PyTorch参数不更新：深入理解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 shares 非负
    final_shares = final_shares.clamp(0.)
    # 计算市值 (market value)
    mv = torch.multiply(final_shares, prices)
    # 计算权重 (weights)
    w = torch.div(mv, torch.sum(mv))
    # print(w) # 调试时可以打印权重变化
    return loss_func(w, target_weight)

def main():
    position_count = 16
    cash_buffer = .001
    # 初始参数值，范围在1到50之间
    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)

    # 定义目标权重向量
    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)

    loss_func = torch.nn.MSELoss() # 使用均方误差损失

    eta = 0.01 # 学习率
    optimizer = torch.optim.SGD([x_param], lr=eta) # 使用SGD优化器

    print(f"初始x_param均值: {x_param.mean().item():.4f}")
    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()
        # 打印梯度信息，辅助调试
        # if epoch % 1000 == 0:
        #     print(f"Epoch {epoch}, Loss: {loss_incurred.item():.6f}, Avg Grad: {x_param.grad.abs().mean().item():.8f}")

        optimizer.step()

    print(f"训练后x_param均值: {x_param.mean().item():.4f}")
    # 最终评估 (使用 .data 访问，不参与梯度计算)
    final_loss = optimize(final_shares=x_param.data, target_weight=target_weights_vec,
                          prices=prices, loss_func=loss_func)
    print(f"最终损失: {final_loss.item():.6f}")

if __name__ == '__main__':
    main()

# ... (代码省略，与原代码相同)
def main():
    # ... (代码省略)
    eta = 100.0 # 将学习率提高到100
    optimizer = torch.optim.SGD([x_param], lr=eta)

    print(f"初始x_param均值: {x_param.mean().item():.4f}")
    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()
        # 打印梯度信息，辅助调试
        if epoch % 1000 == 0:
            print(f"Epoch {epoch}, Loss: {loss_incurred.item():.6f}, Avg Grad: {x_param.grad.abs().mean().item():.8f}")
            # 打印参数变化，观察更新幅度
            # if epoch > 0:
            #     print(f"Avg param change: {(x_param - prev_x_param).abs().mean().item():.8f}")
            # prev_x_param = x_param.clone().detach() # 保存当前参数值

        optimizer.step()

    print(f"训练后x_param均值: {x_param.mean().item():.4f}")
    final_loss = optimize(final_shares=x_param.data, target_weight=target_weights_vec,
                          prices=prices, loss_func=loss_func)
    print(f"最终损失: {final_loss.item():.6f}")
# ... (代码省略)