0、相关系列文章

迷宫_随机实验_边做边学深度强化学习：PyTorch程序设计实践（1）

1、导入所使用的包

# 导入所使用的包
import numpy as np
import matplotlib.pyplot as plt

2、 定义迷宫

fig = plt.figure(figsize=(5, 5))
ax = plt.gca()

# 画出红色的墙壁
plt.plot([1, 1], [0, 1], color='red', linewidth=2)
plt.plot([1, 2], [2, 2], color='red', linewidth=2)
plt.plot([2, 2], [2, 1], color='red', linewidth=2)
plt.plot([2, 3], [1, 1], color='red', linewidth=2)

# 画出表示状态的文字S0-S8
plt.text(0.5, 2.5, 'S0', size=14, ha='center')
plt.text(1.5, 2.5, 'S1', size=14, ha='center')
plt.text(2.5, 2.5, 'S2', size=14, ha='center')
plt.text(0.5, 1.5, 'S3', size=14, ha='center')
plt.text(1.5, 1.5, 'S4', size=14, ha='center')
plt.text(2.5, 1.5, 'S5', size=14, ha='center')
plt.text(0.5, 0.5, 'S6', size=14, ha='center')
plt.text(1.5, 0.5, 'S7', size=14, ha='center')
plt.text(2.5, 0.5, 'S8', size=14, ha='center')
plt.text(0.5, 2.3, 'START', ha='center')
plt.text(2.5, 0.3, 'GOAL', ha='center')

# 设定画图的范围
ax.set_xlim(0, 3)
ax.set_ylim(0, 3)
ax.set_title("Random")
plt.tick_params(axis='both', which='both', bottom='off', top='off',
                labelbottom='off', right='off', left='off', labelleft='off')

# 当前位置S0用绿色圆圈画出
line, = ax.plot([0.5], [2.5], marker="o", color='g', markersize=60)

3、定义迷宫动作

# 设定参数θ的初始值theta_0,用于确定初始方案

# 行为状态0~7，列为用↑、→、↓、←表示的移动方向
theta_0 = np.array([[np.nan, 1, 1, np.nan],  # s0
                    [np.nan, 1, np.nan, 1],  # s1
                    [np.nan, np.nan, 1, 1],  # s2
                    [1, 1, 1, np.nan],  # s3
                    [np.nan, np.nan, 1, 1],  # s4
                    [1, np.nan, np.nan, np.nan],  # s5
                    [1, np.nan, np.nan, np.nan],  # s6
                    [1, 1, np.nan, np.nan],  # s7，s8是目标，无策略
                    ])

效果：

4、策略参数θ转换为行动策略π

# 策略参数θ转换为行动策略π
def simple_convert_into_pi_from_theta(theta):
    
    [m,n] = theta.shape
    pi = np.zeros((m,n))
    
    for i in range(0,m):
        pi[i,:] = theta[i,:] / np.nansum(theta[i,:])
        
    pi = np.nan_to_num(pi)
    
    return pi

5、定义动作和状态获取函数

# 获得动作
def get_action(s, Q, epsilon, pi_0):
    direction = ["up", "right", "down", "left"]
    
    # 确定行动
    if np.random.rand() < epsilon:
        # 以ε概率随机行动
        next_direction = np.random.choice(direction, p=pi_0[s, :])
    else:
        # 采用Q的最大值对应的动作
        next_direction = direction[np.nanargmax(Q[s,:])]

    # 为动作加上索引
    if next_direction == "up":
        action = 0
    elif next_direction == "right":
        action = 1
    elif next_direction == "down":
        action = 2
    elif next_direction == "left":
        action = 3

    return action

def get_s_next(s, a, Q, epsilon, pi_0):
    direction = ["up", "right", "down", "left"]
    
    next_direction = direction[a]

    # 由动作确定下一个状态
    if next_direction == "up":
        s_next = s - 3  # 向上移动时状态的数字减少3
    elif next_direction == "right":
        s_next = s + 1  # 向右移动时状态的数字增加1
    elif next_direction == "down":
        s_next = s + 3  # 向下移动时状态的数字增加3
    elif next_direction == "left":
        s_next = s - 1  # 想做移动时状态的数字减少1

    return s_next

6、定义Sarsa算法

1、（策略梯度法）对策略进行更新，选择能够更快到达目标的策略下所执行的动作，即借鉴成功案例
2、（价值迭代法）从目标反向计算在目标的前一步、前两步的位置（状态）等，一步步引导智能体的行为，即给目标以外的位置也附加价值

# 基于Sarsa更新动作价值函数
def Sarsa(s, a, r, s_next, a_next,Q, eta, gamma):
    if s_next == 8: # 已到达目标
        Q[s,a] = Q[s,a] + eta * (r - Q[s, a])
    else:
        Q[s,a] = Q[s,a] + eta * (r + gamma * Q[s_next, a_next] - Q[s, a])
    return Q

7、定义使智能体移动到目标的函数

# 迷宫内使智能体移动到目标，输出状态和动作序列
def goal_maze_ret_s_a_Q(Q, epsilon, eta, gamma, pi):
    s = 0  # 开始地点
    a = a_next = get_action(s, Q, epsilon, pi) # 初始动作
    s_a_history = [[0,np.nan]]  # 记录智能体移动轨迹的列表

    while (1):  # 循环，直至到达目标
        a = a_next # 更新动作
        
        s_a_history[-1][1] = a  # 将动作放在现在的状态下
        
        s_next = get_s_next(s, a, Q, epsilon, pi) # 有效的下一个状态
        
        s_a_history.append([s_next, np.nan])

        if s_next == 8:  # 到达目标地点则终止
            r = 1 # 到达目标，给予奖励
            a_next = np.nan
            break
        else:
            r = 0
            a_next = get_action(s_next, Q, epsilon, pi)
        
        # 更新价值函数
        Q = Sarsa(s, a, r, s_next, a_next, Q, eta, gamma)
        
        if s_next == 8:
            break
        else:
            s = s_next

    return [s_a_history,Q]

8、初始化

# 设置初始的动作价值函数
[a,b] = theta_0.shape # 将行列数放入a、b
Q = np.random.rand(a,b) * theta_0 # 将theta_0乘到各元素上，使得Q的墙壁方向的值为nan

# 求初始策略π
pi_0 = simple_convert_into_pi_from_theta(theta_0)
pi_0

9、智能体移动到目标

eta = 0.1
gamma = 0.9
epsilon = 0.5
v = np.nanmax(Q, axis=1)
is_continue = True
episode = 1
ypoints = []

while is_continue:
    print("当前回合："+ str(episode))
    
    epsilon = epsilon / 2
    
    [s_a_history,Q] = goal_maze_ret_s_a_Q(Q, epsilon, eta, gamma, pi_0)
    
    new_v = np.nanmax(Q, axis=1)
    print(np.sum(np.abs(new_v - v)))
    
    # 可视化
    ypoints.append(np.sum(np.abs(new_v - v)))
    
    v = new_v

    print("求解迷宫问题所需要的步数是：" + str(len(s_a_history) - 1))
    print(np.sum(np.abs(new_v - v))) # 输出策略的变化的绝对值

    episode = episode + 1
    if episode > 100:
        break

        
# 可视化策略变化的绝对值
#plt.figure(figsize = (20,10))
#plt.plot(ypoints[1:])
# plt.show()
# 可视化状态价值函数Q
print(Q)

10、运行路径可视化

# 参考URL http://louistiao.me/posts/notebooks/embedding-matplotlib-animations-in-jupyter-notebooks/
from matplotlib import animation
from IPython.display import HTML

def init():
    '''初始化背景图像'''
    line.set_data([], [])
    return (line,)

def animate(i):
    '''每一帧的画面内容'''
    state = state_history[i]  # 画出当前的位置
    x = (state % 3) + 0.5  # 状态的x坐标为状态数除以3的余数加0.5
    y = 2.5 - int(state / 3)  # 状态y坐标为2.5减去状态数除以3的商
    line.set_data(x, y)
    return (line,)

#　用初始化函数和绘图函数来生成动画
anim = animation.FuncAnimation(fig, animate, init_func=init, frames=len(
    state_history), interval=200, repeat=False)

anim.save('result/maze_Random.gif',writer='pillow')
HTML(anim.to_jshtml())

11、最终结果

12、代码下载

跳转到下载地址

13、参考资料

[1]边做边学深度强化学习：PyTorch程序设计实践