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A ConstrainedOptimizer based on external-regret minimization.
tf.contrib.constrained_optimization.AdditiveExternalRegretOptimizer(
optimizer, constraint_optimizer=None, maximum_multiplier_radius=None
)
This ConstrainedOptimizer uses the given tf.compat.v1.train.Optimizers to
jointly minimize over the model parameters, and maximize over Lagrange
multipliers, with the latter maximization using additive updates and an
algorithm that minimizes external regret.
For more specifics, please refer to:
Cotter, Jiang and Sridharan. "Two-Player Games for Efficient Non-Convex Constrained Optimization". https://arxiv.org/abs/1804.06500
The formulation used by this optimizer--which is simply the usual Lagrangian
formulation--can be found in Definition 1, and is discussed in Section 3. It
is most similar to Algorithm 3 in Appendix C.3, with the two differences being
that it uses proxy constraints (if they're provided) in the update of the
model parameters, and uses tf.compat.v1.train.Optimizers, instead of SGD,
for the "inner" updates.
Args | |
|---|---|
optimizer
|
tf.compat.v1.train.Optimizer, used to optimize the objective and proxy_constraints portion of ConstrainedMinimizationProblem. If constraint_optimizer is not provided, this will also be used to optimize the Lagrange multipliers. |
constraint_optimizer
|
optional tf.compat.v1.train.Optimizer, used to optimize the Lagrange multipliers. |
maximum_multiplier_radius
|
float, an optional upper bound to impose on the sum of the Lagrange multipliers. |
Raises | |
|---|---|
ValueError
|
If the maximum_multiplier_radius parameter is nonpositive. |
Attributes | |
|---|---|
constraint_optimizer
|
Returns the tf.compat.v1.train.Optimizer used for the Lagrange multipliers.
|
optimizer
|
Returns the tf.compat.v1.train.Optimizer used for optimization.
|
Methods
minimize
minimize(
minimization_problem, unconstrained_steps=None, global_step=None, var_list=None,
gate_gradients=train_optimizer.Optimizer.GATE_OP, aggregation_method=None,
colocate_gradients_with_ops=False, name=None, grad_loss=None
)
Returns an Operation for minimizing the constrained problem.
This method combines the functionality of minimize_unconstrained and
minimize_constrained. If global_step < unconstrained_steps, it will
perform an unconstrained update, and if global_step >= unconstrained_steps,
it will perform a constrained update.
The reason for this functionality is that it may be best to initialize the constrained optimizer with an approximate optimum of the unconstrained problem.
| Args | |
|---|---|
minimization_problem
|
ConstrainedMinimizationProblem, the problem to optimize. |
unconstrained_steps
|
int, number of steps for which we should perform unconstrained updates, before transitioning to constrained updates. |
global_step
|
as in tf.compat.v1.train.Optimizer's minimize method.
|
var_list
|
as in tf.compat.v1.train.Optimizer's minimize method.
|
gate_gradients
|
as in tf.compat.v1.train.Optimizer's minimize method.
|
aggregation_method
|
as in tf.compat.v1.train.Optimizer's minimize
method.
|
colocate_gradients_with_ops
|
as in tf.compat.v1.train.Optimizer's
minimize method.
|
name
|
as in tf.compat.v1.train.Optimizer's minimize method.
|
grad_loss
|
as in tf.compat.v1.train.Optimizer's minimize method.
|
| Returns | |
|---|---|
Operation, the train_op.
|
| Raises | |
|---|---|
ValueError
|
If unconstrained_steps is provided, but global_step is not. |
minimize_constrained
minimize_constrained(
minimization_problem, global_step=None, var_list=None,
gate_gradients=train_optimizer.Optimizer.GATE_OP, aggregation_method=None,
colocate_gradients_with_ops=False, name=None, grad_loss=None
)
Returns an Operation for minimizing the constrained problem.
Unlike minimize_unconstrained, this function attempts to find a solution
that minimizes the objective portion of the minimization problem while
satisfying the constraints portion.
| Args | |
|---|---|
minimization_problem
|
ConstrainedMinimizationProblem, the problem to optimize. |
global_step
|
as in tf.compat.v1.train.Optimizer's minimize method.
|
var_list
|
as in tf.compat.v1.train.Optimizer's minimize method.
|
gate_gradients
|
as in tf.compat.v1.train.Optimizer's minimize method.
|
aggregation_method
|
as in tf.compat.v1.train.Optimizer's minimize
method.
|
colocate_gradients_with_ops
|
as in tf.compat.v1.train.Optimizer's
minimize method.
|
name
|
as in tf.compat.v1.train.Optimizer's minimize method.
|
grad_loss
|
as in tf.compat.v1.train.Optimizer's minimize method.
|
| Returns | |
|---|---|
Operation, the train_op.
|
minimize_unconstrained
minimize_unconstrained(
minimization_problem, global_step=None, var_list=None,
gate_gradients=train_optimizer.Optimizer.GATE_OP, aggregation_method=None,
colocate_gradients_with_ops=False, name=None, grad_loss=None
)
Returns an Operation for minimizing the unconstrained problem.
Unlike minimize_constrained, this function ignores the constraints (and
proxy_constraints) portion of the minimization problem entirely, and only
minimizes objective.
| Args | |
|---|---|
minimization_problem
|
ConstrainedMinimizationProblem, the problem to optimize. |
global_step
|
as in tf.compat.v1.train.Optimizer's minimize method.
|
var_list
|
as in tf.compat.v1.train.Optimizer's minimize method.
|
gate_gradients
|
as in tf.compat.v1.train.Optimizer's minimize method.
|
aggregation_method
|
as in tf.compat.v1.train.Optimizer's minimize
method.
|
colocate_gradients_with_ops
|
as in tf.compat.v1.train.Optimizer's
minimize method.
|
name
|
as in tf.compat.v1.train.Optimizer's minimize method.
|
grad_loss
|
as in tf.compat.v1.train.Optimizer's minimize method.
|
| Returns | |
|---|---|
Operation, the train_op.
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