class  BVFIM

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Description

Calculation of the gradient of the ul model variables with BVFIM method

Implements the ul optimization procedure of Value-Function Best- Response (VFBR) type BLO methods, named i-level Value-Function-basedInterior-point Method(BVFIM) [1].

A wrapper of ll model that has been optimized in the ll optimization will be used in this procedure.

Note that this ul optimization module should only use both.ll_optimize.Bvfim module to finish ll optimization procedure.

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Parameters

• ul_objective: callable
  The main optimization problem in a hierarchical optimization problem.

  Callable with signature callable(state). Defined based on modeling of the specific problem that need to be solved. Computing the loss of ul problem. The state object contains the following:

  • "data"(Tensor) - Data used in the ul optimization phase.
  • "target"(Tensor) - Target used in the ul optimization phase.
  • "ul_model"(Module) - ul model of the bi-level model structure.
  • "ll_model"(Module) - ll model of the bi-level model structure.

• ul_model: Module
  ul model in a hierarchical model structure whose parameters will be updated with ul objective and trained ll model.

• ll_objective: callable
  An optimization problem which is considered as the constraint of ul problem.

  Callable with signature callable(state). Defined based on modeling of the specific problem that need to be solved. Computing the loss of ul problem. The state object contains the following:

  • "data"(Tensor) - Data used in the ul optimization phase.
  • "target"(Tensor) - Target used in the ul optimization phase.
  • "ul_model"(Module) - ul model of the bi-level model structure.
  • "ll_model"(Module) - ll model of the bi-level model structure.

• z_l2_reg (optional): float, default=0.1 Weight of L2 regularization term in the value function of the regularized LL problem, which is $\displaystyle f_\mu^*(x) = \min_{y\in\mathbb{R}^n} f(x,y) + \frac{\mu_1}{2}\|y\|^2 + \mu_2$.

• y_l2_reg (optional): float, default=0.01 Weight of L2 regularization term in the value function of the regularized UL problem, which is $\displaystyle \varphi(x) = \min_{y\in\mathbb{R}^n} F(x,y) + \frac{\theta}{2}\|y\|^2 - \tau\ln(f_\mu^*(x)-f(x,y))$.

• y_ln_reg (optional): float, default=10. Weight of the log-barrier penalty term in the value function of the regularized UL problem, as y_l2_reg.

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Methods

compute_gradients(validate_data, validate_target, auxiliary_model, train_data, train_target, reg_decay)

Compute the grads of ul variable with one single set of validation data samples in the batch using ul objective. The grads will be saved in the passed in ul model.

Note that the implemented ul optimization procedure will only compute the grads of ul variables with one single set of data samples in a batch. After that the update operation of ul variables needs to be done outside this module.

Parameters:

• validate_data(Tensor) - The validation data used for ul problem optimization.

• validate_target(Tensor) - The labels of the samples in the validation data.

• auxiliary_model(_MonkeyPatchBase) - Wrapper of ll model encapsulated by module higher, has been optimized in ll optimization phase.

• auxiliary_model_extra(Module) -

• train_data(Tensor) - The training data used for ll problem optimization.

• train_target(Tensor) - The labels of the samples in the train data.

• reg_decay(float) - Weight decay coefficient of L2 regularization term and log-barrier penalty term. The value increases with the number of iterations.

Returns

        ul_loss(Tensor) - The loss value of ul objective.

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References

[1] R. Liu, X. Liu, X. Yuan, S. Zeng and J. Zhang, "A Value-Function-based Interior-point Method for Non-convex Bi-level Optimization", in ICML, 2021.