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import argparse
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from collections import deque
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import numpy as np
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START, END, WALL, ROAD = 0, 1, 2, 3 # 分别是起点 终点 障碍 道路
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ACTION_DELTAS = ((-1, 0), (1, 0), (0, -1), (0, 1)) # 动作: 0上 1下 2左 3右
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ARROWS = "↑↓←→"
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CHARS = {START: "S", END: "G", WALL: "#", ROAD: "."}
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def generate_maze(rows, cols, seed=0, braid=0.0):
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"""按 seed 随机生成可解迷宫（递归回溯法），行列须为不小于 3 的奇数。
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保证起点 (0,0) 到终点 (rows-1, cols-1) 连通。
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braid: 0~1, 生成后按该概率拆掉剩余内墙形成环路。
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0 = 完美迷宫（唯一通路, 长走廊多）；越大环路越多、可选路径越多。
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"""
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if rows < 3 or cols < 3 or rows % 2 == 0 or cols % 2 == 0:
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raise ValueError("行列必须为不小于 3 的奇数")
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rng = np.random.default_rng(seed)
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maze = np.full((rows, cols), WALL, dtype=np.int8)
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maze[0, 0] = ROAD
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stack = [(0, 0)]
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while stack:
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r, c = stack[-1]
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neighbors = [
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(r + dr, c + dc, r + dr // 2, c + dc // 2)
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for dr, dc in ((-2, 0), (2, 0), (0, -2), (0, 2))
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if 0 <= r + dr < rows and 0 <= c + dc < cols
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and maze[r + dr, c + dc] == WALL
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]
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if neighbors:
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nr, nc, mr, mc = neighbors[int(rng.integers(len(neighbors)))]
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maze[mr, mc] = maze[nr, nc] = ROAD
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stack.append((nr, nc))
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else:
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stack.pop()
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if braid > 0:
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for r in range(1, rows - 1):
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for c in range(1, cols - 1):
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if maze[r, c] == WALL and rng.random() < braid and (
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(maze[r - 1, c] != WALL and maze[r + 1, c] != WALL)
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or (maze[r, c - 1] != WALL and maze[r, c + 1] != WALL)
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):
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maze[r, c] = ROAD # 拆掉两侧都是路的墙, 形成环路
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maze[0, 0], maze[rows - 1, cols - 1] = START, END
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return maze
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class MazeEnv:
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def __init__(self, maze, start_pos=None,
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step_reward=-1.0, wall_penalty=-10.0, goal_reward=100.0, max_steps=200):
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self.maze = np.asarray(maze)
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self.shape = self.maze.shape
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self.n_actions = len(ACTION_DELTAS)
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self.start_pos = self._find(START) if start_pos is None else tuple(start_pos)
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self.goal = self._find(END)
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r, c = self.start_pos
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if not (0 <= r < self.shape[0] and 0 <= c < self.shape[1]) or self.maze[r, c] == WALL:
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raise ValueError(f"非法起点: {self.start_pos}")
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if self.start_pos == self.goal:
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raise ValueError("起点不能与终点重合")
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self.step_reward = step_reward
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self.wall_penalty = wall_penalty
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self.goal_reward = goal_reward
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self.max_steps = max_steps
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self.steps = 0
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self._pos = self.start_pos
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def _find(self, cell):
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hits = np.argwhere(self.maze == cell)
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if len(hits) == 0:
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raise ValueError(f"迷宫中找不到格子类型 {cell}")
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return tuple(int(v) for v in hits[0])
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def reset(self):
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self._pos = self.start_pos
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self.steps = 0
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return self._pos
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def step(self, action):
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if not 0 <= action < self.n_actions:
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raise ValueError(f"非法动作: {action}")
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dr, dc = ACTION_DELTAS[action]
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nr, nc = self._pos[0] + dr, self._pos[1] + dc
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self.steps += 1
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if (
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not (0 <= nr < self.shape[0] and 0 <= nc < self.shape[1])
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or self.maze[nr][nc] == WALL
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):
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# 遇到边界或者撞墙
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return self._pos, self.wall_penalty, False
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self._pos = (nr, nc)
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if self._pos == self.goal:
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# 到达迷宫终点
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return self._pos, self.goal_reward, True
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# 每步 -1, 促使走最短路
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return self._pos, self.step_reward, False
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def shortest_path_len(env):
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"""BFS 求起点到终点的最短步数（不通返回 -1）。"""
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dist = {env.start_pos: 0}
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queue = deque([env.start_pos])
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while queue:
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pos = queue.popleft()
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if pos == env.goal:
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return dist[pos]
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for dr, dc in ACTION_DELTAS:
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nr, nc = pos[0] + dr, pos[1] + dc
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nxt = (nr, nc)
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if (0 <= nr < env.shape[0] and 0 <= nc < env.shape[1]
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and env.maze[nr, nc] != WALL and nxt not in dist):
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dist[nxt] = dist[pos] + 1
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queue.append(nxt)
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return -1
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def train(env, episodes=500, alpha=0.1,
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gamma=0.9, epsilon=1.0, eps_min=0.05, eps_decay=0.99, seed=0, snap_at=()):
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rng = np.random.default_rng(seed)
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Q = np.zeros((*env.shape, env.n_actions)) # Q_{s, a} 这里是 Q[r, c, a]
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rewards, successes, ep_steps, eps_hist = [], [], [], []
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snapshots = [] # [(局数, Q副本), ...]
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snap_at = sorted({int(e) for e in snap_at if 0 < int(e) <= episodes})
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si = 0
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for ep in range(1, episodes + 1):
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pos, total_r, done = env.reset(), 0.0, False
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while env.steps < env.max_steps: # 单局步数上限
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# ε-greedy选动作 explore or exploit
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if rng.random() < epsilon:
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a = int(rng.integers(env.n_actions))
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else:
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a = int(Q[pos].argmax())
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nxt, r, done = env.step(a)
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# Q-Learning 更新；终点是终止状态，目标值仅为 r
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Q[pos][a] += alpha * (r if done else r + gamma * Q[nxt].max() - Q[pos][a])
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pos = nxt
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total_r += r
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if done:
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break
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epsilon = max(eps_min, epsilon * eps_decay) # 逐渐减少探索
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rewards.append(total_r)
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successes.append(done)
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ep_steps.append(env.steps)
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eps_hist.append(epsilon)
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if si < len(snap_at) and ep == snap_at[si]:
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snapshots.append((ep, Q.copy()))
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si += 1
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return Q, rewards, successes, ep_steps, eps_hist, snapshots
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def evaluate(env, Q, episodes=100):
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"""纯贪心策略（无探索）评测, 返回 (成功率, 成功局平均步数)。"""
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wins, steps_list = 0, []
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for _ in range(episodes):
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pos, done = env.reset(), False
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while not done and env.steps < env.max_steps:
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pos, _, done = env.step(int(Q[pos].argmax()))
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if done:
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wins += 1
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steps_list.append(env.steps)
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avg_steps = float(np.mean(steps_list)) if steps_list else float("nan")
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return wins / episodes, avg_steps
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def show_maze(env):
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print(f"迷宫 {env.shape[0]}x{env.shape[1]}（S起点 G终点 #墙）:")
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for r in range(env.shape[0]):
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print("".join(CHARS[env.maze[r][c]] for c in range(env.shape[1])))
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def show_policy(env, Q):
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print("学到的策略（每格最优动作）:")
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for r in range(env.shape[0]):
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row = ""
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for c in range(env.shape[1]):
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if env.maze[r][c] == WALL:
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row += " # "
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elif (r, c) == env.goal:
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row += " G "
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else:
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row += f" {ARROWS[int(Q[r, c].argmax())]} "
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print(row)
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def show_path(env, Q):
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print("\n贪心策略走出的一条路径:")
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pos, path, done = env.reset(), [env.start_pos], False
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while not done and env.steps < env.max_steps:
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pos, _, done = env.step(int(Q[pos].argmax()))
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path.append(pos)
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grid = [[CHARS[env.maze[r][c]] for c in range(env.shape[1])]
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for r in range(env.shape[0])]
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for i, (r, c) in enumerate(path):
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if (r, c) not in (env.start_pos, env.goal):
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grid[r][c] = str(i % 10) # 若重复经过同一格，显示最后一步序号
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print("\n".join(" ".join(row) for row in grid))
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print(f"到达终点: {'是' if done else '否'}，共 {len(path) - 1} 步")
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# ─────────────────── 训练过程可视化（需 matplotlib） ───────────────────
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def _setup_plt():
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import matplotlib
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matplotlib.use("Agg") # 不弹窗，直接保存图片
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import matplotlib.pyplot as plt
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plt.rcParams["font.sans-serif"] = ["Microsoft YaHei", "SimHei"] # 中文字体
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plt.rcParams["axes.unicode_minus"] = False # 正常显示负号
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return plt
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def moving_avg(x, k=20):
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x = np.asarray(x, dtype=float)
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if len(x) < k:
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return np.array([])
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return np.convolve(x, np.ones(k) / k, mode="valid")
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def _plot_ma(ax, x, window, color, label):
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x = np.asarray(x, dtype=float)
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ax.plot(x, color="gray", alpha=0.35, label="逐局值")
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ma = moving_avg(x, window)
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if len(ma):
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ax.plot(np.arange(window - 1, window - 1 + len(ma)), ma,
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color=color, lw=2, label=f"滑动平均(窗口{window})")
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ax.set_xlabel("训练局数 Episode")
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ax.legend()
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def plot_training(env, rewards, successes, ep_steps, eps_hist,
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window=20, out="qlearning_training.png"):
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"""四联图: 回报曲线 / 滑动成功率 / 单局步数 / ε 衰减。"""
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plt = _setup_plt()
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fig, axes = plt.subplots(2, 2, figsize=(12, 8))
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fig.suptitle("Q-Learning 走迷宫训练过程", fontsize=15)
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ax = axes[0][0]
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_plot_ma(ax, rewards, window, "C0", None)
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ax.set_ylabel("单局回报")
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ax.set_title("逐局回报（越高越好）")
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ax = axes[0][1]
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_plot_ma(ax, successes, window, "C1", None)
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ax.set_ylim(-0.05, 1.05)
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ax.set_ylabel("成功率")
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ax.set_title(f"滑动成功率（窗口{window}）")
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ax = axes[1][0]
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_plot_ma(ax, ep_steps, window, "C2", None)
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sp = shortest_path_len(env)
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if sp >= 0:
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ax.axhline(sp, color="red", ls="--", lw=1.5, label=f"最短路 {sp} 步")
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ax.set_ylabel("单局步数")
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ax.set_title("单局步数（降到红线 = 学会最短路）")
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ax.legend()
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ax = axes[1][1]
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ax.plot(eps_hist, color="C3", lw=2)
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ax.set_xlabel("训练局数 Episode")
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ax.set_ylabel("ε")
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ax.set_title(f"探索率 ε 衰减（{eps_hist[0]:.2f} → {eps_hist[-1]:.2f}）")
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fig.tight_layout(rect=[0, 0, 1, 0.96])
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fig.savefig(out, dpi=150)
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print(f"\n图片已保存: {out}")
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def plot_snapshots(env, snapshots, Q_final, out="qlearning_snapshots.png"):
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"""V(s)=max Q 热力图随训练的变化：观察价值从终点 G 逐步回传到起点。"""
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plt = _setup_plt()
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panels = snapshots + [("最终", Q_final)]
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vmin = min(float(q.max(axis=2).min()) for _, q in panels)
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vmax = max(float(q.max(axis=2).max()) for _, q in panels)
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if vmin == vmax:
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vmin, vmax = vmin - 1, vmax + 1
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n = len(panels)
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fig, axes = plt.subplots(1, n, figsize=(3 * n, 3.4))
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axes = np.atleast_1d(axes)
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masked_wall = env.maze == WALL
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for ax, (tag, q) in zip(axes, panels):
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V = np.ma.masked_where(masked_wall, q.max(axis=2))
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im = ax.imshow(V, cmap="viridis", vmin=vmin, vmax=vmax, origin="upper")
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fs = 8 if max(env.shape) <= 7 else 5
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for r in range(env.shape[0]):
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for c in range(env.shape[1]):
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if masked_wall[r, c]:
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ax.text(c, r, "█", ha="center", va="center",
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color="black", fontsize=fs)
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else:
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ax.text(c, r, f"{V[r, c]:.0f}", ha="center", va="center",
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color="white", fontsize=fs)
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ax.set_xticks([])
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ax.set_yticks([])
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ax.set_title(f"第 {tag} 局后" if tag != "最终" else "训练结束")
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fig.suptitle("状态价值 V(s)=max Q 的学习过程（价值从 G 逐步回传）", fontsize=13)
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fig.colorbar(im, ax=axes, fraction=0.03, pad=0.02)
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fig.savefig(out, dpi=150, bbox_inches="tight")
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print(f"图片已保存: {out}")
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if __name__ == "__main__":
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parser = argparse.ArgumentParser(description="Q-Learning 走迷宫（numpy 表格型实现）")
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parser.add_argument("--seed", type=int, default=0, help="迷宫生成随机种子")
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parser.add_argument("--rows", type=int, default=9, help="迷宫行数（奇数）")
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parser.add_argument("--cols", type=int, default=9, help="迷宫列数（奇数）")
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parser.add_argument("--episodes", type=int, default=500, help="训练局数")
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parser.add_argument("--braid", type=float, default=0.0,
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help="拆墙成环概率 0~1, 越大岔路/环路越多")
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parser.add_argument("--plot", action="store_true",
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help="生成 qlearning_training.png 与 qlearning_snapshots.png")
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args = parser.parse_args()
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env = MazeEnv(generate_maze(args.rows, args.cols, seed=args.seed, braid=args.braid))
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show_maze(env)
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snap_at = (1, 10, 50, 200, 500) if args.plot else ()
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Q, rewards, successes, ep_steps, eps_hist, snapshots = train(
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env, episodes=args.episodes, snap_at=snap_at)
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show_policy(env, Q)
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show_path(env, Q)
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rate, avg_steps = evaluate(env, Q)
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print(f"\n前50局平均回报: {np.mean(rewards[:50]):6.1f} "
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f"后50局平均回报: {np.mean(rewards[-50:]):6.1f}")
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print(f"后50局成功率: {np.mean(successes[-50:]):.0%}")
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print(f"评测(100局贪心): 成功率 {rate:.0%}，平均 {avg_steps:.1f} 步到达终点")
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if args.plot:
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plot_training(env, rewards, successes, ep_steps, eps_hist)
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plot_snapshots(env, snapshots, Q)
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