MC3-Project-2

Draft

This project is in draft mode. This note will be removed once it it finalized.

Overview

In this project you will implement the Q-Learning and Dyna-Q solutions to the reinforcement learning problem. You will apply them to a navigation problem in this project. In a later project you will apply them to trading. The reason for working with the navigation problem first is that, as you will see, navigation is an easy problem to work with and understand. Note that your Q-Learning code really shouldn't care which problem it is solving. The difference is that you need to wrap the learner in different code that frames the problem for the learner as necessary.

For the navigation problem we have created testqlearner.py that automates testing of your Q-Learner in the navigation problem.

Overall, your tasks for this project include:

• Code a Q-Learner
• Code the Dyna-Q feature of Q-Learning
• Test/debug the Q-Learner in navigation problems

For this assignment we will test only your code (there is no report component).

Template and Data

• Update your local mc3_p3 directory using github.
• Implement the QLearner class in mc3_p3/QLearner.py.
• To test your Q-learner, run python testqlearner.py from the mc3_p3/ directory.
• Note that example navigation problems are provided in the mc3_p3/testworlds directory

Part 1: Implement Q-Learner

Your QLearner class should be implemented in the file QLearner.py. It should implement EXACTLY the API defined below. DO NOT import any modules besides those allowed below. Your class should implement the following methods:

The constructor QLearner() should reserve space for keeping track of Q[s, a] for the number of states and actions. It should initialize Q[] with uniform random values between -1.0 and 1.0. Details on the input arguments to the constructor:

• num_states integer, the number of states to consider
• num_actions integer, the number of actions available.
• alpha float, the learning rate used in the update rule. Should range between 0.0 and 1.0 with 0.2 as a typical value.
• gamma float, the discount rate used in the update rule. Should range between 0.0 and 1.0 with 0.9 as a typical value.
• rar float, random action rate: the probability of selecting a random action at each step. Should range between 0.0 (no random actions) to 1.0 (always random action) with 0.5 as a typical value.
• radr float, random action decay rate, after each update, rar = rar * radr. Ranges between 0.0 (immediate decay to 0) and 1.0 (no decay). Typically 0.99.
• dyna integer, conduct this number of dyna updates for each regular update. When Dyna is used, 200 is a typical value.
• verbose boolean, if True, your class is allowed to print debugging statements, if False, all printing is prohibited.

query(s_prime, r) is the core method of the Q-Learner. It should keep track of the last state s and the last action a, then use the new information s_prime and r to update the Q table. The learning instance, or experience tuple is <s, a, s_prime, r>. query() should return an integer, which is the next action to take. Note that it should choose a random action with probability rar, and that it should update rar according to the decay rate radr at each step. Details on the arguments:

• s_prime integer, the the new state.
• r float, a real valued immediate reward.

querysetstate(s) A special version of the query method that sets the state to s, and returns an integer action according to the same rules as query() (including choosing a random action sometimes), but it does not execute an update to the Q-table. It also does not update rar. There are two main uses for this method: 1) To set the initial state, and 2) when using a learned policy, but not updating it.

Here's an example of the API in use:

import QLearner as ql

learner = ql.QLearner(num_states = 100, \ 
    num_actions = 4, \
    alpha = 0.2, \
    gamma = 0.9, \
    rar = 0.98, \
    radr = 0.999, \
    dyna = 0, \
    verbose = False)

s = 99 # our initial state

a = learner.querysetstate(s) # action for state s

s_prime = 5 # the new state we end up in after taking action a in state s

r = 0 # reward for taking action a in state s

next_action = learner.query(s_prime, r)

Part 2: Navigation Problem Test Cases

We will test your Q-Learner with a navigation problem as follows. Note that your Q-Learner does not need to be coded specially for this task. In fact the code doesn't need to know anything about it. The code necessary to test your learner with this navigation task is implemented in testqlearner.py for you. The navigation task takes place in a 10 x 10 grid world. The particular environment is expressed in a CSV file of integers, where the value in each position is interpreted as follows:

• 0: blank space.
• 1: an obstacle.
• 2: the starting location for the robot.
• 3: the goal location.
• 5: quicksand.

An example navigation problem (CSV file) is shown below. Following python conventions, [0,0] is upper left, or northwest corner, [9,9] lower right or southeast corner. Rows are north/south, columns are east/west.

0,0,0,0,3,0,0,0,0,0
0,0,0,0,0,0,0,0,0,0
0,0,0,0,0,0,0,0,0,0
0,0,1,1,1,1,1,0,0,0
0,0,1,0,0,0,1,0,0,0
0,0,1,0,0,0,1,0,0,0
0,0,1,0,0,0,1,0,0,0
0,0,0,0,0,0,0,0,0,0
0,0,0,0,0,0,0,0,0,0
0,0,0,0,2,0,0,0,0,0

In this example the robot starts at the bottom center, and must navigate to the top center. Note that a wall of obstacles blocks its path. The objective is for the robot to learn how to navigate from the starting location to the goal at the lowest cost. We define the cost for each step as:

• 1 if the robot moves to an empty or blank space
• 100 if the robot moves to a quicksand space
• 0 if the robot moves to the goal space

Overall, we will assess the performance of a policy as the average cost it incurs to travel from the start to the goal (lower cost is better). We assess a learner in terms of the cost it converges to over a given number of training iterations (trips from start to goal). Important note: the problem includes random actions. So, for example, if your learner responds with a "move north" action, there is some probability that the robot will actually move in a different direction. For this reason, the "wise" learner develops policies that keep the robot well away from quicksand. We map this problem to a reinforcement learning problem as follows:

• State: The state is the location of the robot, it is computed (discretized) as: column location * 10 + row location.
• Actions: There are 4 possible actions, 0: move north, 1: move east, 2: move south, 3: move west.
• R: The reward is:
  • +1.0 if the last action caused the robot to reach the goal.
  • -100.0 if the last action caused the robot to step in quicksand.
  • -1.0 otherwise.
• T: The transition matrix can be inferred from the CSV map and the actions.

Note that R and T are not known by or available to the learner. The testing code testqlearner.py will test your code as follows (pseudo code):

Instantiate the learner with the constructor QLearner()
s = initial_location
a = querysetstate(s)
s_prime = new location according to action a
r = -1.0
while not converged:
    a = query(s_prime, r) 
    s_prime = new location according to action a
    if s_prime == goal:
        r = +1
        s_prime = start location
    else if s_prime == quicksand:
        r = -100
    else:
        r = -1

A few things to note about this code: The learner always receives a reward of -1.0 (or -100.0) until it reaches the goal, when it receives a reward of +1.0. As soon as the robot reaches the goal, it is immediately returned to the starting location.

Here are example solutions:

mc3_p3_examples

mc3_p3_dyna_examples

Part 3: Implement Dyna

Add additional components to your QLearner class so that multiple "hallucinated" experience tuples are used to update the Q-table for each "real" experience. The addition of this component should speed convergence in terms of the number of calls to query().

Note that it is not important that you implement Dyna exactly as described in the lecture. The key requirement is that your code should somehow hallucinate additional experiences. The precise method you use for discovering those experiences is flexible. We will test your code on several test worlds with 50 iterations and with dyna = 100. Our expectation is that with Dyna, the solution should be much better after 50 iterations than without.

Contents of Report

There is no report component of this assignment. However, if you would like to impress us with your Machine Learning prowess, you are invited to submit a succinct report.

Hints & resources

This paper by Kaelbling, Littman and Moore, is a good resource for RL in general: http://www.jair.org/media/301/live-301-1562-jair.pdf See Section 4.2 for details on Q-Learning.

There is also a chapter in the Mitchell book on Q-Learning.

For implementing Dyna, you may find the following resources useful:

• https://webdocs.cs.ualberta.ca/~sutton/book/ebook/node96.html
• http://www-anw.cs.umass.edu/~barto/courses/cs687/Chapter%209.pdf

What to turn in

Turn your project in via t-square. All of your code must be contained within QLearner.py and StrategyLearner.py.

• Your QLearner as QLearner.py
• Do not submit any other files.

Rubric

Only your QLearner class will be tested.

• For basic Q-Learning (dyna = 0) we will test your learner against 10 test worlds with 500 iterations. Each test should complete in less than 2 seconds. For the test to be successful, your learner should find a path to the goal <= 1.5 x the number of steps our reference solution finds. We will check this by taking the min of all the 500 runs. Each test case is worth 8 points. We will initialize your learner with the following parameter values:

    learner = ql.QLearner(num_states=100,\
        num_actions = 4, \
        alpha = 0.2, \
        gamma = 0.9, \
        rar = 0.98, \
        radr = 0.999, \
        dyna = 0, \
        verbose=False) #initialize the learner

• For Dyna-Q, we will set dyna = 200. We will test your learner against world03.csv with 50 iterations. The test should complete in less than 10 seconds. For the test to be successful, your learner should find a path to the goal <= 1.5 x the number of steps our reference solution finds. We will check this by taking the min of all 50 runs. The test case is worth 5 points. We will initialize your learner with the following parameter values:

    learner = ql.QLearner(num_states=100,\
        num_actions = 4, \
        alpha = 0.2, \
        gamma = 0.9, \
        rar = 0.5, \
        radr = 0.99, \
        dyna = 200, \
        verbose=False) #initialize the learner

Required, Allowed & Prohibited

Required:

• Your project must be coded in Python 2.7.x.
• Your code must run on one of the university-provided computers (e.g. buffet02.cc.gatech.edu), or on one of the provided virtual images.

Allowed:

• You can develop your code on your personal machine, but it must also run successfully on one of the university provided machines or virtual images.
• Your code may use standard Python libraries.
• You may use the NumPy, SciPy, matplotlib and Pandas libraries. Be sure you are using the correct versions.
• You may reuse sections of code (up to 5 lines) that you collected from other students or the internet.
• Code provided by the instructor, or allowed by the instructor to be shared.
• Use util.py (only) for reading data.

Prohibited:

• Any libraries not listed in the "allowed" section above.
• Any code you did not write yourself (except for the 5 line rule in the "allowed" section).
• Any Classes (other than Random) that create their own instance variables for later use (e.g., learners like kdtree).
• Print statements outside "verbose" checks (they significantly slow down auto grading).
• Any method for reading data besides util.py

Legacy

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