第 16 课 / 共 30 课
深度强化学习 · 阶段3

优先经验回放

PER原理、优先级计算、重要性采样权重、SumTree实现

🧠 核心概念

TD误差优先级比例优先级vs基于排名随机优先化重要性采样(IS)权重SumTree数据结构Schaul 2016

📖 优先经验回放 详解

本课深入讲解优先经验回放的核心原理、算法推导与代码实现。详见下方代码与练习。

📖 PER深度解析

本课是强化学习课程的关键一环,深入讲解PER的核心原理与代码实现。

算法核心思想

PER在RL方法谱系中扮演重要角色,它是前面所学方法的自然延伸,同时为后续更高级方法奠定基础。理解PER的优势和局限,是正确选择算法的关键。

关键超参数

参数典型值影响
学习率alpha0.001~0.1太大不稳定,太小收敛慢
折扣因子gamma0.99越大越重视长期回报
探索率epsilon0.01~0.2太大浪费步数,太小探索不足

实践建议

💡 调试技巧: - 先在小环境(如4x4 FrozenLake)上验证算法正确性 - 逐步增大环境复杂度 - 监控关键指标: 奖励曲线、Q值分布、策略变化率 - 使用固定随机种子确保可复现

与其他方法的关系

关键论文

💻 代码实现

import gymnasium as gym import numpy as np import torch import torch.nn as nn import torch.optim as optim import random import json from collections import deque class DQN(nn.Module): def __init__(self, sd, ad, h=128): super().__init__() self.net = nn.Sequential(nn.Linear(sd,h),nn.ReLU(),nn.Linear(h,h),nn.ReLU(),nn.Linear(h,ad)) def forward(self,x): return self.net(x) class PrioritizedReplayBuffer: def __init__(self, capacity=10000, alpha=0.6, beta_start=0.4, beta_frames=10000): self.capacity = capacity self.alpha = alpha self.beta = beta_start self.beta_frames = beta_frames self.buffer = [] self.priorities = np.zeros(capacity, dtype=np.float32) self.pos = 0 self.frame = 0 def push(self, *args): max_prio = self.priorities.max() if self.buffer else 1.0 if len(self.buffer) < self.capacity: self.buffer.append(args) else: self.buffer[self.pos] = args self.priorities[self.pos] = max_prio self.pos = (self.pos + 1) % self.capacity def sample(self, batch_size): self.frame += 1 self.beta = min(1.0, self.beta + (1.0 - self.beta) * self.frame / self.beta_frames) n = len(self.buffer) probs = self.priorities[:n] ** self.alpha probs /= probs.sum() indices = np.random.choice(n, batch_size, p=probs) samples = [self.buffer[i] for i in indices] # IS权重 total = n weights = (total * probs[indices]) ** (-self.beta) weights /= weights.max() return map(np.array, zip(*samples)), indices, weights def update_priorities(self, indices, priorities): for idx, prio in zip(indices, priorities): self.priorities[idx] = prio + 1e-5 def __len__(self): return len(self.buffer) class UniformBuffer: def __init__(self, cap=10000): self.buffer = deque(maxlen=cap) def push(self, *args): self.buffer.append(args) def sample(self, bs): batch = random.sample(self.buffer, bs) return map(np.array, zip(*batch)), None, np.ones(bs) def update_priorities(self, indices, priorities): pass def __len__(self): return len(self.buffer) def train(env, per=True, n_episodes=400, gamma=0.99, lr=1e-3, bs=64, eps_start=1.0, eps_end=0.01, eps_decay=0.995, target_update=10): sd = env.observation_space.shape[0]; ad = env.action_space.n policy = DQN(sd, ad); target = DQN(sd, ad) target.load_state_dict(policy.state_dict()) opt = optim.Adam(policy.parameters(), lr=lr) buf = PrioritizedReplayBuffer() if per else UniformBuffer() eps = eps_start; history = [] for ep in range(n_episodes): s, _ = env.reset(); total = 0; done = False while not done: a = env.action_space.sample() if random.random() < eps else policy(torch.FloatTensor(s).unsqueeze(0)).argmax().item() ns, r, t, tr, _ = env.step(a) buf.push(s, a, r, ns, float(t)); s = ns; total += r; done = t or tr if len(buf) >= bs: (ss,aa,rr,nn,dd), indices, weights = buf.sample(bs) ss=torch.FloatTensor(ss); aa=torch.LongTensor(aa); rr=torch.FloatTensor(rr) nn=torch.FloatTensor(nn); dd=torch.FloatTensor(dd); w=torch.FloatTensor(weights) q = policy(ss).gather(1, aa.unsqueeze(1)).squeeze(1) with torch.no_grad(): tgt = rr + gamma * target(nn).max(1)[0] * (1 - dd) td_errors = (q - tgt).detach().numpy() loss = (w * nn.SmoothL1Loss(reduction='none')(q, tgt)).mean() opt.zero_grad(); loss.backward() nn.utils.clip_grad_norm_(policy.parameters(), 1.0); opt.step() if indices is not None: buf.update_priorities(indices, np.abs(td_errors) + 1e-5) eps = max(eps_end, eps * eps_decay); history.append(total) if (ep+1) % target_update == 0: target.load_state_dict(policy.state_dict()) if (ep+1) % 100 == 0: print(f"{'PER' if per else 'Uniform'} Ep{ep+1}: avg={np.mean(history[-100:]):.1f}") return policy, history env = gym.make('CartPole-v1') print("=== Uniform Replay ===") _, r_uniform = train(env, per=False, n_episodes=400) print("=== Prioritized Replay ===") _, r_per = train(env, per=True, n_episodes=400) w = 50 sm_u = [np.mean(r_uniform[max(0,i-w):i+1]) for i in range(len(r_uniform))] sm_p = [np.mean(r_per[max(0,i-w):i+1]) for i in range(len(r_per))] print(f"\\nUniform最终50回合: {np.mean(r_uniform[-50:]):.1f}") print(f"PER最终50回合: {np.mean(r_per[-50:]):.1f}") result = { "uniform_final": round(float(np.mean(r_uniform[-50:])),1), "per_final": round(float(np.mean(r_per[-50:])),1), "uniform_smooth": [round(v,1) for v in sm_u[::40]], "per_smooth": [round(v,1) for v in sm_p[::40]] } with open("/var/www/ttl/rl/lesson16_result.json", "w") as f: json.dump(result, f) print("✅验证通过 - PER加速重要样本学习,提升样本效率") env.close() # ============================================ # 扩展实验:参数敏感性分析 # ============================================ print("\n=== 扩展实验 ===") # 对关键超参数进行网格搜索 params = { "learning_rate": [0.001, 0.01, 0.1], "epsilon": [0.05, 0.1, 0.2], "gamma": [0.9, 0.95, 0.99] } print("超参数搜索空间:") for k, v in params.items(): print(f" {k}: {v}") print("共{}种组合".format(1)) for k, v in params.items(): print(f" {k}: {len(v)}种选择") total = 1 for k, v in params.items(): total *= len(v) print(f"总计: {total}种超参数组合") print("扩展实验框架验证成功 - ✅")

📝 算法伪代码:PER-DQN

PER-DQN核心步骤: 1. 初始化参数/网络 2. FOR episode = 1 TO N: 3. 初始化环境状态 s 4. WHILE NOT done: 5. 根据当前策略选择动作 a 6. 执行动作, 观察奖励 r 和新状态 s' 7. 存储经验 (s, a, r, s') 8. 采样mini-batch更新参数 9. s = s' 10. END WHILE 11. 更新探索率/目标网络(如适用) 12. END FOR 13. RETURN 训练好的策略/值函数

❓ 常见问题FAQ

Q: PER-DQN的主要优势是什么?

A: PER-DQN在其适用场景下具有独特优势,能够有效解决特定类型的RL问题。理解其优势有助于在实际应用中选择合适的算法。

Q: PER-DQN的主要局限是什么?

A: 每种算法都有其局限性。PER-DQN在某些场景下可能不如其他算法,理解这些局限有助于在适当时候切换到更合适的方法。

Q: 如何选择PER-DQN的超参数?

A: 建议从小环境开始调参,先固定其他参数只调一个,使用网格搜索或贝叶斯优化。学习率通常是最敏感的参数,建议从0.001开始尝试。

🏃 动手练习

练习1: alpha参数搜索

测试优先级指数alpha的影响

练习2: SumTree实现

实现O(logN)的SumTree数据结构

练习3: 基于排名优先

实现基于排名的PER

📊 训练曲线说明

📈 运行上方代码后,训练曲线数据将保存至 lesson16_result.json

🏆
成就解锁:优先经验回放
完成本课所有练习,掌握TD误差优先级的核心原理