$$\def\vepsi{\varepsilon} \def\bold#1{{\bf #1}}$$ $$\def\Hcal{{\mathcal{H}}} \def\bold#1{{\bf #1}}$$ $$\def\RR{{\bf R}} \def\bold#1{{\bf #1}}$$ $$\def\LL{{\bf L}} \def\bold#1{{\bf #1}}$$ $$\def\xv{{\bf x}} \def\bold#1{{\bf #1}}$$ $$\def\uv{{\bf u}} \def\bold#1{{\bf #1}}$$ $$\def\qv{{\bf q}} \def\bold#1{{\bf #1}}$$ $$\def\vv{{\bf v}} \def\bold#1{{\bf #1}}$$ $$\def\Xv{{\bf X}} \def\bold#1{{\bf #1}}$$ $$\def\cv{{\bf c}} \def\bold#1{{\bf #1}}$$ $$\def\gv{{\bf g}} \def\bold#1{{\bf #1}}$$ $$\def\wv{{\bf w}} \def\bold#1{{\bf #1}}$$ $$\def\Omegamat{{\bf \Omega}} \def\bold#1{{\bf #1}}$$ $$\def\Smat{{\bf S}} \def\bold#1{{\bf #1}}$$ $$\def\Pmat{{\bf P}} \def\bold#1{{\bf #1}}$$ $$\def\Hmat{{\bf H}} \def\bold#1{{\bf #1}}$$ $$\def\Imat{{\bf I}} \def\bold#1{{\bf #1}}$$ $$\def\Gmat{{\bf G}} \def\bold#1{{\bf #1}}$$ $$\def\Gammamat{{\bf \Gamma}} \def\bold#1{{\bf #1}}$$ $$\def\Qmat{{\bf Q}} \def\bold#1{{\bf #1}}$$ $$\def\Rmat{{\bf R}} \def\bold#1{{\bf #1}}$$ $$\def\omegas{{\bf \omega^{\star}}} \def\bold#1{{\bf #1}}$$ $$\def\hf{{\frac{1}{2}}}$$ $$\def\nablau{\nabla_{\uv}^{2}} \def\bold#1{{\bf #1}}$$ $$\def\nablav{\nabla_{\vv}^{2}} \def\bold#1{{\bf #1}}$$ $$\def\nablaw{\nabla_{\wv}^{2}} \def\bold#1{{\bf #1}}$$ $$\def\nablavv{\nabla_{\vv\vv}^{2}} \def\bold#1{{\bf #1}}$$ $$\def\xbar{\overset{-}{\xv}} \def\bold#1{{\bf #1}}$$ $$\def\ubar{\overset{-}{\uv}} \def\bold#1{{\bf #1}}$$ $$\def\vbar{\overset{-}{\vv}} \def\bold#1{{\bf #1}}$$

# MGDA Platform

Multiple Gradient Descent Algorithm for Multi Objective Differentiable Optimization.

# Stochastic formulations

## Abstract

For stochastic problems that are formulated through cost functions expressed as expectations of random functions, the classical stochastic gradient algorithm can be combined efficiently with MGDA. This approach has been developed at Onera with F. Poirion and Q. Mercier, and demonstrated in problems of data variability and reliability.

## Bibliography

Q. Mercier, F. Poirion, and J.-A. Désidéri. A stochastic multiple gradient descent algorithm. European Journal of Operational Research, ELSEVIER Publish., 271(3):808-817, 16 December 2018.