我有一个自定义神经网络，我正在对数据进行训练，并试图将网络的输出值限制在两个任意常数之间：[lower_bound,upper_bound]. 在损失函数中编码这个约束是否有任何最佳实践？
下面我写了一个最小的工作示例，我在生成的数据上构建和训练神经网络。[lower_bound,upper_bound] = [-0.5,0.75]此外，我在被优化的损失函数中设置了输出应该介于两者之间的任意约束。但是我尝试使用一种相对粗略的方法来查找预测值超出范围的所有实例，然后简单地将这些项的损失函数设为一个较大的值（如果预测值在给定范围内，则为零）：
lower_bound = -0.5 #a guessed a priori lower bound on the output
upper_bound = 0.75 #a guessed a priori upper bound on the output
cond_v1_1 = tf.greater(self.v1_pred[:,0], upper_bound*tf.ones(tf.shape(self.v1_pred[:,0])))
cond_v1_2 = tf.greater(-1.0*self.v1_pred[:,0], lower_bound*tf.ones(tf.shape(self.v1_pred[:,0])))
self.red_v1 = tf.where(cond_v1_1, 100000.0*tf.ones(tf.shape(self.v1_pred[:,0])), 0.0*tf.zeros(tf.shape(self.v1_pred[:,0])))
self.red_v1 = tf.where(cond_v1_2, 100000.0*tf.ones(tf.shape(self.v1_pred[:,0])), self.red_v1)
self.loss_cond = tf.reduce_sum(1.0*tf.square(self.red_v1))
但是在训练神经网络时，有什么方法或损失函数可以更好地编码这个约束吗？也许优化器更容易处理和/或修改我的代码本身的更平滑的损失函数？任何关于在以下代码中惩罚/训练神经网络的最佳实践的评论和进一步的想法给定输出的界限将不胜感激。
import numpy as np
import tensorflow as tf
end_it = 1000 #number of iterations
frac_train = 1.0 #randomly sampled fraction of data to create training set
frac_sample_train = 0.01 #randomly sampled fraction of data from training set to train in batches
layers = [2, 20, 20, 20, 1]
#Generate training data
len_data = 10000
x_x = np.array([np.linspace(0.,1.,len_data)])
x_y = np.array([np.linspace(0.,1.,len_data)])
y_true = np.array([np.linspace(-0.2,0.2,len_data)])
N_train = int(frac_train*len_data)
idx = np.random.choice(len_data, N_train, replace=False)
x_train = x_x.T[idx,:]
y_train = x_y.T[idx,:]
v1_train = y_true.T[idx,:]
sample_batch_size = int(frac_sample_train*N_train)
np.random.seed(1234)
tf.set_random_seed(1234)
import logging
logging.getLogger('tensorflow').setLevel(logging.ERROR)
tf.logging.set_verbosity(tf.logging.ERROR)
class NeuralNet:
def __init__(self, x, y, v1, layers):
X = np.concatenate([x, y], 1)
self.lb = X.min(0)
self.ub = X.max(0)
self.X = X
self.x = X[:,0:1]
self.y = X[:,1:2]
self.v1 = v1
self.layers = layers
self.weights_v1, self.biases_v1 = self.initialize_NN(layers)
self.sess = tf.Session(config=tf.ConfigProto(allow_soft_placement=False,
log_device_placement=False))
self.x_tf = tf.placeholder(tf.float32, shape=[None, self.x.shape[1]])
self.y_tf = tf.placeholder(tf.float32, shape=[None, self.y.shape[1]])
self.v1_tf = tf.placeholder(tf.float32, shape=[None, self.v1.shape[1]])
self.v1_pred = self.net(self.x_tf, self.y_tf)
lower_bound = -0.5 #a guessed a priori lower bound on the output
upper_bound = 0.75 #a guessed a priori upper bound on the output
cond_v1_1 = tf.greater(self.v1_pred[:,0], upper_bound*tf.ones(tf.shape(self.v1_pred[:,0])))
cond_v1_2 = tf.greater(-1.0*self.v1_pred[:,0], lower_bound*tf.ones(tf.shape(self.v1_pred[:,0])))
self.red_v1 = tf.where(cond_v1_1, 100000.0*tf.ones(tf.shape(self.v1_pred[:,0])), 0.0*tf.zeros(tf.shape(self.v1_pred[:,0])))
self.red_v1 = tf.where(cond_v1_2, 100000.0*tf.ones(tf.shape(self.v1_pred[:,0])), self.red_v1)
self.loss_cond = tf.reduce_sum(1.0*tf.square(self.red_v1))
self.loss_data = tf.reduce_mean(tf.square(self.v1_tf - self.v1_pred))
self.loss = self.loss_cond + self.loss_data
self.optimizer = tf.contrib.opt.ScipyOptimizerInterface(self.loss,
var_list=self.weights_v1+self.biases_v1,
method = 'L-BFGS-B',
options = {'maxiter': 50,
'maxfun': 50000,
'maxcor': 50,
'maxls': 50,
'ftol' : 1.0 * np.finfo(float).eps})
self.optimizer_Adam = tf.train.AdamOptimizer()
self.train_op_Adam_v1 = self.optimizer_Adam.minimize(self.loss, var_list=self.weights_v1+self.biases_v1)
init = tf.global_variables_initializer()
self.sess.run(init)
def initialize_NN(self, layers):
weights = []
biases = []
num_layers = len(layers)
for l in range(0,num_layers-1):
W = self.xavier_init(size=[layers[l], layers[l+1]])
b = tf.Variable(tf.zeros([1,layers[l+1]], dtype=tf.float32), dtype=tf.float32)
weights.append(W)
biases.append(b)
return weights, biases
def xavier_init(self, size):
in_dim = size[0]
out_dim = size[1]
xavier_stddev = np.sqrt(2/(in_dim + out_dim))
return tf.Variable(tf.truncated_normal([in_dim, out_dim], stddev=xavier_stddev), dtype=tf.float32)
def neural_net(self, X, weights, biases):
num_layers = len(weights) + 1
H = 2.0*(X - self.lb)/(self.ub - self.lb) - 1.0
for l in range(0,num_layers-2):
W = weights[l]
b = biases[l]
H = tf.tanh(tf.add(tf.matmul(H, W), b))
W = weights[-1]
b = biases[-1]
Y = tf.add(tf.matmul(H, W), b)
return Y
def net(self, x, y):
v1_out = self.neural_net(tf.concat([x,y], 1), self.weights_v1, self.biases_v1)
v1 = v1_out[:,0:1]
return v1
def callback(self, loss):
global Nfeval
print(str(Nfeval)+' - Loss in loop: %.3e' % (loss))
Nfeval += 1
def fetch_minibatch(self, x_in, y_in, v1_in, N_train_sample):
idx_batch = np.random.choice(len(x_in), N_train_sample, replace=False)
x_batch = x_in[idx_batch,:]
y_batch = y_in[idx_batch,:]
v1_batch = v1_in[idx_batch,:]
return x_batch, y_batch, v1_batch
def train(self, end_it):
it = 0
while it < end_it:
x_res_batch, y_res_batch, v1_res_batch = self.fetch_minibatch(self.x, self.y, self.v1, sample_batch_size) # Fetch residual mini-batch
tf_dict = {self.x_tf: x_res_batch, self.y_tf: y_res_batch,
self.v1_tf: v1_res_batch}
self.sess.run(self.train_op_Adam_v1, tf_dict)
self.optimizer.minimize(self.sess,
feed_dict = tf_dict,
fetches = [self.loss],
loss_callback = self.callback)
it = it + 1
def predict(self, x_star, y_star):
tf_dict = {self.x_tf: x_star, self.y_tf: y_star}
v1_star = self.sess.run(self.v1_pred, tf_dict)
return v1_star
model = NeuralNet(x_train, y_train, v1_train, layers)
Nfeval = 1
model.train(end_it)