tf.contrib.constrained_optimization.AdditiveExternalRegretOptimizer

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

View source

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

View source

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

View source

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.