odtlearn.utils.callbacks

Classes

BendersCallback	This class contains a function that is called by the solver at
RobustBendersCallback	A callback class for generating Benders' cuts in the Robust Tree optimization.

Functions

benders_subproblem(→ Union[Tuple[int, List[int], ...)	Solve the Benders' subproblem for a given datapoint.
robust_tree_subproblem(master, i, terminal_nodes, ...)	Solve the robust tree subproblem for a given datapoint.

Module Contents

odtlearn.utils.callbacks.benders_subproblem(main_model_obj: BendersOCT, b: Dict[Tuple[int, numpy.str_], float] | Dict[Tuple[int, str], float], p: Dict[int, float], w: Dict[Tuple[int, numpy.int64], float], i: int) → Tuple[int, List[int], List[Any], List[int]] | Tuple[int, List[Any], List[int], List[int]] | Tuple[int, List[int], List[int], List[int]]

Solve the Benders’ subproblem for a given datapoint.

Parameters:

main_model_objobject

The main model object.

bdict

The dictionary of binary decision variables representing the branching decisions.

pdict

The dictionary of binary decision variables representing the prediction decisions.

wdict

The dictionary of binary decision variables representing the class assignments.

iint

The index of the current datapoint.

Returns:

tuple

A tuple containing the subproblem value, left nodes, right nodes, and target nodes.

class odtlearn.utils.callbacks.BendersCallback(X: pandas.core.frame.DataFrame, obj: BendersOCT, solver: odtlearn.utils.solver.Solver, **kwargs)

Bases: mip.ConstrsGenerator

This class contains a function that is called by the solver at every node through the branch-&-bound tree while we solve the model.

We are specifically interested at nodes where we get an integer solution for the master problem. When we get an integer solution for b and p, for every data-point we solve the sub-problem which is a minimum cut and check if g[i] <= value of sub-problem[i]. If this is violated we add the corresponding benders constraint as lazy constraint to the master problem and proceed. Whenever we have no violated constraint, it means that we have found the optimal solution.

generate_constrs(model: mip.Model, depth: int = 0, npass: int = 0) → None

Generate Benders’ cuts at the current node in the branch-and-bound tree.

Parameters:

modelModel

The optimization model.

depthint, optional

The depth of the current node in the branch-and-bound tree.

npassint, optional

The pass number in the branch-and-bound process.

odtlearn.utils.callbacks.robust_tree_subproblem(master, i, terminal_nodes, terminal_path_dict, terminal_features_dict, terminal_assignments_dict, terminal_cutoffs_dict, initial_xi={}, initial_mins={}, initial_maxes={})

Solve the robust tree subproblem for a given datapoint.

The robust tree subproblem aims to find the shortest path from the root node to a terminal node that minimizes the cost while satisfying the robustness constraints. It takes into account the feature perturbations and label perturbations to ensure the robustness of the solution.

Parameters:

masterobject

The master problem object containing the problem data and variables.

iint

The index of the current datapoint.

terminal_nodeslist

The list of terminal nodes in the decision tree.

terminal_path_dictdict

A dictionary mapping each terminal node to its corresponding path from the root node.

terminal_features_dictdict

A dictionary mapping each terminal node to the list of features encountered along its path.

terminal_assignments_dictdict

A dictionary mapping each terminal node to its class assignment.

terminal_cutoffs_dictdict

A dictionary mapping each terminal node to the list of cutoff values encountered along its path.

initial_xidict, optional

The initial dictionary of feature perturbations. Default is an empty dictionary.

initial_minsdict, optional

The initial dictionary of minimum feature values. Default is an empty dictionary.

initial_maxesdict, optional

The initial dictionary of maximum feature values. Default is an empty dictionary.

Returns:

tuple

A tuple containing the following elements: - target : list

The list of nodes whose edges to the sink node are part of the minimum cut.

• xidict

  The dictionary of feature perturbations that achieve the minimum cost.

• costfloat

  The minimum cost of the robust tree subproblem.

• vbool

  A boolean indicating whether the label of the datapoint is perturbed in the optimal solution.

class odtlearn.utils.callbacks.RobustBendersCallback(X, obj, solver, **kwargs)

Bases: mip.ConstrsGenerator

A callback class for generating Benders’ cuts in the Robust Tree optimization.

This class contains a function that is called by the solver at every node in the branch-and-bound tree while solving the model. It checks for integer solutions to the master problem and generates Benders’ cuts based on the subproblem solutions in the Robust Tree optimization.

Parameters:

XDataFrame

The input data.

objobject

The main model object.

solverSolver

The solver object used for solving the optimization problem.

bdict

The dictionary of decision variables representing the branching decisions.

wdict

The dictionary of decision variables representing the class assignments.

tdict

The dictionary of decision variables representing the subproblem objective values.

Methods

generate_constrs(model, depth=0, npass=0)

Generate Benders’ cuts at the current node in the branch-and-bound tree.

generate_constrs(model: mip.Model, depth: int = 0, npass: int = 0)

Generate Benders’ cuts at the current node in the branch-and-bound tree.

Parameters:

modelModel

The optimization model.

depthint, optional

The depth of the current node in the branch-and-bound tree.

npassint, optional

The pass number in the branch-and-bound process.