PyTorch参数更新不明显？深度解析学习率与梯度尺度的影响

import torch
import numpy as np

np.random.seed(10)

def optimize(final_shares: torch.Tensor, target_weight, prices, loss_func=None):
    # 确保份额非负
    final_shares = final_shares.clamp(0.)
    # 计算市值
    mv = torch.multiply(final_shares, prices)
    # 计算权重
    w = torch.div(mv, torch.sum(mv))
    # print(w) # 调试时可以打印权重
    return loss_func(w, target_weight)

def main():
    position_count = 16
    cash_buffer = .001
    starting_shares = torch.tensor(np.random.uniform(low=1, high=50, size=position_count), dtype=torch.float64)
    prices = torch.tensor(np.random.uniform(low=1, high=100, size=position_count), dtype=torch.float64)
    prices[-1] = 1.

    # 定义可学习参数
    x_param = torch.nn.Parameter(starting_shares, requires_grad=True)

    # 定义目标权重
    target_weights = ((1 - cash_buffer) / (position_count - 1))
    target_weights_vec = [target_weights] * (position_count - 1)
    target_weights_vec.append(cash_buffer)
    target_weights_vec = torch.tensor(target_weights_vec, dtype=torch.float64)

    # 定义损失函数
    loss_func = torch.nn.MSELoss()

    # 初始化优化器，学习率 eta 设置为 0.01
    eta = 0.01 
    optimizer = torch.optim.SGD([x_param], lr=eta)

    print(f"初始参数 x_param: {x_param.data[:5]}") # 打印前5个初始参数
    initial_loss = optimize(final_shares=x_param, target_weight=target_weights_vec,
                            prices=prices, loss_func=loss_func)
    print(f"初始损失: {initial_loss.item():.6f}")

    for epoch in range(10000):
        optimizer.zero_grad()
        loss_incurred = optimize(final_shares=x_param, target_weight=target_weights_vec,
                                 prices=prices, loss_func=loss_func)
        loss_incurred.backward()

        # 可以在此处打印梯度信息进行调试
        # if epoch % 1000 == 0:
        #     print(f"Epoch {epoch}, Loss: {loss_incurred.item():.6f}, Avg Grad: {x_param.grad.abs().mean().item():.8f}")
        #     print(f"x_param (before step): {x_param.data[:5]}")

        optimizer.step()

        # if epoch % 1000 == 0:
        #     print(f"x_param (after step): {x_param.data[:5]}")

    final_loss = optimize(final_shares=x_param.data, target_weight=target_weights_vec,
                          prices=prices, loss_func=loss_func)
    print(f"最终参数 x_param: {x_param.data[:5]}") # 打印前5个最终参数
    print(f"最终损失: {final_loss.item():.6f}")

if __name__ == '__main__':
    main()

# ... (代码省略，与上文相同的部分) ...

    # 初始化优化器，学习率 eta 调整为 100
    eta = 100 
    optimizer = torch.optim.SGD([x_param], lr=eta)

    print(f"初始参数 x_param: {x_param.data[:5]}")
    initial_loss = optimize(final_shares=x_param, target_weight=target_weights_vec,
                            prices=prices, loss_func=loss_func)
    print(f"初始损失: {initial_loss.item():.6f}")

    for epoch in range(10000):
        optimizer.zero_grad()
        loss_incurred = optimize(final_shares=x_param, target_weight=target_weights_vec,
                                 prices=prices, loss_func=loss_func)
        loss_incurred.backward()
        optimizer.step()

        # 打印中间结果以便观察
        if epoch % 1000 == 0 or epoch == 9999:
            print(f"Epoch {epoch}, Loss: {loss_incurred.item():.6f}, Avg Grad: {x_param.grad.abs().mean().item():.8f}")
            print(f"x_param (after step, first 5): {x_param.data[:5]}")


    final_loss = optimize(final_shares=x_param.data, target_weight=target_weights_vec,
                          prices=prices, loss_func=loss_func)
    print(f"最终参数 x_param: {x_param.data[:5]}")
    print(f"最终损失: {final_loss.item():.6f}")

# ... (main 函数和 if __name__ == '__main__': 保持不变) ...