Outlier-Robust WDRO

class dro.src.linear_model.or_wasserstein_dro.ORWDRO(input_dim, model_type='svm', solver='MOSEK', eps=0.0, eta=0.0, dual_norm=1)

Bases: BaseLinearDRO

Outlier-Robust Wasserstein Distributionally Robust Optimization (OR-WDRO) model.

Implements TV-corrupted p-Wasserstein DRO with dual norm constraints:

\[\min_{\theta} \sup_{Q \in \mathcal{B}_\epsilon(P)} \mathbb{E}_Q[\ell(\theta;X,y)] + \eta \cdot \text{TV}(P,Q)\]

where \(\mathcal{B}_\epsilon(P)\) is the Wasserstein ball and \(\text{TV}\) is total variation.

ORWDRO_Paper: https://arxiv.org/pdf/2311.05573

Initialize OR-WDRO model with anomaly-robust parameters.

Parameters:

  • input_dim (int) – Feature space dimension. Must be ≥ 1

  • model_type (str) –

    Base learner type. Supported:

    • 'svm': Hinge loss (classification)

    • 'lad': Least absolute deviation (regression)

  • eps (float) –

    Wasserstein robustness radius. Defaults to 0.0

    • 0: Standard empirical risk minimization

    • >0: Controls distributional robustness

  • eta (float) – Expected outlier fraction. Must satisfy \(0 \leq \eta \leq 0.5\). Defaults to 0.0

  • dual_norm (int) –

    Wasserstein dual norm order. Valid values:

    • 1: ℓ¹-Wasserstein (transportation cost)

    • 2: ℓ²-Wasserstein (default)

  • solver (str)

Raises:

ValueError –

  • If input_dim < 1

  • If model_type not in allowed set

  • If eps < 0 or eta < 0 or eta > 0.5

  • If dual_norm ∉ {1, 2}

Example:
>>> model = ORWDRO(
...     input_dim=5,
...     model_type='svm',
...     eps=0.1,
...     eta=0.05,
...     dual_norm=2
... )
>>> model.sigma  # sqrt(5) ≈ 2.236

Note

  • Computation complexity scales as \(O(\epsilon^{-2})\)

  • Set eta=0 to disable outlier robustness

update(config)

Update robustness parameters for OR-WDRO optimization.

Parameters:

config (dict[str, Any]) –

Dictionary containing parameters to update. Valid keys:

  • 'eps': New Wasserstein radius (ε ≥ 0)

  • 'eta': New outlier fraction (0 ≤ η ≤ 0.5)

  • 'dual_norm': Norm order (1 or 2)

Raises:

ValueError –

  • If parameter values violate type or range constraints

  • If unknown parameters are provided

Return type:

None

Example:
>>> model.update({
...     'eps': 0.2,
...     'eta': 0.1,
...     'dual_norm': 2
... })  # Updates multiple parameters atomically
fit(X, y)
Parameters:

  • X (numpy.ndarray) – Training feature matrix of shape (n_samples, n_features). Must satisfy n_features == self.input_dim.

  • Y (numpy.ndarray) –

    Target values of shape (n_samples,). Format requirements:

    • Classification: ±1 labels

    • Regression: Continuous values

  • y (ndarray)

Returns:

Dictionary containing trained parameters:

  • theta: Weight vector of shape (n_features,)

Return type:

Dict[str, Any]

worst_distribution(X, y)

Compute the worst-case distribution.

Reference: Theorem 3 in https://arxiv.org/pdf/2311.05573

Return type:

Dict[str, Any]

Parameters:
Args:

X (np.ndarray): Input feature matrix with shape (n_samples, n_features). y (np.ndarray): Target vector with shape (n_samples,).

Returns:

Dict[str, Any]: Dictionary containing ‘sample_pts’ and ‘weight’ keys for worst-case distribution.

Raises:

ORWDROError: If the worst-case distribution optimization fails.