Problems about L2 Regularization excluding bias

I have implemented a simple network with nn.Module and I encountered the problem about regularization. The optimizer provides ‘weight_decay’, but it includes all the parameters. I want to do L2 excluding bias with which may cause underfitting.
I calculated the regular cost and separated the weight and bias. However when I applied them to torch.optim.Adam using param_groups the loss did not drop.
I wondered if there was any wrong with my code.

class CatNetwork(nn.Module):
    def __init__(self, in_dim, n_hidden_1, out_dim):
        super(CatNetwork, self).__init__()
        self.layer1 = nn.Sequential(
            nn.Linear(in_dim, n_hidden_1),
        self.layer2 = nn.Sequential(
            nn.Linear(n_hidden_1, out_dim),
    def forward(self, x):
        x = self.layer1(x)
        x = self.layer2(x)
        return x

    # Regularization cost
    def regularization(self, model, weight_decay):
        parameter_list = model.state_dict().keys()         # parameter list odict_keys(['layer1.0.weight', 'layer1.0.bias', 'layer2.0.weight', 'layer2.0.bias'])
        loss_reg = 0                                       
        for para in parameter_list:
            loss_reg += torch.sum(torch.square(model.state_dict()[para]))
        return weight_decay * loss_reg

model = CatNetwork(n_input, 16, 1)

# Separate weight and bias
weight_list = []; bias_list = []
for i in range(1, 3):
    para_weight = 'layer' + str(i) + '.0.weight'
    para_bias = 'layer' + str(i) + '.0.bias'
    weight_list += [model.state_dict()[para_weight]]
    bias_list += [model.state_dict()[para_bias]]

# loss function
criterion = nn.BCELoss()

# optimizer
optimizer = torch.optim.Adam([{'params': weight_list, 'weight_decay':1}, {'params': bias_list, 'weight_decay':0}], lr=lr)

for i in range(epoch_number);
    out = model(x)                                             
    loss = criterion(out, y) + model.regularization(model, weight_decay)  # loss + reg_cost
# I'm not sure whether I should add the regularization cost as I don't know how the 'weight_decay' method of optimizer really works.
# But it has no difference to the result whether I keep it or drop it.

You could check, if the parameters are updated using the current approach, as I’m not sure if your approach of using the state_dict to separate the weight and bias parameters would work.
Directly accessing the parameters would work:

weight_list = [p for n, p in model.named_parameters() if 'weight' in n]
bias_list = [p for n, p in model.named_parameters() if 'bias' in n]

Besides that you are using two weight decay approaches via the optimizer as well as your custom regularization so you should also check if you want to remove the regularization usage.

1 Like

Thanks a lot. I was even trying with nn.Parameters() to figure it out but failed.
Your method really works.