tf.contrib.constrained_optimization.MultiplicativeSwapRegretOptimizer

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.

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.