如何将 gpflow GPR 的批量训练编译成 tf.function？

Question

我需要使用自定义损失函数在每个时期的多个批次中训练 GPR 模型。我想使用 GPflow 来执行此操作，并且我想使用 tf.function 来编译我的训练以提高效率。但是，每次提供新数据时都必须重新实例化 gpflow.GPR，因此每次都必须重新跟踪 tf.function。这会使代码变慢而不是变快。

这是初始设置：

import numpy as np
from itertools import islice
import tensorflow as tf
import tensorflow_probability as tfp
tfb = tfp.bijectors
from sklearn.model_selection import train_test_split
import gpflow
from gpflow.kernels import SquaredExponential
import time

data_size = 1000
train_fract = 0.8
batch_size = 250
n_epochs = 3
iterations_per_epoch = int(train_fract * data_size/batch_size)
tf.random.set_seed(3)

# Generate dummy data
x = np.arange(data_size)
y = np.arange(data_size) + np.random.rand(data_size)

# Slice into train and validate sets
x_train, x_validate, y_train, y_validate = train_test_split(x, y, random_state = 1, test_size = 1-train_fract )

# Convert data into tensorflow constants
x_train = tf.constant(x_train[:, np.newaxis], dtype=np.float64)
x_validate = tf.constant(x_validate[:, np.newaxis], dtype=np.float64)
y_train = tf.constant(y_train[:, np.newaxis], dtype=np.float64)
y_validate = tf.constant(y_validate[:, np.newaxis], dtype=np.float64)

# Batch data
batched_dataset = (
    tf.data.Dataset.from_tensor_slices((x_train, y_train)) 
    .shuffle(buffer_size=len(x_train), seed=1) 
    .repeat(count=None)
    .batch(batch_size)
)    

# Create kernel
constrain_positive = tfb.Shift(np.finfo(np.float64).tiny)(tfb.Exp())
amplitude = tfp.util.TransformedVariable(initial_value=1, bijector=constrain_positive, dtype=np.float64, name="amplitude")
len_scale = tfp.util.TransformedVariable(initial_value=10, bijector=constrain_positive, dtype=np.float64, name="len_scale")
kernel = SquaredExponential(variance=amplitude, lengthscales=len_scale, name="squared_exponential_kernel")
obs_noise = tfp.util.TransformedVariable(initial_value=1e-3, bijector=constrain_positive, dtype=np.float64, name="observation_noise")


# Define custom loss function
@tf.function(autograph=False, experimental_compile=False)
def my_custom_loss(y_predict, y_true):
    return tf.math.reduce_mean(tf.math.squared_difference(y_predict, y_true))

#optimizer = tf.keras.optimizers.Adam(learning_rate=0.1)
optimizer = tf.keras.optimizers.SGD(learning_rate=0.1)

这就是我在没有 tf.function 的情况下训练的方式：

gpr_model_j_i = gpflow.models.GPR(data=(x_train, y_train), kernel=kernel, noise_variance=obs_noise)

# Start training loop
for j in range(n_epochs):
    for i, (x_train_j_i, y_train_j_i) in enumerate(islice(batched_dataset, iterations_per_epoch)):
        with tf.GradientTape() as tape:
            gpr_model_j_i = gpflow.models.GPR(data=(x_train_j_i, y_train_j_i), kernel=kernel, noise_variance=gpr_model_j_i.likelihood.variance)
            y_predict_j_i = gpr_model_j_i.predict_f(x_validate)[0]
            loss_j_i = my_custom_loss(y_predict_j_i, y_validate)

        grads_j_i = tape.gradient(loss_j_i, gpr_model_j_i.trainable_variables)
        optimizer.apply_gradients(zip(grads_j_i, gpr_model_j_i.trainable_variables))

这就是我用 tf.function:

训练的方式

@tf.function(autograph=False, experimental_compile=False)
def tf_function_attempt_3(model): #, optimizer):
    with tf.GradientTape() as tape:
        y_predict_j_i = model.predict_f(x_validate)[0]
        loss_j_i = my_custom_loss(y_predict_j_i, y_validate)

    grads_j_i = tape.gradient(loss_j_i, model.trainable_variables)
    optimizer.apply_gradients(zip(grads_j_i, model.trainable_variables))
    print("TRACING...", end="")



for j in range(n_epochs):
    for i, (x_train_j_i, y_train_j_i) in enumerate(islice(batched_dataset, iterations_per_epoch)):
        gpr_model_j_i = gpflow.models.GPR(data=(x_train_j_i, y_train_j_i), kernel=kernel, noise_variance=gpr_model_j_i.likelihood.variance)
        tf_function_attempt_3(gpr_model_j_i)#, optimizer)

tf.function 对每个批次进行回溯，比正常训练慢得多。

有没有办法在使用自定义损失函数和 GPflow 的同时使用 tf.function 加速我的 GPR 模型的批量训练？如果没有，我愿意接受关于替代方法的建议。

Answer 1

您不必每次都重新实例化 GPR。您可以构造 tf.Variable 个形状不受约束的支架，然后 .assign 给它们：

import gpflow
import numpy as np
import tensorflow as tf

input_dim = 1
initial_x, initial_y = np.zeros((0, input_dim)), np.zeros((0, 1))  # or your first batch
x_var = tf.Variable(initial_x, shape=(None, input_dim), dtype=tf.float64)
y_var = tf.Variable(initial_y, shape=(None,1), dtype=tf.float64)
# in principle you could also set shape=(None, None)...

m = gpflow.models.GPR((x_var, y_var), gpflow.kernels.SquaredExponential())
loss = m.training_loss_closure()  # compile=True default wraps in tf.function()

N1 = 3
x1, y1 = np.random.randn(N1, input_dim), np.random.randn(N1, 1)
m.data[0].assign(x1)
m.data[1].assign(y1)
loss()  # traces the first time

N2 = 7
x2, y2 = np.random.randn(N2, input_dim), np.random.randn(N2, 1)
m.data[0].assign(x2)
m.data[1].assign(y2)
loss()  # does not trace again

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