根据该文件第四章第三节的双闭环上下级对抗MAB算法，在内环中加入上下文信息，加入专家多样性一部分专家在内环学习上下文信息，一部分专家模仿学习，一部分专家自学习，请给出上下文信息应该如何学习，并给出详细的算法

### 上下文信息学习及其在双闭环上下级对抗MAB算法中的集成

#### 1. 上下文信息学习
上下文信息是指在特定时间和地点可用于指导决策的相关信息。在水声通信网络中，上下文信息可能包括信道条件、干扰强度、中继节点的位置等。为了在双闭环上下级对抗MAB算法中有效利用上下文信息，我们需要设计一种机制，使得内环中的专家能够学习和利用这些信息。

##### 1.1 上下文信息的收集
上下文信息可以从以下几个方面收集：
- **信道状态信息 (Channel State Information, CSI)**：实时测量当前信道的传输质量。
- **干扰信息**：检测周围的干扰源及其强度。
- **中继节点位置**：记录中继节点的地理位置，以便优化路径选择。
- **历史数据**：存储过去的通信数据，用于预测未来的信道状态。

##### 1.2 上下文信息的预处理
收集到的上下文信息需要进行预处理，以便于后续的机器学习算法使用。预处理步骤包括：
- **特征提取**：从原始数据中提取有用的特征，例如信道增益、信噪比等。
- **归一化**：将特征值归一化到相同的范围内，通常为 [0, 1]。
- **降维**：使用主成分分析 (PCA) 或其他降维技术减少特征的维度，提高计算效率。

#### 2. 内环专家学习上下文信息
在内环中，专家不仅学习推理信息，还学习上下文信息。我们将专家分为三类：
- **上下文信息学习专家**：专门学习上下文信息，并将其融入决策过程。
- **模仿学习专家**：模仿上级（决策者）的实际决策。
- **自学习专家**：根据自身生成的建议向量进行学习。

##### 2.1 上下文信息学习专家
上下文信息学习专家的任务是利用上下文信息来优化策略建议。具体步骤如下：

1. **初始化**：初始化上下文信息学习专家的参数。

   context_experts = []
   for i in range(num_context_experts):
       expert = {
           'context_weights': np.random.rand(context_dim),
           'strategy_weights': np.ones(K)
       }
       context_experts.append(expert)

2. **上下文信息的融合**：将上下文信息与策略建议结合起来。

   def fuse_context_and_strategy(context, expert):
       context_value = np.dot(context, expert['context_weights'])
       fused_weights = expert['strategy_weights'] * context_value
       return normalized(fused_weights)

3. **更新上下文信息学习专家的权重**：

   def update_context_expert(context, expert, actual_utility, inferred_utilities):
       # 更新上下文权重
       context_gradient = compute_context_gradient(context, actual_utility, inferred_utilities)
       expert['context_weights'] += learning_rate * context_gradient
       # 更新策略权重
       inferred_max_utility = max(inferred_utilities)
       best_strategy = inferred_utilities.index(inferred_max_utility)
       expert['strategy_weights'][best_strategy] *= np.exp(learning_rate * inferred_max_utility)
       expert['strategy_weights'] /= sum(expert['strategy_weights'])

##### 2.2 模仿学习专家
模仿学习专家的任务是模仿上级的实际决策。具体步骤如下：

1. **初始化**：初始化模仿学习专家的参数。

   imitation_experts = []
   for i in range(num_imitation_experts):
       expert = {
           'strategy_weights': np.ones(K)
       }
       imitation_experts.append(expert)

2. **更新模仿学习专家的权重**：

   def update_imitation_expert(expert, actual_utility, selected_strategy):
       expert['strategy_weights'][selected_strategy] *= np.exp(learning_rate * actual_utility)
       expert['strategy_weights'] /= sum(expert['strategy_weights'])

##### 2.3 自学习专家
自学习专家的任务是根据自身生成的建议向量进行学习。具体步骤如下：

1. **初始化**：初始化自学习专家的参数。

   self_learning_experts = []
   for i in range(num_self_learning_experts):
       expert = {
           'strategy_weights': np.ones(K)
       }
       self_learning_experts.append(expert)

2. **更新自学习专家的权重**：

   def update_self_learning_expert(expert, virtual_utility, selected_strategy):
       expert['strategy_weights'][selected_strategy] *= np.exp(learning_rate * virtual_utility)
       expert['strategy_weights'] /= sum(expert['strategy_weights'])

#### 3. 完整的双闭环上下级对抗MAB算法
以下是完整的双闭环上下级对抗MAB算法，包括上下文信息学习专家、模仿学习专家和自学习专家。

import numpy as np

def initialize_experts(num_context_experts, num_imitation_experts, num_self_learning_experts, context_dim, K):
    context_experts = []
    for _ in range(num_context_experts):
        expert = {
            'context_weights': np.random.rand(context_dim),
            'strategy_weights': np.ones(K)
        }
        context_experts.append(expert)

    imitation_experts = []
    for _ in range(num_imitation_experts):
        expert = {
            'strategy_weights': np.ones(K)
        }
        imitation_experts.append(expert)

    self_learning_experts = []
    for _ in range(num_self_learning_experts):
        expert = {
            'strategy_weights': np.ones(K)
        }
        self_learning_experts.append(expert)

    return context_experts, imitation_experts, self_learning_experts

def fuse_context_and_strategy(context, expert):
    context_value = np.dot(context, expert['context_weights'])
    fused_weights = expert['strategy_weights'] * context_value
    return normalized(fused_weights)

def normalized(weights):
    return weights / sum(weights)

def compute_context_gradient(context, actual_utility, inferred_utilities):
    inferred_max_utility = max(inferred_utilities)
    gradient = (actual_utility - inferred_max_utility) * context
    return gradient

def update_context_expert(context, expert, actual_utility, inferred_utilities):
    context_gradient = compute_context_gradient(context, actual_utility, inferred_utilities)
    expert['context_weights'] += learning_rate * context_gradient
    inferred_max_utility = max(inferred_utilities)
    best_strategy = inferred_utilities.index(inferred_max_utility)
    expert['strategy_weights'][best_strategy] *= np.exp(learning_rate * inferred_max_utility)
    expert['strategy_weights'] /= sum(expert['strategy_weights'])

def update_imitation_expert(expert, actual_utility, selected_strategy):
    expert['strategy_weights'][selected_strategy] *= np.exp(learning_rate * actual_utility)
    expert['strategy_weights'] /= sum(expert['strategy_weights'])

def update_self_learning_expert(expert, virtual_utility, selected_strategy):
    expert['strategy_weights'][selected_strategy] *= np.exp(learning_rate * virtual_utility)
    expert['strategy_weights'] /= sum(expert['strategy_weights'])

def double_closed_loop_mab_with_edl(T, context_dim, K, num_context_experts, num_imitation_experts, num_self_learning_experts, learning_rate):
    context_experts, imitation_experts, self_learning_experts = initialize_experts(
        num_context_experts, num_imitation_experts, num_self_learning_experts, context_dim, K
    )

    for t in range(T):
        # 获取当前上下文信息
        context = get_current_context()

        # 外环：上级学习实际信息
        combined_weights = np.zeros(K)
        for expert in context_experts + imitation_experts + self_learning_experts:
            combined_weights += expert['strategy_weights']
        combined_weights /= len(combined_weights)

        selected_strategy = np.random.choice(K, p=combined_weights)
        actual_utility = execute_strategy(selected_strategy)

        # 内环：专家学习推理信息和上下文信息
        inferred_utilities = infer_utilities(selected_strategy, actual_utility)

        for expert in context_experts:
            fused_weights = fuse_context_and_strategy(context, expert)
            selected_strategy = np.random.choice(K, p=fused_weights)
            virtual_utility = inferred_utilities[selected_strategy]
            update_context_expert(context, expert, actual_utility, inferred_utilities)

        for expert in imitation_experts:
            update_imitation_expert(expert, actual_utility, selected_strategy)

        for expert in self_learning_experts:
            selected_strategy = np.random.choice(K, p=expert['strategy_weights'])
            virtual_utility = inferred_utilities[selected_strategy]
            update_self_learning_expert(expert, virtual_utility, selected_strategy)

    return context_experts, imitation_experts, self_learning_experts

# 示例调用
T = 1000
context_dim = 5
K = 10
num_context_experts = 5
num_imitation_experts = 5
num_self_learning_experts = 5
learning_rate = 0.1

context_experts, imitation_experts, self_learning_experts = double_closed_loop_mab_with_edl(
    T, context_dim, K, num_context_experts, num_imitation_experts, num_self_learning_experts, learning_rate
)

### 总结
通过在双闭环上下级对抗MAB算法中引入上下文信息学习专家，我们可以更有效地利用环境中的相关信息，提高决策的准确性。同时，模仿学习专家和自学习专家的结合确保了算法的多样性和鲁棒性，从而在复杂多变的水声通信环境中取得了更好的性能。