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variational_koopman_model.py
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variational_koopman_model.py
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import numpy as np
import tensorflow.compat.v1 as tf
import pdb
tf.disable_v2_behavior()
class VariationalKoopman():
def __init__(self, args):
"""Constructs Deep Variational Koopman Model
Args:
args: Various arguments and specifications
"""
# Placeholder for states inputs
self.x = tf.Variable(np.zeros((2*args.batch_size*args.seq_length, args.state_dim), dtype=np.float32), trainable=False, name="state_values")
# Parameters to be set externally
self.learning_rate = tf.Variable(0.0, trainable=False, name="learning_rate")
self.kl_weight = tf.Variable(0.0, trainable=False, name="kl_weight")
# Normalization parameters to be stored
self.shift = tf.Variable(np.zeros(args.state_dim), trainable=False, name="state_shift", dtype=tf.float32)
self.scale = tf.Variable(np.zeros(args.state_dim), trainable=False, name="state_scale", dtype=tf.float32)
# Create the computational graph
self._create_feature_extractor_params(args)
self._create_feature_extractor(args)
self._create_temporal_encoder(args)
self._create_inference_network_params(args)
self._infer_observations(args)
self._create_prior_network(args)
self._propagate_solution(args)
self._create_decoder_params(args)
self._generate_predictions(args)
self._create_optimizer(args)
def _create_feature_extractor_params(self, args):
"""Create parameters to comprise feature extractor
Args:
args: Various arguments and specifications
"""
self.extractor_w = []
self.extractor_b = []
# Loop through elements of feature extractor and define parameters
for i in range(len(args.extractor_size)):
if i == 0:
prev_size = args.state_dim
else:
prev_size = args.extractor_size[i-1]
self.extractor_w.append(tf.get_variable("extractor_w"+str(i), [prev_size, args.extractor_size[i]],
regularizer=tf.keras.regularizers.l2(args.reg_weight)))
self.extractor_b.append(tf.get_variable("extractor_b"+str(i), [args.extractor_size[i]]))
# Last set of weights to map to output
self.extractor_w.append(tf.get_variable("extractor_w_end", [args.extractor_size[-1], args.latent_dim],
regularizer=tf.keras.regularizers.l2(args.reg_weight)))
self.extractor_b.append(tf.get_variable("extractor_b_end", [args.latent_dim]))
def _get_extractor_output(self, args, states):
"""Function to run inputs through extractor
Args:
args: Various arguments and specifications
states: states to feed into extractor [2*batch_size*seq_length, state_dim]
Returns:
Extracted features
"""
extractor_input = states
for i in range(len(args.extractor_size)):
extractor_input = tf.nn.relu(tf.nn.xw_plus_b(extractor_input, self.extractor_w[i], self.extractor_b[i]))
output = tf.nn.xw_plus_b(extractor_input, self.extractor_w[-1], self.extractor_b[-1])
return output
def _create_feature_extractor(self, args):
"""Create feature extractor (maps state -> features, assumes feature same dimensionality as latent states)
Args:
args: Various arguments and specifications
"""
features = self._get_extractor_output(args, self.x)
self.features = tf.reshape(features, [args.batch_size, 2*args.seq_length, args.latent_dim])
def _create_temporal_encoder(self, args):
"""Bidirectional LSTM to generate temporal encoding (also generate distribution over g1 here)
Args:
args: Various arguments and specifications
"""
# Define forward and backward layers
fwd_cell = tf.nn.rnn_cell.LSTMCell(args.rnn_size, initializer=tf.keras.initializers.glorot_normal())
bwd_cell = tf.nn.rnn_cell.LSTMCell(args.rnn_size, initializer=tf.keras.initializers.glorot_normal())
# Construct input
rnn_input = self.features[:, :args.seq_length]
# Get outputs from rnn and concatenate
outputs, _ = tf.nn.bidirectional_dynamic_rnn(fwd_cell, bwd_cell, rnn_input, dtype=tf.float32)
output_fw, output_bw = outputs
output = tf.concat([output_fw[:, -1], output_bw[:, -1]], axis=1)
# Single transformation and affine layer into temporal encoding
hidden = tf.layers.dense(output,
units=args.transform_size,
activation=tf.nn.relu,
kernel_regularizer=tf.keras.regularizers.l2(args.reg_weight))
self.temporal_encoding = tf.layers.dense(hidden,
units=args.latent_dim,
kernel_regularizer=tf.keras.regularizers.l2(args.reg_weight))
# Now construct distribution over g1 through transformation with single hidden layer
g_input = tf.concat([self.temporal_encoding, self.features[:, 0]], axis=1)
hidden = tf.layers.dense(g_input,
units=args.transform_size,
activation=tf.nn.relu,
kernel_regularizer=tf.keras.regularizers.l2(args.reg_weight))
self.g1_dist = tf.layers.dense(hidden,
units=2*args.latent_dim,
kernel_regularizer=tf.keras.regularizers.l2(args.reg_weight))
def _create_inference_network_params(self, args):
"""Create parameters to comprise inference network
Args:
args: Various arguments and specifications
"""
self.inference_w = []
self.inference_b = []
# Loop through elements of inference network and define parameters
for i in range(len(args.inference_size)):
if i == 0:
prev_size = 3*args.latent_dim
else:
prev_size = args.inference_size[i-1]
self.inference_w.append(tf.get_variable("inference_w"+str(i), [prev_size, args.inference_size[i]],
regularizer=tf.keras.regularizers.l2(args.reg_weight)))
self.inference_b.append(tf.get_variable("inference_b"+str(i), [args.inference_size[i]]))
# Last set of weights to map to output
self.inference_w.append(tf.get_variable("inference_w_end", [args.inference_size[-1], 2*args.latent_dim],
regularizer=tf.keras.regularizers.l2(args.reg_weight)))
self.inference_b.append(tf.get_variable("inference_b_end", [2*args.latent_dim]))
def _get_inference_distribution(self, args, features, g_enc):
"""Function to infer distribution over g
Args:
args: Various arguments and specifications
features: Extracted features [batch_size, latent_dim]
g_enc: Temporal encoding of previous g-values [batch_size, latent_dim]
Returns:
Next g-value
"""
inference_input = tf.concat([features, self.temporal_encoding, g_enc], axis=1)
for i in range(len(args.inference_size)):
inference_input = tf.nn.relu(tf.nn.xw_plus_b(inference_input, self.inference_w[i], self.inference_b[i]))
g_dist = tf.nn.xw_plus_b(inference_input, self.inference_w[-1], self.inference_b[-1])
return g_dist
def _gen_sample(self, args, dist_params):
"""Function to generate samples given distribution parameters
Args:
args: Various arguments and specifications
dist_params: Mean and logstd of distribution [batch_size, 2*latent_dim]
Returns:
g: Sampled g-value [batch_size, latent_dim]
"""
g_mean, g_logstd = tf.split(dist_params, [args.latent_dim, args.latent_dim], axis=1)
# Make standard deviation estimates better conditioned, otherwise could be problem early in training
g_std = tf.minimum(tf.exp(g_logstd) + 1e-6, 10.0)
samples = tf.random_normal([args.batch_size, args.latent_dim], seed=args.seed)
g = samples*g_std + g_mean
return g
def _infer_observations(self, args):
"""Step through time and determine g_t distributions and values
Args:
args: Various arguments and specifications
"""
# Sample value for initial observation from distribution
self.g_t = self._gen_sample(args, self.g1_dist)
# Start list of g-distributions and sampled values
self.g_vals = [tf.expand_dims(self.g_t, axis=1)]
self.g_dists = [tf.expand_dims(self.g1_dist, axis=1)]
# Create parameters for transformation to be performed at output of GRU in observation encoder
W_g_out = tf.get_variable("w_g_out", [args.rnn_size, args.transform_size],
regularizer=tf.keras.regularizers.l2(args.reg_weight))
b_g_out = tf.get_variable("b_g_out", [args.transform_size])
W_to_g_enc = tf.get_variable("w_to_g_enc", [args.transform_size, args.latent_dim],
regularizer=tf.keras.regularizers.l2(args.reg_weight))
b_to_g_enc = tf.get_variable("b_to_g_enc", [args.latent_dim])
# Initialize single-layer GRU network to create observation encodings
cell = tf.nn.rnn_cell.GRUCell(args.rnn_size, kernel_initializer=tf.keras.initializers.glorot_normal())
self.rnn_state = cell.zero_state(args.batch_size, tf.float32)
g_t = self.g_t
for t in range(1, args.seq_length):
# Generate temporal encoding
self.rnn_output, self.rnn_state = cell(g_t, self.rnn_state)
hidden = tf.nn.relu(tf.nn.xw_plus_b(self.rnn_output, W_g_out, b_g_out))
g_enc = tf.nn.xw_plus_b(hidden, W_to_g_enc, b_to_g_enc)
# Now get distribution over g_t and sample value
g_dist = self._get_inference_distribution(args, self.features[:, t], g_enc)
g_t = self._gen_sample(args, g_dist)
# Append values to list
self.g_vals.append(tf.expand_dims(g_t, axis=1))
self.g_dists.append(tf.expand_dims(g_dist, axis=1))
# Finally, stack inferred observations
self.g_vals = tf.reshape(tf.stack(self.g_vals, axis=1), [args.batch_size, args.seq_length, args.latent_dim])
self.g_dists = tf.reshape(tf.stack(self.g_dists, axis=1), [args.batch_size*args.seq_length, 2*args.latent_dim])
def _create_prior_network(self, args):
"""Construct network and generate paramaters for conditional prior distributions
Args:
args: Various arguments and specifications
"""
gvals_reshape = tf.reshape(self.g_vals[:, :-1], [args.batch_size*(args.seq_length-1), args.latent_dim])
prior_input = gvals_reshape
# Construct layers of prior network
for ps in args.prior_size:
prior_input = tf.layers.dense(prior_input,
units=ps,
activation=tf.nn.relu,
kernel_regularizer=tf.keras.regularizers.l2(args.reg_weight))
# Final affine transform to dist params
prior_params = tf.layers.dense(prior_input,
units=2*args.latent_dim,
kernel_regularizer=tf.keras.regularizers.l2(args.reg_weight))
prior_params = tf.reshape(prior_params, [args.batch_size, args.seq_length-1, 2*args.latent_dim])
# Construct diagonal unit Gaussian prior params for g1
g1_prior = tf.concat([tf.zeros([args.batch_size, 1, args.latent_dim]), tf.ones([args.batch_size, 1, args.latent_dim])], axis=2)
# Combine and reshape to get full set of prior distribution parameter values
g_prior = tf.concat([g1_prior, prior_params], axis=1)
# Combine and reshape to get full set of prior distribution parameter values
self.g_prior = tf.reshape(g_prior, [args.batch_size*args.seq_length, 2*args.latent_dim])
def _propagate_solution(self, args):
"""Perform least squares to get A- and B-matrices and propagate forward
Args:
args: Various arguments and specifications
"""
# Define X- and Y-matrices
X = self.g_vals[:, :-1]
Y = self.g_vals[:, 1:]
# Solve for A and B using least-squares
self.K = tf.matrix_solve_ls(X, Y, l2_regularizer=args.l2_regularizer)
self.A = self.K[:, :args.latent_dim]
self.B = self.K[:, args.latent_dim:]
# Perform least squares to find A-inverse
self.A_inv = tf.matrix_solve_ls(Y, self.g_vals[:, :-1], l2_regularizer=args.l2_regularizer)
# Get predicted code at final time step
self.z_t = self.g_vals[:, -1]
# Create recursive predictions for z
z_t = tf.expand_dims(self.z_t, axis=1)
z_vals = [z_t]
for t in range(args.seq_length-2, -1, -1):
z_t = tf.matmul(z_t, self.A_inv)
z_vals.append(z_t)
self.z_vals_reshape = tf.stack(z_vals, axis=1)
# Flip order
self.z_vals_reshape = tf.squeeze(tf.reverse(self.z_vals_reshape, [1]))
# Reshape predicted z-values
self.z_vals = tf.reshape(self.z_vals_reshape, [args.batch_size*args.seq_length, args.latent_dim])
def _create_decoder_params(self, args):
"""Create parameters to comprise decoder network
Args:
args: Various arguments and specifications
"""
self.decoder_w = []
self.decoder_b = []
# Loop through elements of decoder network and define parameters
for i in range(len(args.extractor_size)-1, -1, -1):
if i == len(args.extractor_size)-1:
prev_size = args.latent_dim
else:
prev_size = args.extractor_size[i+1]
self.decoder_w.append(tf.get_variable("decoder_w"+str(len(args.extractor_size)-i), [prev_size, args.extractor_size[i]],
regularizer=tf.keras.regularizers.l2(args.reg_weight)))
self.decoder_b.append(tf.get_variable("decoder_b"+str(len(args.extractor_size)-i), [args.extractor_size[i]]))
# Last set of weights to map to output
self.decoder_w.append(tf.get_variable("decoder_w_end", [args.extractor_size[0], args.state_dim],
regularizer=tf.keras.regularizers.l2(args.reg_weight)))
self.decoder_b.append(tf.get_variable("decoder_b_end", [args.state_dim]))
def _get_decoder_output(self, args, encodings):
"""Function to run inputs through decoder
Args:
args: Various arguments and specifications
encodings: Input to decoder [2*batch_size*seq_length, latent_dim]
Returns:
output: Reconstructed states [2*batch_size*seq_length, state_dim]
"""
decoder_input = encodings
for i in range(len(args.extractor_size)):
decoder_input = tf.nn.elu(tf.nn.xw_plus_b(decoder_input, self.decoder_w[i], self.decoder_b[i]))
output = tf.nn.xw_plus_b(decoder_input, self.decoder_w[-1], self.decoder_b[-1])
return output
def _generate_predictions(self, args):
"""Generate predictions for how system will evolve given z1, and A (not used during training)
Args:
args: Various arguments and specifications
"""
self.z1 = tf.squeeze(self.z_vals_reshape[:, -1])
z_t = tf.expand_dims(self.z1, axis=1)
z_pred = [z_t]
for t in range(args.seq_length, 2*args.seq_length):
z_t = tf.matmul(z_t, self.A)
z_pred.append(z_t)
z_pred = tf.stack(z_pred, axis=1)
# Reshape predicted z-values
self.z_pred_reshape = z_pred[:, 1:]
z_pred = tf.reshape(z_pred[:, 1:], [args.batch_size*args.seq_length, args.latent_dim])
self.x_future_norm = tf.reshape(self._get_decoder_output(args, z_pred), [args.batch_size, args.seq_length, args.state_dim])
self.x_future = self.x_future_norm*self.scale + self.shift
def _get_cost(self, args, z_t):
"""Get cost associated with a set of states
Args:
args: Various arguments and specifications
z_t: Latent state at given time step [batch_size, state_dim]
Returns:
Cost [batch_size]
"""
states = self._get_decoder_output(args, z_t)*self.scale + self.shift
if args.domain_name == 'Pendulum-v0':
return tf.square(tf.atan2(states[:, 1], states[:, 0])) + 0.1*tf.square(states[:, 2])
else:
raise NotImplementedError
def _create_optimizer(self, args):
"""Create optimizer to minimize loss
Args:
args: Various arguments and specifications
"""
# First extract mean and std for prior dists, dist over g, and dist over x
g_prior_mean, g_prior_logstd = tf.split(self.g_prior, [args.latent_dim, args.latent_dim], axis=1)
g_prior_std = tf.exp(g_prior_logstd) + 1e-6
g_mean, g_logstd = tf.split(self.g_dists, [args.latent_dim, args.latent_dim], axis=1)
g_std = tf.exp(g_logstd) + 1e-6
# Get predictions for x and reconstructions
self.x_pred_norm = self._get_decoder_output(args, self.z_vals)
self.x_pred = self.x_pred_norm*self.scale + self.shift
# First component of loss: NLL of observed states
x_reshape = tf.reshape(self.x, [args.batch_size, 2*args.seq_length, args.state_dim])
x_pred_reshape = tf.reshape(self.x_pred_norm, [args.batch_size, args.seq_length, args.state_dim])
self.x_pred_init = x_pred_reshape*self.scale + self.shift # needed for ilqr
# Add in predictions for how system will evolve
self.x_pred_reshape = tf.concat([x_pred_reshape, self.x_future_norm], axis=1)
self.x_pred_reshape_unnorm = self.x_pred_reshape*self.scale + self.shift
# Prediction loss
self.pred_loss = tf.reduce_sum(tf.square(x_reshape - self.x_pred_reshape))
# Weight loss at t = T more heavily
self.pred_loss += 20.0*tf.reduce_sum(tf.square(x_reshape[:, args.seq_length-1]\
- x_pred_reshape[:, args.seq_length-1]))
# Define reconstructed state needed for ilqr
self.rec_state = self._get_decoder_output(args, self.z1)*self.scale + self.shift
# Second component of loss: KLD between approximate posterior and prior
g_prior_dist = tf.distributions.Normal(loc=g_prior_mean, scale=g_prior_std)
g_dist = tf.distributions.Normal(loc=g_mean, scale=g_std)
self.kl_loss = tf.reduce_sum(tf.distributions.kl_divergence(g_dist, g_prior_dist))
# Sum with regularization losses to form total cost
self.cost = self.pred_loss + self.kl_weight*self.kl_loss + tf.reduce_sum(tf.losses.get_regularization_losses())
# Perform parameter update
optimizer = tf.train.AdamOptimizer(self.learning_rate)
tvars = [v for v in tf.trainable_variables()]
self.grads, _ = tf.clip_by_global_norm(tf.gradients(self.cost, tvars), args.grad_clip)
self.train = optimizer.apply_gradients(zip(self.grads, tvars))