Two-stage Baseline

The two-stage approach trains a regression model \(\hat{\mathbf{c}} = g(\mathbf{x}; \boldsymbol{\theta})\) with a prediction loss such as mean squared error. At inference time, the model first predicts \(\hat{\mathbf{c}}\), then the predicted costs are used to solve the optimization problem.

The two-stage model does not train through the optimization model, but it is evaluated with the same decision-quality metrics as end-to-end methods.

When to Use It

Use a two-stage baseline when:

• true cost labels are available;

• the prediction model can be trained with a standard regression loss;

• the experiment needs a non-end-to-end baseline.

After training, evaluate the predictor with pyepo.metric.regret or pyepo.metric.unambRegret.

pyepo.twostage.sklearnPred(pmodel: BaseEstimator) → MultiOutputRegressor

Wrap a scikit-learn estimator into a multi-output regressor for two-stage baselines.

The two-stage approach trains a regression model to minimize prediction error (e.g. MSE on cost coefficients) and only afterwards plugs the predicted costs into the optimization solver. This helper turns any single-output scikit-learn estimator (LinearRegression, RandomForestRegressor, MLPRegressor, …) into a multi-output regressor suitable for predicting the full cost vector.

Parameters:

pmodel – a scikit-learn single-output regression estimator

Returns:

scikit-learn multi-output regression wrapper

Return type:

MultiOutputRegressor

pyepo.twostage.sklearnPred is a helper function that wraps a scikit-learn estimator into a multi-output regressor.

Minimal Example

import pyepo
from sklearn.linear_model import LinearRegression
from torch.utils.data import DataLoader

grid = (5, 5)
model = pyepo.model.shortestPathModel(grid)

feat, costs = pyepo.data.shortestpath.genData(
    num_data=1000,
    num_features=5,
    grid=grid,
    deg=4,
    noise_width=0.5,
    seed=135,
)

reg = LinearRegression()
twostage_model = pyepo.twostage.sklearnPred(reg)
twostage_model.fit(feat, costs)

dataset = pyepo.data.dataset.optDataset(model, feat, costs)
dataloader = DataLoader(dataset, batch_size=32, shuffle=False)
# regret takes a callable mapping features to costs; pass the predictor's .predict
regret = pyepo.metric.regret(twostage_model.predict, model, dataloader)