# Optimizers

The Optimizer base class provides methods to compute gradients for a loss and apply gradients to variables. A collection of subclasses implement classic optimization algorithms such as GradientDescent and Adagrad.

You never instantiate the Optimizer class itself, but instead instantiate one of the subclasses.

### class tf.train.Optimizer

Base class for optimizers.

This class defines the API to add Ops to train a model. You never use this class directly, but instead instantiate one of its subclasses such as GradientDescentOptimizer, AdagradOptimizer, or MomentumOptimizer.

### Usage

# Create an optimizer with the desired parameters.
# Add Ops to the graph to minimize a cost by updating a list of variables.
# "cost" is a Tensor, and the list of variables contains tf.Variable
# objects.
opt_op = opt.minimize(cost, var_list=<list of variables>)


In the training program you will just have to run the returned Op.

# Execute opt_op to do one step of training:
opt_op.run()


### Processing gradients before applying them.

Calling minimize() takes care of both computing the gradients and applying them to the variables. If you want to process the gradients before applying them you can instead use the optimizer in three steps:

1. Compute the gradients with compute_gradients().
2. Process the gradients as you wish.
3. Apply the processed gradients with apply_gradients().

Example:

# Create an optimizer.

# Compute the gradients for a list of variables.

# grads_and_vars is a list of tuples (gradient, variable).  Do whatever you
# need to the 'gradient' part, for example cap them, etc.
capped_grads_and_vars = [(MyCapper(gv[0]), gv[1]) for gv in grads_and_vars]

# Ask the optimizer to apply the capped gradients.


#### tf.train.Optimizer.__init__(use_locking, name) {:#Optimizer.init}

Create a new Optimizer.

This must be called by the constructors of subclasses.

##### Args:
• use_locking: Bool. If True apply use locks to prevent concurrent updates to variables.
• name: A non-empty string. The name to use for accumulators created for the optimizer.
##### Raises:
• ValueError: If name is malformed.

#### tf.train.Optimizer.minimize(loss, global_step=None, var_list=None, gate_gradients=1, aggregation_method=None, colocate_gradients_with_ops=False, name=None, grad_loss=None)

Add operations to minimize loss by updating var_list.

This method simply combines calls compute_gradients() and apply_gradients(). If you want to process the gradient before applying them call compute_gradients() and apply_gradients() explicitly instead of using this function.

##### Args:
• loss: A Tensor containing the value to minimize.
• global_step: Optional Variable to increment by one after the variables have been updated.
• var_list: Optional list of Variable objects to update to minimize loss. Defaults to the list of variables collected in the graph under the key GraphKeys.TRAINABLE_VARIABLES.
• gate_gradients: How to gate the computation of gradients. Can be GATE_NONE, GATE_OP, or GATE_GRAPH.
• aggregation_method: Specifies the method used to combine gradient terms. Valid values are defined in the class AggregationMethod.
• colocate_gradients_with_ops: If True, try colocating gradients with the corresponding op.
• name: Optional name for the returned operation.
• grad_loss: Optional. A Tensor holding the gradient computed for loss.
##### Returns:

An Operation that updates the variables in var_list. If global_step was not None, that operation also increments global_step.

##### Raises:
• ValueError: If some of the variables are not Variable objects.

#### tf.train.Optimizer.compute_gradients(loss, var_list=None, gate_gradients=1, aggregation_method=None, colocate_gradients_with_ops=False, grad_loss=None)

Compute gradients of loss for the variables in var_list.

This is the first part of minimize(). It returns a list of (gradient, variable) pairs where "gradient" is the gradient for "variable". Note that "gradient" can be a Tensor, an IndexedSlices, or None if there is no gradient for the given variable.

##### Args:
• loss: A Tensor containing the value to minimize.
• var_list: Optional list of tf.Variable to update to minimize loss. Defaults to the list of variables collected in the graph under the key GraphKey.TRAINABLE_VARIABLES.
• gate_gradients: How to gate the computation of gradients. Can be GATE_NONE, GATE_OP, or GATE_GRAPH.
• aggregation_method: Specifies the method used to combine gradient terms. Valid values are defined in the class AggregationMethod.
• colocate_gradients_with_ops: If True, try colocating gradients with the corresponding op.
• grad_loss: Optional. A Tensor holding the gradient computed for loss.
##### Returns:

A list of (gradient, variable) pairs. Variable is always present, but gradient can be None.

##### Raises:
• TypeError: If var_list contains anything else than Variable objects.
• ValueError: If some arguments are invalid.

#### tf.train.Optimizer.apply_gradients(grads_and_vars, global_step=None, name=None)

Apply gradients to variables.

This is the second part of minimize(). It returns an Operation that applies gradients.

##### Args:
• grads_and_vars: List of (gradient, variable) pairs as returned by compute_gradients().
• global_step: Optional Variable to increment by one after the variables have been updated.
• name: Optional name for the returned operation. Default to the name passed to the Optimizer constructor.
##### Returns:

An Operation that applies the specified gradients. If global_step was not None, that operation also increments global_step.

##### Raises:
• TypeError: If grads_and_vars is malformed.
• ValueError: If none of the variables have gradients.

Both minimize() and compute_gradients() accept a gate_gradients argument that controls the degree of parallelism during the application of the gradients.

The possible values are: GATE_NONE, GATE_OP, and GATE_GRAPH.

GATE_NONE: Compute and apply gradients in parallel. This provides the maximum parallelism in execution, at the cost of some non-reproducibility in the results. For example the two gradients of matmul depend on the input values: With GATE_NONE one of the gradients could be applied to one of the inputs before the other gradient is computed resulting in non-reproducible results.

GATE_OP: For each Op, make sure all gradients are computed before they are used. This prevents race conditions for Ops that generate gradients for multiple inputs where the gradients depend on the inputs.

GATE_GRAPH: Make sure all gradients for all variables are computed before any one of them is used. This provides the least parallelism but can be useful if you want to process all gradients before applying any of them.

### Slots

Some optimizer subclasses, such as MomentumOptimizer and AdagradOptimizer allocate and manage additional variables associated with the variables to train. These are called Slots. Slots have names and you can ask the optimizer for the names of the slots that it uses. Once you have a slot name you can ask the optimizer for the variable it created to hold the slot value.

This can be useful if you want to log debug a training algorithm, report stats about the slots, etc.

#### tf.train.Optimizer.get_slot_names()

Return a list of the names of slots created by the Optimizer.

See get_slot().

##### Returns:

A list of strings.

#### tf.train.Optimizer.get_slot(var, name)

Return a slot named name created for var by the Optimizer.

Some Optimizer subclasses use additional variables. For example Momentum and Adagrad use variables to accumulate updates. This method gives access to these Variable objects if for some reason you need them.

Use get_slot_names() to get the list of slot names created by the Optimizer.

##### Args:
• var: A variable passed to minimize() or apply_gradients().
• name: A string.
##### Returns:

The Variable for the slot if it was created, None otherwise.

### class tf.train.GradientDescentOptimizer

Optimizer that implements the gradient descent algorithm.

#### tf.train.GradientDescentOptimizer.__init__(learning_rate, use_locking=False, name='GradientDescent') {:#GradientDescentOptimizer.init}

Construct a new gradient descent optimizer.

##### Args:
• learning_rate: A Tensor or a floating point value. The learning rate to use.
• use_locking: If True use locks for update operations.
• name: Optional name prefix for the operations created when applying gradients. Defaults to "GradientDescent".

### class tf.train.AdadeltaOptimizer

See M. D. Zeiler (pdf)

#### tf.train.AdadeltaOptimizer.__init__(learning_rate=0.001, rho=0.95, epsilon=1e-08, use_locking=False, name='Adadelta') {:#AdadeltaOptimizer.init}

##### Args:
• learning_rate: A Tensor or a floating point value. The learning rate.
• rho: A Tensor or a floating point value. The decay rate.
• epsilon: A Tensor or a floating point value. A constant epsilon used to better conditioning the grad update.
• use_locking: If True use locks for update operations.
• name: Optional name prefix for the operations created when applying gradients. Defaults to "Adadelta".

### class tf.train.AdagradOptimizer

See this paper.

#### tf.train.AdagradOptimizer.__init__(learning_rate, initial_accumulator_value=0.1, use_locking=False, name='Adagrad') {:#AdagradOptimizer.init}

##### Args:
• learning_rate: A Tensor or a floating point value. The learning rate.
• initial_accumulator_value: A floating point value. Starting value for the accumulators, must be positive.
• use_locking: If True use locks for update operations.
• name: Optional name prefix for the operations created when applying gradients. Defaults to "Adagrad".
##### Raises:
• ValueError: If the initial_accumulator_value is invalid.

### class tf.train.AdagradDAOptimizer

Adagrad Dual Averaging algorithm for sparse linear models.

See this paper.

This optimizer takes care of regularization of unseen features in a mini batch by updating them when they are seen with a closed form update rule that is equivalent to having updated them on every mini-batch.

AdagradDA is typically used when there is a need for large sparsity in the trained model. This optimizer only guarantees sparsity for linear models. Be careful when using AdagradDA for deep networks as it will require careful initialization of the gradient accumulators for it to train.

#### tf.train.AdagradDAOptimizer.__init__(learning_rate, global_step, initial_gradient_squared_accumulator_value=0.1, l1_regularization_strength=0.0, l2_regularization_strength=0.0, use_locking=False, name='AdagradDA') {:#AdagradDAOptimizer.init}

##### Args:
• learning_rate: A Tensor or a floating point value. The learning rate.
• global_step: A Tensor containing the current training step number.
• initial_gradient_squared_accumulator_value: A floating point value. Starting value for the accumulators, must be positive.
• l1_regularization_strength: A float value, must be greater than or equal to zero.
• l2_regularization_strength: A float value, must be greater than or equal to zero.
• use_locking: If True use locks for update operations.
• name: Optional name prefix for the operations created when applying gradients. Defaults to "AdagradDA".
##### Raises:
• ValueError: If the initial_gradient_squared_accumulator_value is invalid.

### class tf.train.MomentumOptimizer

Optimizer that implements the Momentum algorithm.

#### tf.train.MomentumOptimizer.__init__(learning_rate, momentum, use_locking=False, name='Momentum', use_nesterov=False) {:#MomentumOptimizer.init}

Construct a new Momentum optimizer.

##### Args:
• learning_rate: A Tensor or a floating point value. The learning rate.
• momentum: A Tensor or a floating point value. The momentum.
• use_locking: If True use locks for update operations.
• name: Optional name prefix for the operations created when applying gradients. Defaults to "Momentum".

### class tf.train.AdamOptimizer

Optimizer that implements the Adam algorithm.

See Kingma et. al., 2014 (pdf).

#### tf.train.AdamOptimizer.__init__(learning_rate=0.001, beta1=0.9, beta2=0.999, epsilon=1e-08, use_locking=False, name='Adam') {:#AdamOptimizer.init}

Construct a new Adam optimizer.

Initialization:

m_0 <- 0 (Initialize initial 1st moment vector)
v_0 <- 0 (Initialize initial 2nd moment vector)
t <- 0 (Initialize timestep)


The update rule for variable with gradient g uses an optimization described at the end of section2 of the paper:

t <- t + 1
lr_t <- learning_rate * sqrt(1 - beta2^t) / (1 - beta1^t)

m_t <- beta1 * m_{t-1} + (1 - beta1) * g
v_t <- beta2 * v_{t-1} + (1 - beta2) * g * g
variable <- variable - lr_t * m_t / (sqrt(v_t) + epsilon)


The default value of 1e-8 for epsilon might not be a good default in general. For example, when training an Inception network on ImageNet a current good choice is 1.0 or 0.1.

Note that in dense implement of this algorithm, m_t, v_t and variable will update even if g is zero, but in sparse implement, m_t, v_t and variable will not update in iterations g is zero.

##### Args:
• learning_rate: A Tensor or a floating point value. The learning rate.
• beta1: A float value or a constant float tensor. The exponential decay rate for the 1st moment estimates.
• beta2: A float value or a constant float tensor. The exponential decay rate for the 2nd moment estimates.
• epsilon: A small constant for numerical stability.
• use_locking: If True use locks for update operations.
• name: Optional name for the operations created when applying gradients. Defaults to "Adam".

### class tf.train.FtrlOptimizer

Optimizer that implements the FTRL algorithm.

See this paper.

#### tf.train.FtrlOptimizer.__init__(learning_rate, learning_rate_power=-0.5, initial_accumulator_value=0.1, l1_regularization_strength=0.0, l2_regularization_strength=0.0, use_locking=False, name='Ftrl') {:#FtrlOptimizer.init}

Construct a new FTRL optimizer.

##### Args:
• learning_rate: A float value or a constant float Tensor.
• learning_rate_power: A float value, must be less or equal to zero.
• initial_accumulator_value: The starting value for accumulators. Only positive values are allowed.
• l1_regularization_strength: A float value, must be greater than or equal to zero.
• l2_regularization_strength: A float value, must be greater than or equal to zero.
• use_locking: If True use locks for update operations.
• name: Optional name prefix for the operations created when applying gradients. Defaults to "Ftrl".
##### Raises:
• ValueError: If one of the arguments is invalid.

### class tf.train.ProximalGradientDescentOptimizer

Optimizer that implements the proximal gradient descent algorithm.

See this paper.

#### tf.train.ProximalGradientDescentOptimizer.__init__(learning_rate, l1_regularization_strength=0.0, l2_regularization_strength=0.0, use_locking=False, name='ProximalGradientDescent') {:#ProximalGradientDescentOptimizer.init}

Construct a new proximal gradient descent optimizer.

##### Args:
• learning_rate: A Tensor or a floating point value. The learning rate to use.
• l1_regularization_strength: A float value, must be greater than or equal to zero.
• l2_regularization_strength: A float value, must be greater than or equal to zero.
• use_locking: If True use locks for update operations.
• name: Optional name prefix for the operations created when applying gradients. Defaults to "GradientDescent".

### class tf.train.ProximalAdagradOptimizer

Optimizer that implements the Proximal Adagrad algorithm.

See this paper.

#### tf.train.ProximalAdagradOptimizer.__init__(learning_rate, initial_accumulator_value=0.1, l1_regularization_strength=0.0, l2_regularization_strength=0.0, use_locking=False, name='ProximalAdagrad') {:#ProximalAdagradOptimizer.init}

##### Args:
• learning_rate: A Tensor or a floating point value. The learning rate.
• initial_accumulator_value: A floating point value. Starting value for the accumulators, must be positive.
• l1_regularization_strength: A float value, must be greater than or equal to zero.
• l2_regularization_strength: A float value, must be greater than or equal to zero.
• use_locking: If True use locks for update operations.
• name: Optional name prefix for the operations created when applying gradients. Defaults to "Adagrad".
##### Raises:
• ValueError: If the initial_accumulator_value is invalid.

### class tf.train.RMSPropOptimizer

Optimizer that implements the RMSProp algorithm.

See the paper.

#### tf.train.RMSPropOptimizer.__init__(learning_rate, decay=0.9, momentum=0.0, epsilon=1e-10, use_locking=False, centered=False, name='RMSProp') {:#RMSPropOptimizer.init}

Construct a new RMSProp optimizer.

Note that in dense implement of this algorithm, m_t and v_t will update even if g is zero, but in sparse implement, m_t and v_t will not update in iterations g is zero.

##### Args:
• learning_rate: A Tensor or a floating point value. The learning rate.
• decay: Discounting factor for the history/coming gradient
• momentum: A scalar tensor.
• epsilon: Small value to avoid zero denominator.
• use_locking: If True use locks for update operation.
• centered: If True, gradients are normalized by the estimated variance of the gradient; if False, by the uncentered second moment. Setting this to True may help with training, but is slightly more expensive in terms of computation and memory. Defaults to False.
• name: Optional name prefix for the operations created when applying gradients. Defaults to "RMSProp".