How to find the Fenchel dual of this expectation
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I'm trying to figure out the Fenchel dual of the following expectation minimization problem:
$$ min_f E[l(x,f(z))] $$
where $xsim S$ and $zsim T$ ($S$ and $T$ are two distributions here).
I'm not very sure if I'm proceeding properly here because I'm trying to use a technique similar to the last few slides on http://homepages.wmich.edu/~ledyaev/zhu-talk2-sp2016.pdf when he derives Kantorovich duals.
Is this even possible? And how would I do this? I'm honestly stuck because it seemed like the constraint qualifications for the Kantorovich duals came out of nowhere.
convex-optimization nonlinear-optimization duality-theorems
asked Nov 27 at 20:46
Glassjawed
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I'm trying to figure out the Fenchel dual of the following expectation minimization problem:
$$ min_f E[l(x,f(z))] $$
where $xsim S$ and $zsim T$ ($S$ and $T$ are two distributions here).
I'm not very sure if I'm proceeding properly here because I'm trying to use a technique similar to the last few slides on http://homepages.wmich.edu/~ledyaev/zhu-talk2-sp2016.pdf when he derives Kantorovich duals.
Is this even possible? And how would I do this? I'm honestly stuck because it seemed like the constraint qualifications for the Kantorovich duals came out of nowhere.
convex-optimization nonlinear-optimization duality-theorems
asked Nov 27 at 20:46
Glassjawed
623516
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I'm trying to figure out the Fenchel dual of the following expectation minimization problem:
$$ min_f E[l(x,f(z))] $$
where $xsim S$ and $zsim T$ ($S$ and $T$ are two distributions here).
I'm not very sure if I'm proceeding properly here because I'm trying to use a technique similar to the last few slides on http://homepages.wmich.edu/~ledyaev/zhu-talk2-sp2016.pdf when he derives Kantorovich duals.
Is this even possible? And how would I do this? I'm honestly stuck because it seemed like the constraint qualifications for the Kantorovich duals came out of nowhere.
convex-optimization nonlinear-optimization duality-theorems
asked Nov 27 at 20:46
Glassjawed
623516
I'm trying to figure out the Fenchel dual of the following expectation minimization problem:
$$ min_f E[l(x,f(z))] $$
where $xsim S$ and $zsim T$ ($S$ and $T$ are two distributions here).
I'm not very sure if I'm proceeding properly here because I'm trying to use a technique similar to the last few slides on http://homepages.wmich.edu/~ledyaev/zhu-talk2-sp2016.pdf when he derives Kantorovich duals.
Is this even possible? And how would I do this? I'm honestly stuck because it seemed like the constraint qualifications for the Kantorovich duals came out of nowhere.
convex-optimization nonlinear-optimization duality-theorems
convex-optimization nonlinear-optimization duality-theorems
asked Nov 27 at 20:46
Glassjawed
623516
asked Nov 27 at 20:46
Glassjawed
623516
asked Nov 27 at 20:46
Glassjawed
623516
asked Nov 27 at 20:46
Glassjawed
623516
asked Nov 27 at 20:46
Glassjawed
623516
623516
add a comment |
add a comment |
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