Project 4 | CS 188 Spring 2023

CS 188 Spring 2023 Projects / Project 4 Due: Tuesday, March 14, 11 : 59 PM PT . Introduction MDPs Question 1 (6 points): Value Iteration Question 2 (5 points): Policies Question 3 (6 points): Q-Learning Question 4 (2 points): Epsilon Greedy Question 5 (2 point): Q-Learning and Pacman Question 6 (4 points): Approximate Q-Learning Submission 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 Pacman. Questions 1 and 2 are on MDPs and are in-scope for the midterm. As in previous projects, this project includes an autograder for you to grade your solutions on your machine. This can be run on all questions with the command: It can be run for one particular question, such as q2, by: It can be run for one particular test by commands of the form: Project 4: Reinforcement Learning TABLE OF CONTENTS • • • • • • • • • Introduction python autograder.py Copy python autograder.py -q q2 Copy

The code for this project contains the following files, available as a zip archive . Files you'll edit: valueIterationAgents.py A value iteration agent for solving known MDPs. qlearningAgents.py Q-learning agents for Gridworld, Crawler and Pacman. analysis.py A file to put your answers to questions given in the project. Files you might want to look at: mdp.py Defines methods on general MDPs. learningAgents.py Defines the base classes ValueEstimationAgent and QLearningAgent , which your agents will extend. util.py Utilities, including util.Counter , which is particularly useful for Q-learners. gridworld.py The Gridworld implementation. featureExtractors.py Classes for extracting features on (state, action) pairs. Used for the approximate Q-learning agent (in qlearningAgents.py ). Supporting files you can ignore: environment.py Abstract class for general reinforcement learning environments. Used by gridworld.py . graphicsGridworldDisplay.py Gridworld graphical display. graphicsUtils.py Graphics utilities. textGridworldDisplay.py Plug-in for the Gridworld text interface. crawler.py The crawler code and test harness. You will run this but not edit it. python autograder.py -t test_cases/q2/1-bridge-grid Copy

To get started, run Gridworld in manual control mode, which uses the arrow keys: You 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: The default agent moves randomly You 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 the true terminal state 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 ( -d to change; 0.9 by default). Look at the console output that accompanies the graphical output (or use -t for all text). You will be told about each transition the agent experiences (to turn this off, use -q ). As in Pacman, positions are represented by (x, y) Cartesian coordinates and 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 ( -r ). MDPs python gridworld.py -m Copy python gridworld.py -h Copy python gridworld.py -g MazeGrid Copy Question 1 (6 points): Value Iteration

Recall the value iteration state update equation: Write a value iteration agent in ValueIterationAgent , which has been partially specified for you in valueIterationAgents.py . Your value iteration agent is an offline planner, not a reinforcement learning agent, and so the relevant training option is the number of iterations of value iteration it should run (option -i ) in its initial planning phase. ValueIterationAgent takes an MDP on construction and runs value iteration for the specified number of iterations before the constructor returns. Value iteration computes -step estimates of the optimal values, . In addition to runValueIteration , implement the following methods for ValueIterationAgent using : computeActionFromValues(state) computes the best action according to the value function given by self.values. computeQValueFromValues(state, action) returns the Q-value of the (state, action) pair given by the value function given by self.values . 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 is computed from a fixed vector (like in lecture), not the “online” version where one single weight vector is updated in place. This means that when a state’s value is updated in iteration based on the values of its successor states, the successor state values used in the value update computation should be those from iteration (even if some of the successor states had already been updated in iteration ). The difference is discussed in Sutton & Barto in Chapter 4.1 on page 91. Note : A policy synthesized from values of depth (which reflect the next rewards) will actually reflect the next rewards (i.e. you return ). Similarly, the Q-values will also reflect one more reward than the values (i.e. you return ). You should return the synthesized policy . Hint : You may optionally use the util.Counter class in util.py , which is a dictionary with a default value of zero. However, be careful with argMax : the actual argmax you want may be a key not in the counter ! V ( s ) ← k +1 T ( s , a , s ) R ( s , a , s ) + γ V ( s ) a max s ′ ∑ ′ [ ′ k ′ ] k V k V k • • V k V k − 1 k k − 1 k k k k + 1 π k +1 Q k +1 π k +1

Grading : 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). Consider the DiscountGrid layout, shown below. This grid has two terminal states with positive payoff (in the middle row), 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, and 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. Question 2 (5 points): Policies

In this question, you will choose settings of the discount, noise, and living reward parameters for this MDP to produce optimal policies of several different types. Your setting of the parameter values for each part should have the property that, if your agent followed its optimal policy without being subject to any noise, it would exhibit the given behavior. If a particular behavior is not achieved for any setting of the parameters, assert that the policy is impossible by returning the string 'NOT POSSIBLE' . Here are the optimal policy types you should attempt to produce: To see what behavior a set of numbers ends up in, run the following command to see a GUI: To check your answers, run the autograder: Prefer the close exit (+1), risking the cliff (-10) 1 Prefer the close exit (+1), but avoiding the cliff (-10) 2 Prefer the distant exit (+10), risking the cliff (-10) 3 Prefer the distant exit (+10), avoiding the cliff (-10) 4 Avoid both exits and the cliff (so an episode should never terminate) 5 python gridworld.py -g DiscountGrid -a value --discount [ YOUR_DISCOUNT] -- Copy

getQValue . This abstraction will be useful for question 10 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: Recall that -k 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.” Hint: to help with debugging, you can turn off noise by using the - -noise 0.0 parameter (though this obviously makes Q-learning less interesting). If you manually steer Pacman north and then east along the optimal path for four episodes, you should see the following Q-values: Grading : We will run your Q-learning agent and check that it learns the same Q-values and policy as our reference implementation when each is presented with the same set python gridworld.py -a q -k 5 -m Copy

of examples. To grade your implementation, run the autograder: Complete your Q-learning agent by implementing epsilon-greedy action selection in getAction , meaning it chooses random actions an epsilon fraction of the time, and follows its current best Q-values otherwise. Note that choosing a random action may result in choosing the best action - that is, you should not choose a random sub- optimal action, but rather any random legal action. 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 util.flipCoin(p) , which returns True with probability p and False with probability 1-p . After implementing the getAction method, observe the following behavior of the agent in GridWorld (with epsilon = 0.3). Your 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 also observe the following simulations for different epsilon values. Does that behavior of the agent match what you expect ? To test your implementation, run the autograder: python autograder.py -q q3 Copy Question 4 (2 points): Epsilon Greedy python gridworld.py -a q -k 100 Copy python gridworld.py -a q -k 100 --noise 0.0 -e 0.1 Copy python gridworld.py -a q -k 100 --noise 0.0 -e 0.9 Copy python autograder.py -q q4 Copy

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. Beware of the argMax function from util.Counter ! To grade your answer, run: Note : If you want to experiment with learning parameters, you can use the option -a , for example -a epsilon=0.1,alpha=0.3,gamma=0.7 . These values will then be accessible as self.epsilon , self.gamma and self.alpha 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 -x 2000 , which designates the first 2000 games for training (no output). Thus, you will only see Pacman 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: During training, you will see output every 100 games with statistics about how Pacman is faring. Epsilon is positive during training, so Pacman 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 between 1000 and 1400 games before Pacman’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 Pacman, with the now complex transitions describing an entire ply of change to that state. The intermediate game configurations in which Pacman has moved but the ghosts have not replied are not MDP states, but are bundled in to the transitions. Once Pacman 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 will find that training the same agent on the seemingly simple python autograder.py -q q5 Copy python pacman.py -p PacmanQAgent -n 10 -l smallGrid -a numTraining = 10 Copy

mediumGrid does not work well. In our implementation, Pacman’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. Pacman 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. 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 ApproximateQAgent class in qlearningAgents.py , which is a subclass of PacmanQAgent . Note : Approximate Q-learning assumes the existence of a feature function over state and action pairs, which yields a vector of feature values. We provide feature functions for you in featureExtractors.py . Feature vectors are util.Counter (like a dictionary) objects containing the non-zero pairs of features and values; all omitted features have value zero. So, instead of an vector where the index in the vector defines which feature is which, we have the keys in the dictionary define the idenity of the feature. The approximate Q-function takes the following form: where each weight is associated with a particular feature . 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 term is the same as in normal Q-learning, and is the experienced reward. Question 6 (4 points): Approximate Q-Learning f ( s , a ) [ f ( s , a ), … , f ( s , a ), … , f ( s , a )] 1 i n Q ( s , a ) = f ( s , a ) w i =1 ∑ n i i w i f ( s , a ) i w ← i w + i α ⋅ difference ⋅ f ( s , a ) i difference = r + γ Q ( s , a ) − ( a ′ max ′ ′ ) Q ( s , a ) difference r

In order to submit your project upload the Python files you edited. For instance, use Gradescope’s upload on all .py files in the project folder. Submission