pytorch interface

The following solvers are implemented in skwdro.

Operations Research

Portfolio Selection

Two losses are implemented in PyTorch: RiskPortfolioLoss_torch et MeanRisk_torch.

The general loss function is given by

$\underset{\theta \in \Theta}{\inf} \mathbb{E}^{\mathbb{P}}(- \langle \theta, \xi \rangle) + \eta \mathbb{P}\text{-CVaR}_{\alpha}(- \langle \theta, \xi \rangle)$

RiskPortfolioLoss_torch thus implements the first term of the loss function which is purely based on the dot product $- \langle \theta, \xi \rangle$ representing the risks associated with return on investment. The idea of implementing this term in a separate class stems from the fact that there are several functions which exist to model these financial risks. Thus, the MeanRisk_torch class implementing the function to be minimized is defined by composition with an instance of the RiskPortfolioLoss_torch class as an attribute to define the first term. This maintains the overall structure of the general class since the definition of a new risk modeling function requires the creation of its own class, and the rest of the loss function is defined by composition with an instance of this class.