试设计一个 BP 改进算法，能通过动态调整学习率显著提升收敛速度. 编程实现该算法，并选择两个 UCI 数据集与标准 BP 算法进行实验 比较

设计一个改进版的BP（Back Propagation）算法通常会考虑动态学习率调整策略，例如使用自适应学习率如Adagrad、RMSprop或Adam等。其中，Adaptive Moment Estimation (Adam) 是一种常见的优化器，它结合了动量（momentum）和指数加权移动平均（exponential moving average）来调整学习率。下面是一个简化的Adam算法示意图：

class AdaptiveLearningRateBP:
    def __init__(self, learning_rate=0.001, beta1=0.9, beta2=0.999, epsilon=1e-8):
        self.learning_rate = learning_rate
        self.m = {}  # First moment estimates
        self.v = {}  # Second moment estimates
        self.beta1, self.beta2 = beta1, beta2
        self.epsilon = epsilon

    def update(self, gradient, weights):
        for layer in weights:
            self.m[layer] = self.beta1 * self.m[layer] + (1 - self.beta1) * gradient[layer]
            self.v[layer] = self.beta2 * self.v[layer] + (1 - self.beta2) * gradient[layer]**2
            m_corrected = self.m[layer] / (1 - self.beta1**(t+1))
            v_corrected = self.v[layer] / (1 - self.beta2**(t+1))
            weights[layer] -= self.learning_rate * m_corrected / (sqrt(v_corrected) + self.epsilon)

# 使用这个改进版BP进行训练
def train(data1, data2, model, epochs, dataset_name):
    for i in range(epochs):
        for batch in DataLoader(data1):  # 或者数据2
            ...  # 步骤类似标准BP，但是更新权重使用AdaptiveLearningRateBP实例
    print(f"完成{dataset_name}的数据集训练")

# 实验对比
data1 = load_data("uci_dataset1.csv")
data2 = load_data("uci_dataset2.csv")
standard_bp_model = StandardBP()
adaptive_bp_model = AdaptiveLearningRateBP()

train(data1, data2, standard_bp_model, epochs, "数据集1")
train(data1, data2, adaptive_bp_model, epochs, "数据集2")

results = compare_models(standard_bp_model, adaptive_bp_model)