Keras implementation of AdamW, SGDW, NadamW, and Warm Restarts, based on paper Decoupled Weight Decay Regularization - plus Learning Rate Multipliers

• Weight decay fix: decoupling L2 penalty from gradient. Why use?
  • Weight decay via L2 penalty yields worse generalization, due to decay not working properly
  • Weight decay via L2 penalty leads to a hyperparameter coupling with lr, complicating search
• Warm restarts (WR): cosine annealing learning rate schedule. Why use?
  • Better generalization and faster convergence was shown by authors for various data and model sizes
• LR multipliers: per-layer learning rate multipliers. Why use?
  • Pretraining; if adding new layers to pretrained layers, using a global lr is prone to overfitting

AdamW(.., weight_decays=weight_decays)
Two methods to set weight_decays = {<weight matrix name>:<weight decay value>,}:

# 1. Use keras_adamw.utils.py
Dense(.., kernel_regularizer=l2(0)) # set weight decays in layers as usual, but to ZERO
wd_dict = get_weight_decays(model)
ordered_values = [1e-4, 1e-3, ..] # print(wd_dict) to see returned matrix names, note their order
weight_decays = fill_dict_in_order(wd_dict, ordered_values)

# 2. Fill manually
model.layers[1].kernel.name # get name of kernel weight matrix of layer indexed 1
weight_decays.update({'conv1d_0/kernel:0':1e-4}) # example

AdamW(.., use_cosine_annealing=True, total_iterations=200) - refer to Use guidelines below

AdamW(.., lr_multipliers=lr_multipliers) - to get, {<layer name>:<multiplier value>,}:

1. (a) Name every layer to be modified (recommended), e.g. Dense(.., name='dense_1') - OR
   (b) Get every layer name, note which to modify: [print(idx,layer.name) for idx,layer in enumerate(model.layers)]
2. (a) lr_multipliers = {'conv1d_0':0.1} # target layer by full name - OR
   (b) lr_multipliers = {'conv1d':0.1} # target all layers w/ name substring 'conv1d'

from keras.layers import Input, Dense, LSTM
from keras.models import Model
from keras.regularizers import l2
from keras_adamw.optimizers import AdamW
from keras_adamw.utils import get_weight_decays, fill_dict_in_order
import numpy as np 

ipt   = Input(shape=(120,4))
x     = LSTM(60, activation='relu',    recurrent_regularizer=l2(0), name='lstm_1')(ipt)
out   = Dense(1, activation='sigmoid', kernel_regularizer   =l2(0), name='output')(x)
model = Model(ipt,out)

wd_dict        = get_weight_decays(model)                # {'lstm_1/recurrent:0':0,   'output/kernel:0':0}
weight_decays  = fill_dict_in_order(wd_dict,[4e-4,1e-4]) # {'lstm_1/recurrent:0':4e-4,'output/kernel:0':1e-4}
lr_multipliers = {'lstm_1':0.5}

optimizer = AdamW(lr=1e-4, weight_decays=weight_decays, lr_multipliers=lr_multipliers,
                  use_cosine_annealing=True, total_iterations=24)
model.compile(optimizer, loss='binary_crossentropy')

for epoch in range(3):
    for iteration in range(24):
        x = np.random.rand(10,120,4) # dummy data
        y = np.random.randint(0,2,(10,1)) # dummy labels
        loss = model.train_on_batch(x,y)
        print("Iter {} loss: {}".format(iteration+1, "%.3f"%loss))
    print("EPOCH {} COMPLETED".format(epoch+1))
    K.set_value(model.optimizer.t_cur, 0) # WARM RESTART: reset cosine annealing argument

(Full example + plot code: example.py)

• Set L2 penalty to ZERO if regularizing a weight via weight_decays - else the purpose of the 'fix' is largely defeated, and weights will be over-decayed --My recommendation
• lambda = lambda_norm * sqrt(batch_size/total_iterations) --> can be changed; the intent is to scale λ to decouple it from other hyperparams - including (but not limited to), train duration & batch size. --Authors (Appendix, pg.1) (A-1)

• Set t_cur = 0 to restart schedule multiplier (see Example). Can be done at compilation or during training. Non-0 is also valid, and will start eta_t at another point on the cosine curve. Details in A-2,3
• Set total_iterations to the # of expected weight updates for the given restart --Authors (A-1,2)
• eta_min=0, eta_max=1 are tunable hyperparameters; e.g., an exponential schedule can be used for eta_max. If unsure, the defaults were shown to work well in the paper. --Authors
• Save/load optimizer state; WR relies on using the optimizer's update history for effective transitions --Authors (A-2)

# 'total_iterations' general purpose example
def get_total_iterations(restart_idx, num_epochs, iterations_per_epoch):
    return num_epochs[restart_idx] * iterations_per_epoch[restart_idx]
get_total_iterations(0, num_epochs=[1,3,5,8], iterations_per_epoch=[240,120,60,30])

• Best used for pretrained layers - e.g. greedy layer-wise pretraining, or pretraining a feature extractor to a classifier network. Can be a better alternative to freezing layer weights. --My recommendation
• It's often best not to pretrain layers fully (till convergence, or even best obtainable validation score) - as it may inhibit their ability to adapt to newly-added layers. --My recommendation
• The more the layers are pretrained, the lower their fraction of new layers' lr should be. --My recommendation