class  BVFIM

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Description

Lower model optimization procedure of Value-Function-based Interior-point Method

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

The implemented lower-level optimization procedure will optimize a wrapper of lower model for further using in the following upper level optimization.

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Parameters

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

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

  • "data"(Tensor) - Data used in the ll optimization phase.
  • "target"(Tensor) - Target used in the ll 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.

• 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) Upper model of the bi-level model structure.
  • "lower_model"(Module) Lower model of the bi-level model structure.

• z_loop (optional): int, default=5 Num of steps to obtain a low ll problem value, i.e. optimize ll variable with ll problem. Regarded as $T_z$ in the paper.

• y_loop (optional): int, default=5 Num of steps to obtain a optimal ll variable under the ll problem value obtained after z_loop, i.e. optimize the updated ll variable with ul problem. Regarded as Regarded as $T_y$ in the paper.

• 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

optimize(train_data, train_target, auxiliary_model, auxiliary_opt, validate_data, validate_target, reg_decay)

Execute the ll optimization procedure with training data samples using ll objective. The passed in wrapper of ll model will be updated.

Parameters:

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

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

• auxiliary_model(_MonkeyPatchBase) - Wrapper of lower model encapsulated by module higher, will be optimized in ll optimization procedure.

• auxiliary_opt(DifferentiableOptimizer) - Wrapper of ll optimizer encapsulated by module higher, will be used in ll optimization procedure.

• auxiliary_model_extra: Module

• auxiliary_opt_extra: Optimizer

• validate_data(Tensor) - The validation data used for ul problem optimization. Needed when using BDA method or IAPTT-GM method.

• validate_target(Tensor) - The labels of the samples in the validation data. Needed when using BDA method or IAPTT-GM method.

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

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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.