📖이론복습

Bellman Equation

• Bellman Expectation Equation
• Bellman Optimal Equation

MDP를 알때의 Planning

• Policy Evaluation
• Policy Iteration
• Value Iteration

05-04-Planning by Dynamic Programming.pdf

📖Grid World - 실습

02.zip

Policy Iteration

• GridWorld Environment

• environment.py

import tkinter as tk
from tkinter import Button
import time
import numpy as np
from PIL import ImageTk, Image

PhotoImage = ImageTk.PhotoImage
UNIT = 100  # 픽셀 수
HEIGHT = 5  # 그리드월드 세로
WIDTH = 5  # 그리드월드 가로
TRANSITION_PROB = 1
POSSIBLE_ACTIONS = [0, 1, 2, 3]  # 좌, 우, 상, 하
ACTIONS = [(-1, 0), (1, 0), (0, -1), (0, 1)]  # 좌표로 나타낸 행동
REWARDS = []

class GraphicDisplay(tk.Tk):
    def __init__(self, agent):
        super(GraphicDisplay, self).__init__()
        self.title('Policy Iteration')
        self.geometry('{0}x{1}'.format(HEIGHT * UNIT, HEIGHT * UNIT + 50))
        self.texts = []
        self.arrows = []
        self.env = Env()
        self.agent = agent
        self.evaluation_count = 0
        self.improvement_count = 0
        self.is_moving = 0
        (self.up, self.down, self.left, self.right), self.shapes = self.load_images()
        self.canvas = self._build_canvas()
        self.text_reward(2, 2, "R : 1.0")
        self.text_reward(1, 2, "R : -1.0")
        self.text_reward(2, 1, "R : -1.0")

    def _build_canvas(self):
        canvas = tk.Canvas(self, bg='white',
                           height=HEIGHT * UNIT,
                           width=WIDTH * UNIT)
        # 버튼 초기화
        iteration_button = Button(self, text="Evaluate",
                                  command=self.evaluate_policy)
        iteration_button.configure(width=10, activebackground="#33B5E5")
        canvas.create_window(WIDTH * UNIT * 0.13, HEIGHT * UNIT + 10,
                             window=iteration_button)
        policy_button = Button(self, text="Improve",
                               command=self.improve_policy)
        policy_button.configure(width=10, activebackground="#33B5E5")
        canvas.create_window(WIDTH * UNIT * 0.37, HEIGHT * UNIT + 10,
                             window=policy_button)
        policy_button = Button(self, text="move", command=self.move_by_policy)
        policy_button.configure(width=10, activebackground="#33B5E5")
        canvas.create_window(WIDTH * UNIT * 0.62, HEIGHT * UNIT + 10,
                             window=policy_button)
        policy_button = Button(self, text="reset", command=self.reset)
        policy_button.configure(width=10, activebackground="#33B5E5")
        canvas.create_window(WIDTH * UNIT * 0.87, HEIGHT * UNIT + 10,
                             window=policy_button)

        # 그리드 생성
        for col in range(0, WIDTH * UNIT, UNIT):  # 0~400 by 80
            x0, y0, x1, y1 = col, 0, col, HEIGHT * UNIT
            canvas.create_line(x0, y0, x1, y1)
        for row in range(0, HEIGHT * UNIT, UNIT):  # 0~400 by 80
            x0, y0, x1, y1 = 0, row, HEIGHT * UNIT, row
            canvas.create_line(x0, y0, x1, y1)

        # 캔버스에 이미지 추가
        self.rectangle = canvas.create_image(50, 50, image=self.shapes[0])
        canvas.create_image(250, 150, image=self.shapes[1])
        canvas.create_image(150, 250, image=self.shapes[1])
        canvas.create_image(250, 250, image=self.shapes[2])

        canvas.pack()

        return canvas

    def load_images(self):
        up = PhotoImage(Image.open("../img/up.png").resize((13, 13)))
        right = PhotoImage(Image.open("../img/right.png").resize((13, 13)))
        left = PhotoImage(Image.open("../img/left.png").resize((13, 13)))
        down = PhotoImage(Image.open("../img/down.png").resize((13, 13)))
        rectangle = PhotoImage(Image.open("../img/rectangle.png").resize((65, 65)))
        triangle = PhotoImage(Image.open("../img/triangle.png").resize((65, 65)))
        circle = PhotoImage(Image.open("../img/circle.png").resize((65, 65)))
        return (up, down, left, right), (rectangle, triangle, circle)

    def reset(self):
        if self.is_moving == 0:
            self.evaluation_count = 0
            self.improvement_count = 0
            for i in self.texts:
                self.canvas.delete(i)

            for i in self.arrows:
                self.canvas.delete(i)
            self.agent.value_table = [[0.0] * WIDTH for _ in range(HEIGHT)]
            self.agent.policy_table = ([[[0.25, 0.25, 0.25, 0.25]] * WIDTH
                                        for _ in range(HEIGHT)])
            self.agent.policy_table[2][2] = []
            x, y = self.canvas.coords(self.rectangle)
            self.canvas.move(self.rectangle, UNIT / 2 - x, UNIT / 2 - y)

    def text_value(self, row, col, contents, font='Helvetica', size=10,
                   style='normal', anchor="nw"):
        origin_x, origin_y = 85, 70
        x, y = origin_y + (UNIT * col), origin_x + (UNIT * row)
        font = (font, str(size), style)
        text = self.canvas.create_text(x, y, fill="black", text=contents,
                                       font=font, anchor=anchor)
        return self.texts.append(text)

    def text_reward(self, row, col, contents, font='Helvetica', size=10,
                    style='normal', anchor="nw"):
        origin_x, origin_y = 5, 5
        x, y = origin_y + (UNIT * col), origin_x + (UNIT * row)
        font = (font, str(size), style)
        text = self.canvas.create_text(x, y, fill="black", text=contents,
                                       font=font, anchor=anchor)
        return self.texts.append(text)

    def rectangle_move(self, action):
        base_action = np.array([0, 0])
        location = self.find_rectangle()
        self.render()
        if action == 0 and location[0] > 0:  # 상
            base_action[1] -= UNIT
        elif action == 1 and location[0] < HEIGHT - 1:  # 하
            base_action[1] += UNIT
        elif action == 2 and location[1] > 0:  # 좌
            base_action[0] -= UNIT
        elif action == 3 and location[1] < WIDTH - 1:  # 우
            base_action[0] += UNIT
        # move agent
        self.canvas.move(self.rectangle, base_action[0], base_action[1])

    def find_rectangle(self):
        temp = self.canvas.coords(self.rectangle)
        x = (temp[0] / 100) - 0.5
        y = (temp[1] / 100) - 0.5
        return int(y), int(x)

    def move_by_policy(self):
        if self.improvement_count != 0 and self.is_moving != 1:
            self.is_moving = 1

            x, y = self.canvas.coords(self.rectangle)
            self.canvas.move(self.rectangle, UNIT / 2 - x, UNIT / 2 - y)

            x, y = self.find_rectangle()
            while len(self.agent.policy_table[x][y]) != 0:
                self.after(100,
                           self.rectangle_move(self.agent.get_action([x, y])))
                x, y = self.find_rectangle()
            self.is_moving = 0

    def draw_one_arrow(self, col, row, policy):
        if col == 2 and row == 2:
            return

        if policy[0] > 0:  # up
            origin_x, origin_y = 50 + (UNIT * row), 10 + (UNIT * col)
            self.arrows.append(self.canvas.create_image(origin_x, origin_y,
                                                        image=self.up))
        if policy[1] > 0:  # down
            origin_x, origin_y = 50 + (UNIT * row), 90 + (UNIT * col)
            self.arrows.append(self.canvas.create_image(origin_x, origin_y,
                                                        image=self.down))
        if policy[2] > 0:  # left
            origin_x, origin_y = 10 + (UNIT * row), 50 + (UNIT * col)
            self.arrows.append(self.canvas.create_image(origin_x, origin_y,
                                                        image=self.left))
        if policy[3] > 0:  # right
            origin_x, origin_y = 90 + (UNIT * row), 50 + (UNIT * col)
            self.arrows.append(self.canvas.create_image(origin_x, origin_y,
                                                        image=self.right))

    def draw_from_policy(self, policy_table):
        for i in range(HEIGHT):
            for j in range(WIDTH):
                self.draw_one_arrow(i, j, policy_table[i][j])

    def print_value_table(self, value_table):
        for i in range(WIDTH):
            for j in range(HEIGHT):
                self.text_value(i, j, value_table[i][j])

    def render(self):
        time.sleep(0.1)
        self.canvas.tag_raise(self.rectangle)
        self.update()

    def evaluate_policy(self):
        self.evaluation_count += 1
        for i in self.texts:
            self.canvas.delete(i)
        self.agent.policy_evaluation()
        self.print_value_table(self.agent.value_table)

    def improve_policy(self):
        self.improvement_count += 1
        for i in self.arrows:
            self.canvas.delete(i)
        self.agent.policy_improvement()
        self.draw_from_policy(self.agent.policy_table)

class Env:
    def __init__(self):
        self.transition_probability = TRANSITION_PROB
        self.width = WIDTH
        self.height = HEIGHT
        self.reward = [[0] * WIDTH for _ in range(HEIGHT)]
        self.possible_actions = POSSIBLE_ACTIONS
        self.reward[2][2] = 1  # (2,2) 좌표 동그라미 위치에 보상 1
        self.reward[1][2] = -1  # (1,2) 좌표 세모 위치에 보상 -1
        self.reward[2][1] = -1  # (2,1) 좌표 세모 위치에 보상 -1
        self.all_state = []

        for x in range(WIDTH):
            for y in range(HEIGHT):
                state = [x, y]
                self.all_state.append(state)

    def get_reward(self, state, action):
        next_state = self.state_after_action(state, action)
        return self.reward[next_state[0]][next_state[1]]

    def state_after_action(self, state, action_index):
        action = ACTIONS[action_index]
        return self.check_boundary([state[0] + action[0], state[1] + action[1]])

    @staticmethod
    def check_boundary(state):
        state[0] = (0 if state[0] < 0 else WIDTH - 1
                    if state[0] > WIDTH - 1 else state[0])
        state[1] = (0 if state[1] < 0 else HEIGHT - 1
                    if state[1] > HEIGHT - 1 else state[1])
        return state

    def get_transition_prob(self, state, action):
        return self.transition_probability

    def get_all_states(self):
        return self.all_state

• policy_iteration.py
  • 두가지 모두 수렴하는가 실험 해보기
    • policy evaluation 여러번 후 policy improvement
    • policy evaluation 과 policy improvement 돌아가면서 반복

import random
from environment import GraphicDisplay, Env

class PolicyIteration:
    def __init__(self, env):
        # 환경에 대한 객체 선언
        self.env = env
        # 가치함수를 2차원 리스트로 초기화
        self.value_table = [[0.0] * env.width for _ in range(env.height)]
        # 상 하 좌 우 동일한 확률로 정책 초기화
        self.policy_table = [[[0.25, 0.25, 0.25, 0.25]] * env.width
                                    for _ in range(env.height)]
        # 마침 상태의 설정
        self.policy_table[2][2] = []
        # 감가율
        self.discount_factor = 0.9

    def policy_evaluation(self):

        # 다음 가치함수 초기화
        next_value_table = [[0.00] * self.env.width
                                    for _ in range(self.env.height)]

        # 모든 상태에 대해서 벨만 기대방정식을 계산
        for state in self.env.get_all_states():
            value = 0.0
            # 마침 상태의 가치 함수 = 0
            if state == [2, 2]:
                next_value_table[state[0]][state[1]] = value
                continue

            # 벨만 기대 방정식
            for action in self.env.possible_actions:
                next_state = self.env.state_after_action(state, action)
                reward = self.env.get_reward(state, action)
                next_value = self.get_value(next_state)
                value += (self.get_policy(state)[action] *
                          (reward + self.discount_factor * next_value))

            next_value_table[state[0]][state[1]] = round(value, 2)

        self.value_table = next_value_table

    # 현재 가치 함수에 대해서 탐욕 정책 발전
    def policy_improvement(self):
        next_policy = self.policy_table
        for state in self.env.get_all_states():
            if state == [2, 2]:
                continue
            value = -99999
            max_index = []
            # 반환할 정책 초기화
            result = [0.0, 0.0, 0.0, 0.0]

            # 모든 행동에 대해서 [보상 + (감가율 * 다음 상태 가치함수)] 계산
            for index, action in enumerate(self.env.possible_actions):
                next_state = self.env.state_after_action(state, action)
                reward = self.env.get_reward(state, action)
                next_value = self.get_value(next_state)
                temp = reward + self.discount_factor * next_value

                # 받을 보상이 최대인 행동의 index(최대가 복수라면 모두)를 추출
                if temp == value:
                    max_index.append(index)
                elif temp > value:
                    value = temp
                    max_index.clear()
                    max_index.append(index)

            # 행동의 확률 계산
            prob = 1 / len(max_index)

            for index in max_index:
                result[index] = prob

            next_policy[state[0]][state[1]] = result

        self.policy_table = next_policy

    # 특정 상태에서 정책에 따른 행동을 반환
    def get_action(self, state):
        # 0 ~ 1 사이의 값을 무작위로 추출
        random_pick = random.randrange(100) / 100

        policy = self.get_policy(state)
        policy_sum = 0.0
        # 정책에 담긴 행동 중에 무작위로 한 행동을 추출
        for index, value in enumerate(policy):
            policy_sum += value
            if random_pick < policy_sum:
                return index

    # 상태에 따른 정책 반환
    def get_policy(self, state):
        if state == [2, 2]:
            return 0.0
        return self.policy_table[state[0]][state[1]]

    # 가치 함수의 값을 반환
    def get_value(self, state):
        # 소숫점 둘째 자리까지만 계산
        return round(self.value_table[state[0]][state[1]], 2)

if __name__ == "__main__":
    env = Env()
    policy_iteration = PolicyIteration(env)
    grid_world = GraphicDisplay(policy_iteration)
    grid_world.mainloop()