我正在尝试使用随机梯度下降作为求解器在Python中实现岭回归的解决方案。我的SGD代码如下：

def fit(self, X, Y):
    # Convert to data frame in case X is numpy matrix
    X = pd.DataFrame(X)

    # Define a function to calculate the error given a weight vector beta and a training example xi, yi

    # Prepend a column of 1s to the data for the intercept
    X.insert(0, 'intercept', np.array([1.0]*X.shape[0]))

    # Find dimensions of train
    m, d = X.shape

    # Initialize weights to random
    beta = self.initializeRandomWeights(d)
    beta_prev = None

    epochs = 0
    prev_error = None
    while (beta_prev is None or epochs < self.nb_epochs):
        print("## Epoch: " + str(epochs))
        indices = range(0, m)
        shuffle(indices)
        for i in indices:   # Pick a training example from a randomly shuffled set
            beta_prev = beta
            xi = X.iloc[i]
            errori = sum(beta*xi) - Y[i]    # Error[i] = sum(beta*x) - y = error of ith training example
            gradient_vector = xi*errori + self.l*beta_prev
            beta = beta_prev - self.alpha*gradient_vector
        epochs += 1

我测试的数据没有标准化，我的实现总是以所有权重为无穷大结束，即使我将权重向量初始化为低值。只有当我将学习率alpha设置为一个非常小的值~ 1 e-8时，算法才能得到有效的权重向量值。
我的理解是，规范化/缩放输入功能只有助于减少收敛时间。但是，如果特征没有归一化，则该算法不应该不能作为整体收敛。我的理解是否正确？