New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Jump to bottom

Momentum step size #20

Open

Banana1530 opened this issue Aug 15, 2018 · 0 comments

Labels

Algorithm Improvements

Collaborator

Banana1530 commented Aug 15, 2018 •

edited

Loading

I notice there are two different versions of FISTA algorithm. To minimize g+h, where h is non-smooth and g smooth, FISTA update goes like this

$y = x ^ { ( k - 1 ) } +\beta_k \left( x ^ { ( k - 1 ) } - x ^ { ( k - 2 ) } \right)$

$x ^ { ( k ) } = \operatorname { prox } _ { t _ { k } h } \left( y - t _ { k } \nabla g ( y ) \right)$

where \beta_k is the momentum stepsize.

[1] uses

$\beta_k = \frac{k-2}{k+1}$

For the original paper [2]

$\beta_k = \frac{t_k-1}{t_k}$

where
$t_1=1,t _ { k + 1 } = \frac { 1 + \sqrt { 1 + 4 t _ { k } ^ { 2 } } } { 2 }$

[1] http://www.seas.ucla.edu/~vandenbe/236C/lectures/fista.pdf Page 3
[2] https://people.rennes.inria.fr/Cedric.Herzet/Cedric.Herzet/Sparse_Seminar/Entrees/2012/11/12_A_Fast_Iterative_Shrinkage-Thresholding_Algorithmfor_Linear_Inverse_Problems_(A._Beck,_M._Teboulle)_files/Breck_2009.pdf

Banana1530 added the Algorithm Improvements label

Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment