skwdro.operations_research package

Module contents

class skwdro.operations_research.NewsVendor(rho: float = 0.01, k: float = 5, u: float = 7, cost: str = 't-NC-1-2', l2_reg: float = 0.0, solver_reg: float = 0.01, n_zeta_samples: int = 10, solver: str = 'entropic', random_state: int = 0, opt_cond: ~skwdro.solvers.optim_cond.OptCondTorch | None = <skwdro.solvers.optim_cond.OptCondTorch object>)[source]

Bases: BaseEstimator

A NewsVendor Wasserstein Distributionally Robust Estimator.

The cost function is XXX Uncertainty is XXX

Parameters:

rhofloat, default=1e-2: Robustness radius
kfloat, default=5: Buying cost
ufloat, default=7: Selling cost
cost: str, default=”n-NC-1-2”: Tiret-separated code to define the transport cost: “<engine>-<cost id>-<k-norm type>-<power>” for $c(x, y):=\|x-y\|_k^p$
solver: str, default=’entropic’: Solver to be used: ‘entropic’, ‘entropic_torch’ (_pre or _post) or ‘dedicated’
n_zeta_samples: int, default=10: number of adversarial samples to draw
opt_cond: Optional[OptCondTorch]: optimality condition, see OptCondTorch

Attributes:

coef_float: parameter vector ( $w$ in the cost function formula)

Examples

>>> from skwdro.operations_research import NewsVendor
>>> import numpy as np
>>> X = np.random.exponential(scale=2.0,size=(20,1))
>>> estimator = NewsVendor()
>>> estimator.fit(X)
NewsVendor()

eval(X)[source]

Evaluates the loss with the theta obtained from the fit function.

Parameters:

Xarray-like, shape (n_samples_test,m): The testing input samples.

fit(X, y=None)[source]

Fits a WDRO model

Parameters:

Xarray-like, shape (n_samples,) or (n_samples,1): The training input samples.

Returns:

selfobject: Returns self.

score(X, y=None)[source]

Score method to estimate the quality of the model.

Parameters:

Xarray-like, shape (n_samples_test,m): The testing input samples.
yNone: The prediction. Always None for a Newsvendor estimator.

class skwdro.operations_research.Portfolio(rho=0.01, eta=0.0, alpha=0.95, C=None, d=None, fit_intercept=None, cost='t-NC-1-1', solver='dedicated', solver_reg=0.001, reparam='softmax', n_zeta_samples: int = 10, seed: int = 0, opt_cond: ~skwdro.solvers.optim_cond.OptCondTorch | None = <skwdro.solvers.optim_cond.OptCondTorch object>)[source]

Bases: BaseEstimator

A Wasserstein Distributionally Robust Mean-Risk Portfolio estimator.

Model for the portfolio optimization problem

$\mathbb{E}[ - \langle x ; \xi \rangle ] + \eta \mathrm{CVar}_\alpha[- \langle x ; \xi \rangle]$

which amounts to using the following loss function

$\ell(x,\tau;\xi) = - \langle x ; \xi \rangle + \eta \tau + \frac{1}{\alpha} \max( - \langle x ; \xi \rangle - \tau ; 0)$

where $\tau$ is an extra real parameter accounting for the threshold of the CVaR (see [Rockafellar and Uryasev (2000)]). The parameter $x$ is constrained to live in the simplex (This is encoded in the constraints of the problem in [Esfahani et al. (2018)] and by an exponential reparametrization for the entropy-regularized version).

Parameters:

rhofloat, default=1e-2: Robustness radius
eta: float > 0, default=0: Risk-aversion parameter linked to the Conditional Value at Risk
alpha: float in (0,1], default=0.95: Confidence level of the Conditional Value at Risk
C(nb_constraints, nb_assets), default=None: Matrix of constraints observed by the user.
d(nb_constraints,), default=None: Vector of constraints observed by the user.
fit_intercept: boolean, default=None: Determines if an intercept is fit or not
cost: str, default=”t-NC-1-1”: Tiret-separated code to define the transport cost: “<engine>-<cost id>-<k-norm type>-<power>” for $c(x, y):=\|x-y\|_k^p$
solver: str, default=’entropic’: Solver to be used: ‘entropic’ or ‘dedicated’
solver_reg: float, default=1.0: regularization value for the entropic solver
reparam: str, default=”softmax”: Reparametrization method of theta for the entropic torch loss
random_state: int, default=None: Seed used by the random number generator when using non-deterministic methods on the estimator
Examples
>>> from skwdro.estimators import Portfolio
>>> import numpy as np
>>> X = np.random.normal(size=(10,2))
>>> estimator = Portfolio()
>>> estimator.fit(X)
Portfolio()
——–

eval(X)[source]

Evaluates the loss with the theta obtained from the fit function.

Parameters:

Xarray-like, shape (n_samples_test,m): The testing input samples.

fit(X, y=None)[source]

Fits the WDRO regressor.

Parameters:

Xarray-like, shape (n_samples_train,m): The training input samples.
yNone: The prediction. Always none for a portfolio estimator.

score(X, y=None)[source]

Score method to estimate the quality of the model.

Parameters:

Xarray-like, shape (n_samples_test,m): The testing input samples.
yNone: The prediction. Always None for a Portfolio estimator.

class skwdro.operations_research.Weber(rho: float = 0.1, kappa: float = 10.0, solver_reg: float = 0.01, sampler_reg: float = 0.01, l2_reg: float = 0.0, n_zeta_samples: int = 10, cost: str = 't-NLC-2-2', solver='entropic_torch', random_state: int = 0, opt_cond: ~skwdro.solvers.optim_cond.OptCondTorch | None = <skwdro.solvers.optim_cond.OptCondTorch object>)[source]

Bases: BaseEstimator

A Weber Wasserstein Distributionally Robust Estimator.

The cost function is XXX Uncertainty is XXX

Parameters:

rhofloat, default=1e-1: Robustness radius
kappa: float, default=10.: For the cost
solver_reg: float, default=1e-2: regularization value for the entropic solver
n_zeta_samples: int, default=10: number of adversarial samples to draw
solver: str, default=’entropic_torch’: Solver to be used: ‘entropic_torch’ (only this is implemented for now)

Attributes:

position_float: parameter vector ( $w$ in the cost function formula)

Examples

>>> from skwdro.operations_research import Weber
>>> import numpy as np
>>> m = 20
>>> X = np.random.exponential(scale=2.0,size=(m,2))
>>> w = np.ones(m)
>>> estimator = Weber()
>>> estimator.fit(X,w)
Weber()

eval(X)[source]

Evaluates the loss with the theta obtained from the fit function.

Parameters:

Xarray-like, shape (n_samples_test,m): The testing input samples.

fit(X, y)[source]

Fits a Weber WDRO model

Parameters:

Xarray-like, shape (n_samples,2): The training input positions.
yarray-like, shape (n_samples,) or (n_samples,1): The training input importance weights

Returns:

selfobject: Returns self.

score(X, y=None)[source]

Score method to estimate the quality of the model.

Parameters:

Xarray-like, shape (n_samples_test,m): The testing input samples.
yNone: The prediction. Always None for a Newsvendor estimator.