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tf.contrib.constrained_optimization.AdditiveSwapRegretOptimizer

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A ConstrainedOptimizer based on swap-regret minimization.

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 additive 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 differences being that it uses tf.compat.v1.train.Optimizers, instead of SGD, for the "inner" updates, and performs additive (instead of multiplicative) updates of the stochastic matrix.

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.

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

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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

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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

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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.