What optimizers does PyTorch provide and how do you configure them?

import torch, torch.nn as nn, torch.optim as optim

model = nn.Linear(128, 10)

# ── SGD with momentum and weight decay
opt_sgd = optim.SGD(
    model.parameters(),
    lr=0.1,
    momentum=0.9,       # Nesterov-style acceleration
    weight_decay=1e-4,  # L2 regularisation
    nesterov=True,
)

# ── Adam
opt_adam = optim.Adam(
    model.parameters(),
    lr=1e-3,
    betas=(0.9, 0.999), # (β1, β2) — momentum terms
    eps=1e-8,
    weight_decay=0,     # Adam + L2 is suboptimal — use AdamW!
)

# ── AdamW (preferred for transformers)
opt_adamw = optim.AdamW(
    model.parameters(),
    lr=1e-3,
    weight_decay=0.01,  # decoupled from gradient update
)

# ── Per-layer learning rates
opt_layerwise = optim.Adam([
    {"params": model.weight, "lr": 1e-4},  # slower for weight
    {"params": model.bias,   "lr": 1e-3},  # faster for bias
])

# ── Standard training step
opt = optim.AdamW(model.parameters(), lr=1e-3)
for x, y in [(torch.randn(32,128), torch.randint(0,10,(32,)))]:
    opt.zero_grad()               # 1. clear old gradients
    loss = nn.CrossEntropyLoss()(model(x), y)  # 2. forward
    loss.backward()              # 3. backward
    opt.step()                   # 4. update parameters