point east, the arrow in (1, 1) should also point east, and the arrow in (2, 1) should point north.
Q-learning
Note that your value iteration agent does not actually learn from experience. Rather, it ponders its MDP model to arrive at a complete policy before ever interacting with a real environment. When it does interact with the environment, it simply follows the precomputed policy (e.g. it becomes a reflex agent). This distinction may be subtle in a simulated environment like a Gridword, but it's very important in the real world, where the real MDP is not available.
Note that your value iteration agent does not actually learn from experience. Rather, it ponders its MDP model to arrive at a complete policy before ever interacting with a real environment. When it does interact with the environment, it simply follows the precomputed policy (e.g. it becomes a reflex agent). This distinction may be subtle in a simulated environment like a Gridword, but it's very important in the real world, where the real MDP is not available.
Question 4 (5 points)
You will now write a q-learning agent, which does very little on construction, but instead learns by trial and error from interactions with the environment through its update(state, action, nextState, reward) method. A stub of a q-learner is specified in pacai.student.qlearningAgents.QLearningAgent and you can select it with the command line option --agent q. For this question, you must implement the update, getQValue, getValue, and getPolicy methods in QLearningAgents.
Note: For getValue and getPolicy, you should break ties randomly for better behavior. The random.choice() function will help. In a particular state, actions that your agent hasn't seen before still have a Q-value, specifically a Q-value of zero, and if all of the actions that your agent has seen before have a negative Q-value, an unseen action may be optimal.
Important: Make sure that you only access Q values by calling getQValue in your getValue and getPolicy functions. This abstraction will be useful for question 9 when you override getQValue to use features of state-action pairs rather than state-action pairs directly.
With the q-learning update in place, you can watch your q-learner learn under manual control, using the keyboard:
python3 -m pacai.bin.gridworld --agent q --episodes 5 --manualRecall that --episodes will control the number of episodes your agent gets to learn. Watch how the agent learns about the state it was just in, not the one it moves to, and "leaves learning in its wake".
You will now write a q-learning agent, which does very little on construction, but instead learns by trial and error from interactions with the environment through its update(state, action, nextState, reward) method. A stub of a q-learner is specified in pacai.student.qlearningAgents.QLearningAgent and you can select it with the command line option --agent q. For this question, you must implement the update, getQValue, getValue, and getPolicy methods in QLearningAgents.
Note: For getValue and getPolicy, you should break ties randomly for better behavior. The random.choice() function will help. In a particular state, actions that your agent hasn't seen before still have a Q-value, specifically a Q-value of zero, and if all of the actions that your agent has seen before have a negative Q-value, an unseen action may be optimal.
Important: Make sure that you only access Q values by calling getQValue in your getValue and getPolicy functions. This abstraction will be useful for question 9 when you override getQValue to use features of state-action pairs rather than state-action pairs directly.
With the q-learning update in place, you can watch your q-learner learn under manual control, using the keyboard:
python3 -m pacai.bin.gridworld --agent q --episodes 5 --manualRecall that --episodes will control the number of episodes your agent gets to learn. Watch how the agent learns about the state it was just in, not the one it moves to, and "leaves learning in its wake".
Question 5 (2 points)
Complete your q-learning agent by implementing epsilon-greedy action selection in getAction, meaning it chooses random actions epsilon of the time, and follows its current best q-values otherwise.
python3 -m pacai.bin.gridworld --agent q --episodes 100Your final q-values should resemble those of your value iteration agent, especially along well-traveled paths. However, your average returns will be lower than the q-values predict because of the random actions and the initial learning phase.
You can choose an element from a list uniformly at random by calling the random.choice function. You can simulate a binary variable with probability p of success by using pacai.util.probability.flipCoin, which returns True with probability p and False with probability 1 - p.
Complete your q-learning agent by implementing epsilon-greedy action selection in getAction, meaning it chooses random actions epsilon of the time, and follows its current best q-values otherwise.
python3 -m pacai.bin.gridworld --agent q --episodes 100Your final q-values should resemble those of your value iteration agent, especially along well-traveled paths. However, your average returns will be lower than the q-values predict because of the random actions and the initial learning phase.
You can choose an element from a list uniformly at random by calling the random.choice function. You can simulate a binary variable with probability p of success by using pacai.util.probability.flipCoin, which returns True with probability p and False with probability 1 - p.
Question 6 (1 points)
First, train a completely random q-learner with the default learning rate on the noiseless BridgeGrid for 50 episodes and observe whether it finds the optimal policy.
python3 -m pacai.bin.gridworld --agent q --episodes 50 --noise 0 --grid BridgeGrid --epsilon 1Now try the same experiment with an epsilon of 0. Is there an epsilon and a learning rate for which it is highly likely (greater than 99%) that the optimal policy will be learned after 50 iterations? Code analysis.question6 to return EITHER a 2-item tuple of (epsilon, learning rate) OR the constant NOT_POSSIBLE if there is none. Epsilon is controlled by --episode, learning rate by --learning-rate.
First, train a completely random q-learner with the default learning rate on the noiseless BridgeGrid for 50 episodes and observe whether it finds the optimal policy.
python3 -m pacai.bin.gridworld --agent q --episodes 50 --noise 0 --grid BridgeGrid --epsilon 1Now try the same experiment with an epsilon of 0. Is there an epsilon and a learning rate for which it is highly likely (greater than 99%) that the optimal policy will be learned after 50 iterations? Code analysis.question6 to return EITHER a 2-item tuple of (epsilon, learning rate) OR the constant NOT_POSSIBLE if there is none. Epsilon is controlled by --episode, learning rate by --learning-rate.
Question 7 (1 point)
With no additional code, you should now be able to run a q-learning crawler robot:
python3 -m pacai.bin.crawlerIf this doesn't work, you've probably written some code too specific to the gridworld problem and you should make it more general to all MDPs. You will receive full credit if the command above works without exceptions.
This will invoke the crawling robot from class using your q-learner. Play around with the various learning parameters to see how they affect the agent's policies and actions. Note that the step delay is a parameter of the simulation, whereas the learning rate and epsilon are parameters of your learning algorithm, and the discount factor is a property of the environment.
With no additional code, you should now be able to run a q-learning crawler robot:
python3 -m pacai.bin.crawlerIf this doesn't work, you've probably written some code too specific to the gridworld problem and you should make it more general to all MDPs. You will receive full credit if the command above works without exceptions.
This will invoke the crawling robot from class using your q-learner. Play around with the various learning parameters to see how they affect the agent's policies and actions. Note that the step delay is a parameter of the simulation, whereas the learning rate and epsilon are parameters of your learning algorithm, and the discount factor is a property of the environment.
Approximate Q-learning and State Abstraction
Question 8 (1 points)
Time to play some Pac-Man! Pac-Man will play games in two phases: training and testing.
In the first phase, training, Pac-Man will begin to learn about the values of positions and actions. Because it takes a very long time to learn accurate q-values even for tiny grids, Pac-Man's training games run in quiet mode by default, with no GUI (or console) display.
Once Pac-Man's training is complete, he will enter testing mode. When testing, Pac-Man's epsilon and alpha will be set to 0.0, effectively stopping q-learning and disabling exploration, in order to allow Pac-Man to exploit his learned policy. Test games are shown in the GUI by default. Without any code changes you should be able to run q-learning Pac-Man for very tiny grids as follows:
python3 -m pacai.bin.pacman -p PacmanQAgent --num-training 2000 --num-games 2010 --layout smallGridNote that pacai.student.qlearningAgent.PacmanQAgent is already defined for you in terms of the QLearningAgent you have already implemented. PacmanQAgent is only different in that it has default learning parameters that are more effective for the Pac-Man problem (epsilon = 0.05, alpha = 0.2, gamma = 0.8). You will receive full credit for this question if the command above works without exceptions and your agent wins at least 80% of the last 10 runs.
Hint: If your QLearningAgent works for gridworld and crawlery but does not seem to be learning a good policy for Pac-Man on smallGrid, it may be because your getAction and/or getPolicy methods do not in some cases properly consider unseen actions. In particular, because unseen actions have by definition a Q-value of zero, if all of the actions that have been seen have negative Q-values, an unseen action may be optimal.
Note: If you want to experiment with learning parameters, you can use the option --agent-args, for example --agent-args epsilon=0.1,alpha=0.3,gamma=0.7. These values will then be accessible as self.getAlpha(), self.getEpsilon(), and self.getGamma() inside the agent.
Note: While a total of 2010 games will be played, the first 2000 games will not be displayed because of the option --num-training 2000, which designates the first 2000 games for training (no output). Thus, you will only see Pac-Man play the last 10 of these games. The number of training games is also passed to your agent as the option numTraining.
Note: If you want to watch 10 training games to see what's going on, use the command:
python3 -m pacai.bin.pacman -p PacmanQAgent --num-games 10 --layout smallGrid --agent-args numTraining=10During training, you will see output every 100 games with statistics about how Pac-Man is faring. Epsilon is positive during training, so Pac-Man will play poorly even after having learned a good policy: this is because he occasionally makes a random exploratory move into a ghost. As a benchmark, it should take about 1,000 games before Pac-Man's rewards for a 100 episode segment becomes positive, reflecting that he's started winning more than losing. By the end of training, it should remain positive and be fairly high (between 100 and 350).
Make sure you understand what is happening here: the MDP state is the exact board configuration facing Pac-Man, with the now complex transitions describing an entire ply of change to that state. The intermediate game configurations in which Pac-Man has moved but the ghosts have not replied are not MDP states, but are bundled in to the transitions.
Once Pac-Man is done training, he should win very reliably in test games (at least 90% of the time), since now he is exploiting his learned policy.
However, you'll find that training the same agent on the seemingly simple mediumGrid may not work well. In our implementation, Pac-Man's average training rewards remain negative throughout training. At test time, he plays badly, probably losing all of his test games. Training will also take a long time, despite its ineffectiveness.
Pac-Man fails to win on larger layouts because each board configuration is a separate state with separate q-values. He has no way to generalize that running into a ghost is bad for all positions. Obviously, this approach will not scale.
Time to play some Pac-Man! Pac-Man will play games in two phases: training and testing.
In the first phase, training, Pac-Man will begin to learn about the values of positions and actions. Because it takes a very long time to learn accurate q-values even for tiny grids, Pac-Man's training games run in quiet mode by default, with no GUI (or console) display.
Once Pac-Man's training is complete, he will enter testing mode. When testing, Pac-Man's epsilon and alpha will be set to 0.0, effectively stopping q-learning and disabling exploration, in order to allow Pac-Man to exploit his learned policy. Test games are shown in the GUI by default. Without any code changes you should be able to run q-learning Pac-Man for very tiny grids as follows:
python3 -m pacai.bin.pacman -p PacmanQAgent --num-training 2000 --num-games 2010 --layout smallGridNote that pacai.student.qlearningAgent.PacmanQAgent is already defined for you in terms of the QLearningAgent you have already implemented. PacmanQAgent is only different in that it has default learning parameters that are more effective for the Pac-Man problem (epsilon = 0.05, alpha = 0.2, gamma = 0.8). You will receive full credit for this question if the command above works without exceptions and your agent wins at least 80% of the last 10 runs.
Hint: If your QLearningAgent works for gridworld and crawlery but does not seem to be learning a good policy for Pac-Man on smallGrid, it may be because your getAction and/or getPolicy methods do not in some cases properly consider unseen actions. In particular, because unseen actions have by definition a Q-value of zero, if all of the actions that have been seen have negative Q-values, an unseen action may be optimal.
Note: If you want to experiment with learning parameters, you can use the option --agent-args, for example --agent-args epsilon=0.1,alpha=0.3,gamma=0.7. These values will then be accessible as self.getAlpha(), self.getEpsilon(), and self.getGamma() inside the agent.
Note: While a total of 2010 games will be played, the first 2000 games will not be displayed because of the option --num-training 2000, which designates the first 2000 games for training (no output). Thus, you will only see Pac-Man play the last 10 of these games. The number of training games is also passed to your agent as the option numTraining.
Note: If you want to watch 10 training games to see what's going on, use the command:
python3 -m pacai.bin.pacman -p PacmanQAgent --num-games 10 --layout smallGrid --agent-args numTraining=10During training, you will see output every 100 games with statistics about how Pac-Man is faring. Epsilon is positive during training, so Pac-Man will play poorly even after having learned a good policy: this is because he occasionally makes a random exploratory move into a ghost. As a benchmark, it should take about 1,000 games before Pac-Man's rewards for a 100 episode segment becomes positive, reflecting that he's started winning more than losing. By the end of training, it should remain positive and be fairly high (between 100 and 350).
Make sure you understand what is happening here: the MDP state is the exact board configuration facing Pac-Man, with the now complex transitions describing an entire ply of change to that state. The intermediate game configurations in which Pac-Man has moved but the ghosts have not replied are not MDP states, but are bundled in to the transitions.
Once Pac-Man is done training, he should win very reliably in test games (at least 90% of the time), since now he is exploiting his learned policy.
However, you'll find that training the same agent on the seemingly simple mediumGrid may not work well. In our implementation, Pac-Man's average training rewards remain negative throughout training. At test time, he plays badly, probably losing all of his test games. Training will also take a long time, despite its ineffectiveness.
Pac-Man fails to win on larger layouts because each board configuration is a separate state with separate q-values. He has no way to generalize that running into a ghost is bad for all positions. Obviously, this approach will not scale.
Question 9 (3 points)
Implement an approximate q-learning agent that learns weights for features of states, where many states might share the same features. Write your implementation in pacai.student.qlearningAgent.ApproximateQAgent, which is a subclass of PacmanQAgent.
Note: Approximate q-learning assumes the existence of a feature function f(s,a) over state and action pairs, which yields a vector f1(s,a) ... fi(s,a) ... fn(s,a) of feature values. We provide feature functions for you in pacai.core.featureExtractors. Feature vectors are dictionary objects containing the non-zero pairs of features and values; all omitted features have value zero.
The approximate q-function takes the following form:
where each weight wi is associated with a particular feature fi(s,a). In your code, you should implement the weight vector as a dictionary mapping features (which the feature extractors will return) to weight values. You will update your weight vectors similarly to how you updated q-values:
Note that the correction term is the same as in normal Q-Learning.
By default ApproximateQAgent uses the pacai.core.featureExtractors.IdentityExtractor. This assigns a single feature to every (state, action) pair. With this feature extractor, your approximate q-learning agent should work identically to PacmanQAgent. You can test this with the following command:
python3 -m pacai.bin.pacman -p ApproximateQAgent --num-training 2000 --num-games 2010 --layout smallGridImportant: ApproximateQAgent is a subclass of QLearningAgent, and it therefore shares several methods like getAction. Make sure that your methods in QLearningAgent call getQValue instead of accessing q-values directly, so that when you override getQValue in your approximate agent, the new approximate q-values are used to compute actions.
Once you're confident that your approximate learner works correctly with the identity features, run your approximate q-learning agent with our custom feature extractor, which can learn to win with ease:
python3 -m pacai.bin.pacman -p ApproximateQAgent --agent-args extractor=pacai.core.featureExtractors.SimpleExtractor --num-training 50 --num-games 60 --layout mediumGridEven much larger layouts should be no problem for your ApproximateQAgent. (Warning: this may take a few minutes to train.)
python3 -m pacai.bin.pacman -p ApproximateQAgent --agent-args extractor=pacai.core.featureExtractors.SimpleExtractor --num-training 50 --num-games 60 --layout mediumClassicIf you have no errors, your approximate q-learning agent should win almost every time with these simple features, even with only 50 training games.
Congratulations! You have a learning Pac-Man agent!
Implement an approximate q-learning agent that learns weights for features of states, where many states might share the same features. Write your implementation in pacai.student.qlearningAgent.ApproximateQAgent, which is a subclass of PacmanQAgent.
Note: Approximate q-learning assumes the existence of a feature function f(s,a) over state and action pairs, which yields a vector f1(s,a) ... fi(s,a) ... fn(s,a) of feature values. We provide feature functions for you in pacai.core.featureExtractors. Feature vectors are dictionary objects containing the non-zero pairs of features and values; all omitted features have value zero.
The approximate q-function takes the following form:
where each weight wi is associated with a particular feature fi(s,a). In your code, you should implement the weight vector as a dictionary mapping features (which the feature extractors will return) to weight values. You will update your weight vectors similarly to how you updated q-values:
Note that the
By default ApproximateQAgent uses the pacai.core.featureExtractors.IdentityExtractor. This assigns a single feature to every (state, action) pair. With this feature extractor, your approximate q-learning agent should work identically to PacmanQAgent. You can test this with the following command:
python3 -m pacai.bin.pacman -p ApproximateQAgent --num-training 2000 --num-games 2010 --layout smallGridImportant: ApproximateQAgent is a subclass of QLearningAgent, and it therefore shares several methods like getAction. Make sure that your methods in QLearningAgent call getQValue instead of accessing q-values directly, so that when you override getQValue in your approximate agent, the new approximate q-values are used to compute actions.
Once you're confident that your approximate learner works correctly with the identity features, run your approximate q-learning agent with our custom feature extractor, which can learn to win with ease:
python3 -m pacai.bin.pacman -p ApproximateQAgent --agent-args extractor=pacai.core.featureExtractors.SimpleExtractor --num-training 50 --num-games 60 --layout mediumGridEven much larger layouts should be no problem for your ApproximateQAgent. (Warning: this may take a few minutes to train.)
python3 -m pacai.bin.pacman -p ApproximateQAgent --agent-args extractor=pacai.core.featureExtractors.SimpleExtractor --num-training 50 --num-games 60 --layout mediumClassicIf you have no errors, your approximate q-learning agent should win almost every time with these simple features, even with only 50 training games.
Congratulations! You have a learning Pac-Man agent!
