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A ConstrainedOptimizer based on swap-regret minimization.
tf.contrib.constrained_optimization.MultiplicativeSwapRegretOptimizer(
optimizer, constraint_optimizer=None, minimum_multiplier_radius=0.001,
initial_multiplier_radius=None
)
This ConstrainedOptimizer uses the given tf.compat.v1.train.Optimizers to
jointly
minimize over the model parameters, and maximize over constraint/objective
weight matrix (the analogue of Lagrange multipliers), with the latter
maximization using multiplicative updates and an algorithm that minimizes swap
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 can be found in Definition 2, and is
discussed in Section 4. It is most similar to Algorithm 2 in Section 4, with
the difference being that it 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 multiplier analogues. |
constraint_optimizer
|
optional tf.compat.v1.train.Optimizer, used to optimize the Lagrange multiplier analogues. |
minimum_multiplier_radius
|
float, each element of the matrix will be lower
bounded by minimum_multiplier_radius divided by one plus the number of
constraints.
|
initial_multiplier_radius
|
float, the initial value of each element of the
matrix associated with a constraint (i.e. excluding those elements
associated with the objective) will be initial_multiplier_radius
divided by one plus the number of constraints. Defaults to the value of
minimum_multiplier_radius.
|
Raises | |
|---|---|
ValueError
|
If the two radius parameters are inconsistent. |
Attributes | |
|---|---|
constraint_optimizer
|
Returns the tf.compat.v1.train.Optimizer used for the matrix.
|
optimizer
|
Returns the tf.compat.v1.train.Optimizer used for optimization.
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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.
|