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