smartcab

# Machine Learning Engineer Nanodegree¶

## Project: Train a Smartcab to Drive¶

Welcome to the fourth project of the Machine Learning Engineer Nanodegree! In this notebook, template code has already been provided for you to aid in your analysis of the Smartcab and your implemented learning algorithm. You will not need to modify the included code beyond what is requested. There will be questions that you must answer which relate to the project and the visualizations provided in the notebook. Each section where you will answer a question is preceded by a 'Question X' header. Carefully read each question and provide thorough answers in the following text boxes that begin with 'Answer:'. Your project submission will be evaluated based on your answers to each of the questions and the implementation you provide in agent.py.

Note: Code and Markdown cells can be executed using the Shift + Enter keyboard shortcut. In addition, Markdown cells can be edited by typically double-clicking the cell to enter edit mode.

## Getting Started¶

In this project, you will work towards constructing an optimized Q-Learning driving agent that will navigate a Smartcab through its environment towards a goal. Since the Smartcab is expected to drive passengers from one location to another, the driving agent will be evaluated on two very important metrics: Safety and Reliability. A driving agent that gets the Smartcab to its destination while running red lights or narrowly avoiding accidents would be considered unsafe. Similarly, a driving agent that frequently fails to reach the destination in time would be considered unreliable. Maximizing the driving agent's safety and reliability would ensure that Smartcabs have a permanent place in the transportation industry.

Safety and Reliability are measured using a letter-grade system as follows:

A+ Agent commits no traffic violations,
and always chooses the correct action.
Agent reaches the destination in time
for 100% of trips.
A Agent commits few minor traffic violations,
such as failing to move on a green light.
Agent reaches the destination on time
for at least 90% of trips.
B Agent commits frequent minor traffic violations,
such as failing to move on a green light.
Agent reaches the destination on time
for at least 80% of trips.
C Agent commits at least one major traffic violation,
such as driving through a red light.
Agent reaches the destination on time
for at least 70% of trips.
D Agent causes at least one minor accident,
such as turning left on green with oncoming traffic.
Agent reaches the destination on time
for at least 60% of trips.
F Agent causes at least one major accident,
such as driving through a red light with cross-traffic.
Agent fails to reach the destination on time
for at least 60% of trips.

To assist evaluating these important metrics, you will need to load visualization code that will be used later on in the project. Run the code cell below to import this code which is required for your analysis.

In [1]:
# Import the visualization code
import visuals as vs

# Pretty display for notebooks
%matplotlib inline


### Understand the World¶

Before starting to work on implementing your driving agent, it's necessary to first understand the world (environment) which the Smartcab and driving agent work in. One of the major components to building a self-learning agent is understanding the characteristics about the agent, which includes how the agent operates. To begin, simply run the agent.py agent code exactly how it is -- no need to make any additions whatsoever. Let the resulting simulation run for some time to see the various working components. Note that in the visual simulation (if enabled), the white vehicle is the Smartcab.

### Question 1¶

In a few sentences, describe what you observe during the simulation when running the default agent.py agent code. Some things you could consider:

• Does the Smartcab move at all during the simulation?
• What kind of rewards is the driving agent receiving?
• How does the light changing color affect the rewards?

Hint: From the /smartcab/ top-level directory (where this notebook is located), run the command

'python smartcab/agent.py'


Here is a brief discussion of my observation of the simulation. First, I observed that there are many iterations that are occuring at the backend of the code. Each iteration is represented as a step. After approximately 124 steps, the simulation starts a new sequence of training and the agent starts at another random position.

Question 1: No, the Smartcab does not move during the simulation. However, it seems to start at a random position after approximately 124 steps.

Question 2: The driving agent is receiving positive and negative rewards based on its action. If it takes a correct action, it will be awarded a positive point, however, if it takes a wrong action, it will be awarded a negative point.

Question 3: Since the default agent is stationary during the course of the simulation, whenever the light is green, it will lose some reward because the normal course of action for the agent at that instance is to go, however if the agent is at a red light, since its position is stationary, it will gain some point because the normal course of action for the agent at that instance is to stop. I think the rationale for the reward system is pretty simple; the agent should stop when the light is red and move when the light is green. Any other actions asides these will result in some form of penalty.

### Understand the Code¶

In addition to understanding the world, it is also necessary to understand the code itself that governs how the world, simulation, and so on operate. Attempting to create a driving agent would be difficult without having at least explored the "hidden" devices that make everything work. In the /smartcab/ top-level directory, there are two folders: /logs/ (which will be used later) and /smartcab/. Open the /smartcab/ folder and explore each Python file included, then answer the following question.

### Question 2¶

• In the agent.py Python file, choose three flags that can be set and explain how they change the simulation.
• In the environment.py Python file, what Environment class function is called when an agent performs an action?
• In the simulator.py Python file, what is the difference between the 'render_text()' function and the 'render()' function?
• In the planner.py Python file, will the 'next_waypoint() function consider the North-South or East-West direction first?

In the agent.py: I chose the following flags

1) Epsilon: which represents the random exploration factor. This flag is used to determine the extent to which the agent should explore the environment. If this value is too low, the agent will not learn any new behavior, also if this value is too high, the agent will be taking a lot of chances. Hence, this value should set a balance between taking risk and learning from previous experience.

2) _Enforcedeadline: This flag is set to impose the number of actions remaining for the Smartcab to reach the destination before running out of time. When this flag is set to true, it will force the driving agent to capture whether it reaches the destination in time.

3) Display: This flag is used to toggle the GUI if PyGame is enabled. If it is set to false, the simulation will run on the console. Otherwise, it will display the simulation on the GUI.

In the environment.py: 1) The environment class function that is called when an agent performs an action is "act"

In the simulator.py: The difference between render_text() and render is: 1) Render_text() - It displays on the console 2) Render() - It displays on the GUI

In the planner.py The next_waypoint() function will consider East-West direction first

## Implement a Basic Driving Agent¶

The first step to creating an optimized Q-Learning driving agent is getting the agent to actually take valid actions. In this case, a valid action is one of None, (do nothing) 'left' (turn left), right' (turn right), or 'forward' (go forward). For your first implementation, navigate to the 'choose_action()' agent function and make the driving agent randomly choose one of these actions. Note that you have access to several class variables that will help you write this functionality, such as 'self.learning' and 'self.valid_actions'. Once implemented, run the agent file and simulation briefly to confirm that your driving agent is taking a random action each time step.

### Basic Agent Simulation Results¶

To obtain results from the initial simulation, you will need to adjust following flags:

• 'enforce_deadline' - Set this to True to force the driving agent to capture whether it reaches the destination in time.
• 'update_delay' - Set this to a small value (such as 0.01) to reduce the time between steps in each trial.
• 'log_metrics' - Set this to True to log the simluation results as a .csv file in /logs/.
• 'n_test' - Set this to '10' to perform 10 testing trials.

Optionally, you may disable to the visual simulation (which can make the trials go faster) by setting the 'display' flag to False. Flags that have been set here should be returned to their default setting when debugging. It is important that you understand what each flag does and how it affects the simulation!

Once you have successfully completed the initial simulation (there should have been 20 training trials and 10 testing trials), run the code cell below to visualize the results. Note that log files are overwritten when identical simulations are run, so be careful with what log file is being loaded! Run the agent.py file after setting the flags from projects/smartcab folder instead of projects/smartcab/smartcab.

In [3]:
# Load the 'sim_no-learning' log file from the initial simulation results
vs.plot_trials('sim_no-learning.csv')


### Question 3¶

Using the visualization above that was produced from your initial simulation, provide an analysis and make several observations about the driving agent. Be sure that you are making at least one observation about each panel present in the visualization. Some things you could consider:

• How frequently is the driving agent making bad decisions? How many of those bad decisions cause accidents?
• Given that the agent is driving randomly, does the rate of reliability make sense?
• What kind of rewards is the agent receiving for its actions? Do the rewards suggest it has been penalized heavily?
• As the number of trials increases, does the outcome of results change significantly?
• Would this Smartcab be considered safe and/or reliable for its passengers? Why or why not?

1. How frequently is the driving agent making bad decisions? How many of those bad decisions cause accidents?

Based on the visualization above, the driving agent is making a bad action at a frequency of around 38% - 43% of the time. The frequency of minor and major violations that the agent accrued is around 12% and 20% respectively. Around 4%-5% of the time, the agent is involved in either a minor or major accident.

2. Given that the agent is driving randomly, does the rate of reliability make sense?

I believe the rate of reliability makes sense since the agent is driving randomly and not really learning the optimal way to navigate. Hence, no matter how much we train the agent, it will probably still have a low reliability until we train it to learn the best way to navigate. So it makes sense that the rate of reliability of the agent is less than 20%.

3. What kind of rewards is the agent receiving for its actions? Do the rewards suggest it has been penalized heavily?

Since the agent is making a lot of bad decisions, it is constantly being penalized with negative reward. Hence, the agent is being penalized heavily for its action and throughout the trials, its reward is between -5 to -4.

4. As the number of trials increases, does the outcome of results change significantly?

The outcome of the result does not change significantly as the number of trials increases. Although the outcome is not a flatline and it has a slight bump sometimes, however, this is not sufficient to improve the reliability from F

5. Would this Smartcab be considered safe and/or reliable for its passengers? Why or why not?

This current version of smartcab would be considered unsafe and unreliable for passengers. First, after 10 simulated testing trials, it has a safety rating of F and a reliability rating of F. The implication of these values is that this agent will most likely gets the passenger to their destination late almost 90% of the time due to its low reliability. Similarly the F safety rating implies the smartcab may gets involved in either a major or minor accident - which may harm the passenger. Hence, since a driving agent that gets the smartcab to its destination while runnning red lights or narrowly avoiding accidents would be considered unsafe. And similarly, a driving agent that frequently fails to reach the destination in time would be considered unreliable. Therefore, this driving agent would considered as a mixture of unsafe and unreliable for its passenger.

## Inform the Driving Agent¶

The second step to creating an optimized Q-learning driving agent is defining a set of states that the agent can occupy in the environment. Depending on the input, sensory data, and additional variables available to the driving agent, a set of states can be defined for the agent so that it can eventually learn what action it should take when occupying a state. The condition of 'if state then action' for each state is called a policy, and is ultimately what the driving agent is expected to learn. Without defining states, the driving agent would never understand which action is most optimal -- or even what environmental variables and conditions it cares about!

### Identify States¶

Inspecting the 'build_state()' agent function shows that the driving agent is given the following data from the environment:

• 'waypoint', which is the direction the Smartcab should drive leading to the destination, relative to the Smartcab's heading.
• 'inputs', which is the sensor data from the Smartcab. It includes
• 'light', the color of the light.
• 'left', the intended direction of travel for a vehicle to the Smartcab's left. Returns None if no vehicle is present.
• 'right', the intended direction of travel for a vehicle to the Smartcab's right. Returns None if no vehicle is present.
• 'oncoming', the intended direction of travel for a vehicle across the intersection from the Smartcab. Returns None if no vehicle is present.
• 'deadline', which is the number of actions remaining for the Smartcab to reach the destination before running out of time.

### Question 4¶

Which features available to the agent are most relevant for learning both safety and efficiency? Why are these features appropriate for modeling the Smartcab in the environment? If you did not choose some features, why are those features not appropriate? Please note that whatever features you eventually choose for your agent's state, must be argued for here. That is: your code in agent.py should reflect the features chosen in this answer.

NOTE: You are not allowed to engineer new features for the smartcab.

For Safety and efficiency, I would consider the following features as being important.

1. inputs : light - The state of the light is critical to ensure the safety of the smartcab. This feature ensures that the smartcab conforms to the standard traffic regulations. In particular, it is used to tell the smartcab to stop when it sees a red light, and to move when it sees a green light.

2. inputs : left/oncoming - This feature is important so the smartcab can know the intended direction of travel for other traffic. For instance, to avoid potential collision, if the light is green and oncoming traffic wants to proceed straight or to the right, the smartcab should yield for this traffic otherwise it could result in a collision. The agent should be able to decide when it is vital to proceed or yield even when the light is green. Furthermore, the smartcab needs to know that it is safe to turn right on red when the car on the left does not want to go straight. Otherwise the car coming from the left and the smartcab may collide.

3. waypoint - I think this feature is important for the smartcab to achieve high efficiency. This will ensure the smartcab reaches the destination in the most efficient manner possible.

Cars coming from right can be ignored since the smartcab won't be turning into that lane. Hence, I won't consider input: right as being important remove it from the list of important features. Similarly, I think the deadline is not an important feature for safety and efficiency. Since it determines the number of actions remaining for the smartcab to reach its destination before running out of time. As long as the agent is aware of the appropriate policy and makes appropriate decision, it should be able to get to its destination in time and safely. Enforcing deadline may make the agent break some important rules in order to achieve the number of actions before running out of time.

### Define a State Space¶

When defining a set of states that the agent can occupy, it is necessary to consider the size of the state space. That is to say, if you expect the driving agent to learn a policy for each state, you would need to have an optimal action for every state the agent can occupy. If the number of all possible states is very large, it might be the case that the driving agent never learns what to do in some states, which can lead to uninformed decisions. For example, consider a case where the following features are used to define the state of the Smartcab:

('is_raining', 'is_foggy', 'is_red_light', 'turn_left', 'no_traffic', 'previous_turn_left', 'time_of_day').

How frequently would the agent occupy a state like (False, True, True, True, False, False, '3AM')? Without a near-infinite amount of time for training, it's doubtful the agent would ever learn the proper action!

### Question 5¶

If a state is defined using the features you've selected from Question 4, what would be the size of the state space? Given what you know about the environment and how it is simulated, do you think the driving agent could learn a policy for each possible state within a reasonable number of training trials?
Hint: Consider the combinations of features to calculate the total number of states!

oncoming: [None, 'forward', 'left', 'right'] = 4 states

inputs: light [red, green] = 2 states

inputs: left : [None, 'forward', 'left', 'right'] = 4 states

waypoint : ['right','forward','left'] = 3 states

This result in a total combination of 4 x 2 x 4 x 3 = 96 states. The size of the state space is 96. Although this seems like a lot of states. However given what I have known about the environment, I believe the agent could learn a policy for each possible states within a reasonable number of training trials.

### Update the Driving Agent State¶

For your second implementation, navigate to the 'build_state()' agent function. With the justification you've provided in Question 4, you will now set the 'state' variable to a tuple of all the features necessary for Q-Learning. Confirm your driving agent is updating its state by running the agent file and simulation briefly and note whether the state is displaying. If the visual simulation is used, confirm that the updated state corresponds with what is seen in the simulation.

Note: Remember to reset simulation flags to their default setting when making this observation!

## Implement a Q-Learning Driving Agent¶

The third step to creating an optimized Q-Learning agent is to begin implementing the functionality of Q-Learning itself. The concept of Q-Learning is fairly straightforward: For every state the agent visits, create an entry in the Q-table for all state-action pairs available. Then, when the agent encounters a state and performs an action, update the Q-value associated with that state-action pair based on the reward received and the iterative update rule implemented. Of course, additional benefits come from Q-Learning, such that we can have the agent choose the best action for each state based on the Q-values of each state-action pair possible. For this project, you will be implementing a decaying, $\epsilon$-greedy Q-learning algorithm with no discount factor. Follow the implementation instructions under each TODO in the agent functions.

Note that the agent attribute self.Q is a dictionary: This is how the Q-table will be formed. Each state will be a key of the self.Q dictionary, and each value will then be another dictionary that holds the action and Q-value. Here is an example:

{ 'state-1': {
'action-1' : Qvalue-1,
'action-2' : Qvalue-2,
...
},
'state-2': {
'action-1' : Qvalue-1,
...
},
...
}

Furthermore, note that you are expected to use a decaying $\epsilon$ (exploration) factor. Hence, as the number of trials increases, $\epsilon$ should decrease towards 0. This is because the agent is expected to learn from its behavior and begin acting on its learned behavior. Additionally, The agent will be tested on what it has learned after $\epsilon$ has passed a certain threshold (the default threshold is 0.05). For the initial Q-Learning implementation, you will be implementing a linear decaying function for $\epsilon$.

### Q-Learning Simulation Results¶

To obtain results from the initial Q-Learning implementation, you will need to adjust the following flags and setup:

• 'enforce_deadline' - Set this to True to force the driving agent to capture whether it reaches the destination in time.
• 'update_delay' - Set this to a small value (such as 0.01) to reduce the time between steps in each trial.
• 'log_metrics' - Set this to True to log the simluation results as a .csv file and the Q-table as a .txt file in /logs/.
• 'n_test' - Set this to '10' to perform 10 testing trials.
• 'learning' - Set this to 'True' to tell the driving agent to use your Q-Learning implementation.

In addition, use the following decay function for $\epsilon$:

$$\epsilon_{t+1} = \epsilon_{t} - 0.05, \hspace{10px}\textrm{for trial number } t$$

If you have difficulty getting your implementation to work, try setting the 'verbose' flag to True to help debug. Flags that have been set here should be returned to their default setting when debugging. It is important that you understand what each flag does and how it affects the simulation!

Once you have successfully completed the initial Q-Learning simulation, run the code cell below to visualize the results. Note that log files are overwritten when identical simulations are run, so be careful with what log file is being loaded!

In [13]:
# Load the 'sim_default-learning' file from the default Q-Learning simulation
vs.plot_trials('sim_default-learning.csv')


### Question 6¶

Using the visualization above that was produced from your default Q-Learning simulation, provide an analysis and make observations about the driving agent like in Question 3. Note that the simulation should have also produced the Q-table in a text file which can help you make observations about the agent's learning. Some additional things you could consider:

• Are there any observations that are similar between the basic driving agent and the default Q-Learning agent?
• Approximately how many training trials did the driving agent require before testing? Does that number make sense given the epsilon-tolerance?
• Is the decaying function you implemented for $\epsilon$ (the exploration factor) accurately represented in the parameters panel?
• As the number of training trials increased, did the number of bad actions decrease? Did the average reward increase?
• How does the safety and reliability rating compare to the initial driving agent?

1. Are there any observations that are similar between the basic driving agent and the default Q-Learning agent?

In terms of safety, the smartcab is still getting a rating of F which shows that it is still unsafe for passengers. However, the reliability rating has gone up significantly from F to A. Comparing it to the basic driving agent, the default Q-learning agent seems to be doing better in terms of reliability.

2. Approximately how many training trials did the driving agent require before testing? Does that number make sense given the epsilon-tolerance?

It will take approximately 20 training trials before the driving agent start testing. This number makes sense given the epsilon-tolerance which is calculated as epsilon = epsilon - 0.05 for each trials, i.e., 1/0.05 = 20

3. Is the decaying function you implemented for ϵϵ (the exploration factor) accurately represented in the parameters panel?

Yes, the decaying function is accurately represented in the parameter value graph. It started from 1 and it was reducing by 0.05

4. As the number of training trials increased, did the number of bad actions decrease? Did the average reward increase?

As the number of training trials increased, some of the bad actions decreased such as major violation, minor accident and major accident. The total bad actions and minor violations are still increasing. However, the average reward is increasing

5. How does the safety and reliability rating compare to the initial driving agent?

At this point, the agent is relatively safety conscious because its reliability rating has gone up to A from F. However, the safety of the agent is still the same (F) with when it was navigating randomly.

## Improve the Q-Learning Driving Agent¶

The third step to creating an optimized Q-Learning agent is to perform the optimization! Now that the Q-Learning algorithm is implemented and the driving agent is successfully learning, it's necessary to tune settings and adjust learning paramaters so the driving agent learns both safety and efficiency. Typically this step will require a lot of trial and error, as some settings will invariably make the learning worse. One thing to keep in mind is the act of learning itself and the time that this takes: In theory, we could allow the agent to learn for an incredibly long amount of time; however, another goal of Q-Learning is to transition from experimenting with unlearned behavior to acting on learned behavior. For example, always allowing the agent to perform a random action during training (if $\epsilon = 1$ and never decays) will certainly make it learn, but never let it act. When improving on your Q-Learning implementation, consider the implications it creates and whether it is logistically sensible to make a particular adjustment.

### Improved Q-Learning Simulation Results¶

To obtain results from the initial Q-Learning implementation, you will need to adjust the following flags and setup:

• 'enforce_deadline' - Set this to True to force the driving agent to capture whether it reaches the destination in time.
• 'update_delay' - Set this to a small value (such as 0.01) to reduce the time between steps in each trial.
• 'log_metrics' - Set this to True to log the simluation results as a .csv file and the Q-table as a .txt file in /logs/.
• 'learning' - Set this to 'True' to tell the driving agent to use your Q-Learning implementation.
• 'optimized' - Set this to 'True' to tell the driving agent you are performing an optimized version of the Q-Learning implementation.

Additional flags that can be adjusted as part of optimizing the Q-Learning agent:

• 'n_test' - Set this to some positive number (previously 10) to perform that many testing trials.
• 'alpha' - Set this to a real number between 0 - 1 to adjust the learning rate of the Q-Learning algorithm.
• 'epsilon' - Set this to a real number between 0 - 1 to adjust the starting exploration factor of the Q-Learning algorithm.
• 'tolerance' - set this to some small value larger than 0 (default was 0.05) to set the epsilon threshold for testing.

Furthermore, use a decaying function of your choice for $\epsilon$ (the exploration factor). Note that whichever function you use, it must decay to 'tolerance' at a reasonable rate. The Q-Learning agent will not begin testing until this occurs. Some example decaying functions (for $t$, the number of trials):

$$\epsilon = a^t, \textrm{for } 0 < a < 1 \hspace{50px}\epsilon = \frac{1}{t^2}\hspace{50px}\epsilon = e^{-at}, \textrm{for } 0 < a < 1 \hspace{50px} \epsilon = \cos(at), \textrm{for } 0 < a < 1$$ You may also use a decaying function for $\alpha$ (the learning rate) if you so choose, however this is typically less common. If you do so, be sure that it adheres to the inequality $0 \leq \alpha \leq 1$.

If you have difficulty getting your implementation to work, try setting the 'verbose' flag to True to help debug. Flags that have been set here should be returned to their default setting when debugging. It is important that you understand what each flag does and how it affects the simulation!

Once you have successfully completed the improved Q-Learning simulation, run the code cell below to visualize the results. Note that log files are overwritten when identical simulations are run, so be careful with what log file is being loaded!

In [24]:
# Load the 'sim_improved-learning' file from the improved Q-Learning simulation
vs.plot_trials('sim_improved-learning.csv')


### Question 7¶

Using the visualization above that was produced from your improved Q-Learning simulation, provide a final analysis and make observations about the improved driving agent like in Question 6. Questions you should answer:

• What decaying function was used for epsilon (the exploration factor)?
• Approximately how many training trials were needed for your agent before begining testing?
• What epsilon-tolerance and alpha (learning rate) did you use? Why did you use them?
• How much improvement was made with this Q-Learner when compared to the default Q-Learner from the previous section?
• Would you say that the Q-Learner results show that your driving agent successfully learned an appropriate policy?
• Are you satisfied with the safety and reliability ratings of the Smartcab?

1. What decaying function was used for epsilon (the exploration factor)? The decaying function that was used for epsilon is e^(-at). Where a = 0.02 and t = number of trials. Hence, the decaying function is e^(-0.02*no_of_trials)

2. Approximately how many training trials were needed for your agent before begining testing? Around 200 training trials were needed before the agent begin testing. After several trial and errors, I chose a to be 0.02 and tolerance of 0.01 because it gives me the highest rating within a short training time. If I choose a to be 0.005 and set the epsilon to the default of 0.05, I will obtain a rating of A+ for both reliability and safety but it will take approximately 600 training trials before the testing commence.

3. What epsilon-tolerance and alpha (learning rate) did you use? Why did you use them? An epsilon-tolerance value of 0.01 and learning rate of 0.5 were used. The reason for using these values is for the agent to learn the optimal policy within reasonable training trials. The epsilon sets the random exploration factor while the alpha sets the learning rate

4. How much improvement was made with this Q-Learner when compared to the default Q-Learner from the previous section? There is a significant improvement with this Q-Learner when compared to the default Q-Learner. The safety rating went up from B to A+ while the reliability rating went from F to A

5. Would you say that the Q-Learner results show that your driving agent successfully learned an appropriate policy? I would say that the Q-Learner resulst show that my driving agent successfully learned an appropriate policy. Although more testing trials need to be conducted.

6. Are you satisfied with the safety and reliability ratings of the Smartcab? I am satisfied with the safey and reliability ratings of the Smartcab.

### Define an Optimal Policy¶

Sometimes, the answer to the important question "what am I trying to get my agent to learn?" only has a theoretical answer and cannot be concretely described. Here, however, you can concretely define what it is the agent is trying to learn, and that is the U.S. right-of-way traffic laws. Since these laws are known information, you can further define, for each state the Smartcab is occupying, the optimal action for the driving agent based on these laws. In that case, we call the set of optimal state-action pairs an optimal policy. Hence, unlike some theoretical answers, it is clear whether the agent is acting "incorrectly" not only by the reward (penalty) it receives, but also by pure observation. If the agent drives through a red light, we both see it receive a negative reward but also know that it is not the correct behavior. This can be used to your advantage for verifying whether the policy your driving agent has learned is the correct one, or if it is a suboptimal policy.

### Question 8¶

1. Please summarize what the optimal policy is for the smartcab in the given environment. What would be the best set of instructions possible given what we know about the environment? You can explain with words or a table, but you should thoroughly discuss the optimal policy.

2. Next, investigate the 'sim_improved-learning.txt' text file to see the results of your improved Q-Learning algorithm. For each state that has been recorded from the simulation, is the policy (the action with the highest value) correct for the given state? Are there any states where the policy is different than what would be expected from an optimal policy?

3. Provide a few examples from your recorded Q-table which demonstrate that your smartcab learned the optimal policy. Explain why these entries demonstrate the optimal policy.

4. Try to find at least one entry where the smartcab did not learn the optimal policy. Discuss why your cab may have not learned the correct policy for the given state.

Be sure to document your state dictionary below, it should be easy for the reader to understand what each state represents.

1. Please summarize what the optimal policy is for the smartcab in the given environment. What would be the best set of instructions possible given what we know about the environment?

Given a tuple of state represented as state = (waypoint, inputs['light'], inputs['left'], inputs['oncoming']), then the optimal policy for the smartcab can be summarised thus;

If the light is red, i.e., input['light']='red', then the optimal action for the smartcab will be to stop. However, a suboptimal action include the smartcab turning right on red at an intersection, although, the smartcab must ensure that there is no oncoming traffic from the left to avoid collision.

Similarly, if the light is green, i.e., input['light']='green', then the optimal action for the smartcab is to proceed straight. However, the smartcab can't turn left at green lights when the oncoming car wants to proceed straight or to its right.

2. For each state that has been recorded from the simulation, is the policy (the action with the highest value) correct for the given state? Are there any states where the policy is different than what would be expected from an optimal policy?

State-action rewards from Q-Learning improved learning follows this rule:

state = (waypoint, inputs['light'], inputs['left'], inputs['oncoming'])

Example 1 ('forward', 'green', None, None) -- forward : 1.92 -- right : 0.97 -- None : -5.72 -- left : 0.41

For the example above, the agent has not successfully learned the optimal policy. For instance, if the smartcab is going forward and the light is green and there is no oncoming traffic, then the optimal action is to go straight. Therefore this policy has the highest reward (1.92), Similarly, it can turn right since there is no oncoming traffic from the left, although this is a suboptimal action, hence it has a lower reward (0.97). However, turning left has a reward of 0.41 which is not an optimal action.

3. Provide a few examples from your recorded Q-table which demonstrate that your smartcab learned the optimal policy. Explain why these entries demonstrate the optimal policy.

Example 2 ('forward', 'green', None, 'forward') -- forward : 2.20 -- right : 0.72 -- None : -4.71 -- left : -9.70

For the second example above, the agent has successfully learned the optimal policy. For instance, when the smartcab is going forward and the light is green and there is no oncoming traffic, then the optimal action is to go straight. Therefore this policy has the highest reward (2.20), Similarly, it can turn right since there is no oncoming traffic from the left and since this is a suboptimal action, it has a lower reward (0.72). Also, if it stops, when it should be moving, it will be penalized (-4.71) and if it turns left, it will be penalized even much more (-9.70).

4. Try to find at least one entry where the smartcab did not learn the optimal policy. Discuss why your cab may have not learned the correct policy for the given state.

('forward', 'green', 'left', 'forward') -- forward : 0.00 -- right : 1.41 -- None : 0.00 -- left : -9.78

I think the agent does not know the optimal policy in the example above because there are more than one actions with no reward nor penalty.

### Optional: Future Rewards - Discount Factor, 'gamma'¶

Curiously, as part of the Q-Learning algorithm, you were asked to not use the discount factor, 'gamma' in the implementation. Including future rewards in the algorithm is used to aid in propagating positive rewards backwards from a future state to the current state. Essentially, if the driving agent is given the option to make several actions to arrive at different states, including future rewards will bias the agent towards states that could provide even more rewards. An example of this would be the driving agent moving towards a goal: With all actions and rewards equal, moving towards the goal would theoretically yield better rewards if there is an additional reward for reaching the goal. However, even though in this project, the driving agent is trying to reach a destination in the allotted time, including future rewards will not benefit the agent. In fact, if the agent were given many trials to learn, it could negatively affect Q-values!

### Optional Question 9¶

There are two characteristics about the project that invalidate the use of future rewards in the Q-Learning algorithm. One characteristic has to do with the Smartcab itself, and the other has to do with the environment. Can you figure out what they are and why future rewards won't work for this project?