Mixing
Which is faster: Proximal gradient descent or block coordinate gradient descent?
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Given a non-smooth convex optimization function which one could solve both with proximal gradient descent and block coordinate descent. I would like to know the difference in scalability and convergence rates between these methods.
The objective function that I want to solve is sum of
$l(x) + g(x)$ where $l(x)$ is smooth and differentiable, but $g(x)$ is non-smooth and non-differentiable. Moreover, for $g(x)$ I do have analytical solution for proximal operator.
optimization convex-optimization
asked Jan 31 at 19:27
user2806363user2806363
12011
$endgroup$
add a comment |
$begingroup$
Given a non-smooth convex optimization function which one could solve both with proximal gradient descent and block coordinate descent. I would like to know the difference in scalability and convergence rates between these methods.
The objective function that I want to solve is sum of
$l(x) + g(x)$ where $l(x)$ is smooth and differentiable, but $g(x)$ is non-smooth and non-differentiable. Moreover, for $g(x)$ I do have analytical solution for proximal operator.
optimization convex-optimization
asked Jan 31 at 19:27
user2806363user2806363
12011
$endgroup$
1
$begingroup$
I'm not sure any of them is uniformly faster than the other. Also when you say faster, what do you mean? For instance one might need less iterations by factor $ k $ but what if it requires doing more complex operation in each iteration by a factor of $ 2k $, then, which is faster?
$endgroup$
– Royi
Jan 31 at 21:03
2
$begingroup$
What's the specific block structure of the problem? How do you solve the coordinate descent subproblems in the block coordinate descent method? In the proximal gradient descent method, how do compute the prox operator? You can't say much without knowing answers to all of these questions.
$endgroup$
– Brian Borchers
Feb 1 at 0:51
$begingroup$
@Brian, it's sum of smooth and non-smooth function. For the non-smooth part, I do have analytical solution for proximal operator.
$endgroup$
– user2806363
Feb 1 at 9:08
$begingroup$
Experimentation is your answer here, in my view.
$endgroup$
– Michael Grant
Feb 3 at 21:09
add a comment |
$begingroup$
Given a non-smooth convex optimization function which one could solve both with proximal gradient descent and block coordinate descent. I would like to know the difference in scalability and convergence rates between these methods.
The objective function that I want to solve is sum of
$l(x) + g(x)$ where $l(x)$ is smooth and differentiable, but $g(x)$ is non-smooth and non-differentiable. Moreover, for $g(x)$ I do have analytical solution for proximal operator.
optimization convex-optimization
asked Jan 31 at 19:27
user2806363user2806363
12011
$endgroup$
Given a non-smooth convex optimization function which one could solve both with proximal gradient descent and block coordinate descent. I would like to know the difference in scalability and convergence rates between these methods.
The objective function that I want to solve is sum of
$l(x) + g(x)$ where $l(x)$ is smooth and differentiable, but $g(x)$ is non-smooth and non-differentiable. Moreover, for $g(x)$ I do have analytical solution for proximal operator.
optimization convex-optimization
optimization convex-optimization
asked Jan 31 at 19:27
user2806363user2806363
12011
asked Jan 31 at 19:27
user2806363user2806363
12011
edited Feb 1 at 9:07
user2806363
asked Jan 31 at 19:27
user2806363user2806363
12011
asked Jan 31 at 19:27
user2806363user2806363
12011
asked Jan 31 at 19:27
user2806363user2806363
12011
12011
1
$begingroup$
I'm not sure any of them is uniformly faster than the other. Also when you say faster, what do you mean? For instance one might need less iterations by factor $ k $ but what if it requires doing more complex operation in each iteration by a factor of $ 2k $, then, which is faster?
$endgroup$
– Royi
Jan 31 at 21:03
2
$begingroup$
What's the specific block structure of the problem? How do you solve the coordinate descent subproblems in the block coordinate descent method? In the proximal gradient descent method, how do compute the prox operator? You can't say much without knowing answers to all of these questions.
$endgroup$
– Brian Borchers
Feb 1 at 0:51
$begingroup$
@Brian, it's sum of smooth and non-smooth function. For the non-smooth part, I do have analytical solution for proximal operator.
$endgroup$
– user2806363
Feb 1 at 9:08
$begingroup$
Experimentation is your answer here, in my view.
$endgroup$
– Michael Grant
Feb 3 at 21:09
add a comment |
1
$begingroup$
I'm not sure any of them is uniformly faster than the other. Also when you say faster, what do you mean? For instance one might need less iterations by factor $ k $ but what if it requires doing more complex operation in each iteration by a factor of $ 2k $, then, which is faster?
$endgroup$
– Royi
Jan 31 at 21:03
2
$begingroup$
What's the specific block structure of the problem? How do you solve the coordinate descent subproblems in the block coordinate descent method? In the proximal gradient descent method, how do compute the prox operator? You can't say much without knowing answers to all of these questions.
$endgroup$
– Brian Borchers
Feb 1 at 0:51
$begingroup$
@Brian, it's sum of smooth and non-smooth function. For the non-smooth part, I do have analytical solution for proximal operator.
$endgroup$
– user2806363
Feb 1 at 9:08
$begingroup$
Experimentation is your answer here, in my view.
$endgroup$
– Michael Grant
Feb 3 at 21:09
1
1
$begingroup$
I'm not sure any of them is uniformly faster than the other. Also when you say faster, what do you mean? For instance one might need less iterations by factor $ k $ but what if it requires doing more complex operation in each iteration by a factor of $ 2k $, then, which is faster?
$endgroup$
– Royi
Jan 31 at 21:03
$begingroup$
I'm not sure any of them is uniformly faster than the other. Also when you say faster, what do you mean? For instance one might need less iterations by factor $ k $ but what if it requires doing more complex operation in each iteration by a factor of $ 2k $, then, which is faster?
$endgroup$
– Royi
Jan 31 at 21:03
2
2
$begingroup$
What's the specific block structure of the problem? How do you solve the coordinate descent subproblems in the block coordinate descent method? In the proximal gradient descent method, how do compute the prox operator? You can't say much without knowing answers to all of these questions.
$endgroup$
– Brian Borchers
Feb 1 at 0:51
$begingroup$
What's the specific block structure of the problem? How do you solve the coordinate descent subproblems in the block coordinate descent method? In the proximal gradient descent method, how do compute the prox operator? You can't say much without knowing answers to all of these questions.
$endgroup$
– Brian Borchers
Feb 1 at 0:51
$begingroup$
@Brian, it's sum of smooth and non-smooth function. For the non-smooth part, I do have analytical solution for proximal operator.
$endgroup$
– user2806363
Feb 1 at 9:08
$begingroup$
@Brian, it's sum of smooth and non-smooth function. For the non-smooth part, I do have analytical solution for proximal operator.
$endgroup$
– user2806363
Feb 1 at 9:08
$begingroup$
Experimentation is your answer here, in my view.
$endgroup$
– Michael Grant
Feb 3 at 21:09
$begingroup$
Experimentation is your answer here, in my view.
$endgroup$
– Michael Grant
Feb 3 at 21:09
add a comment |
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1
$begingroup$
I'm not sure any of them is uniformly faster than the other. Also when you say faster, what do you mean? For instance one might need less iterations by factor $ k $ but what if it requires doing more complex operation in each iteration by a factor of $ 2k $, then, which is faster?
$endgroup$
– Royi
Jan 31 at 21:03
2
$begingroup$
What's the specific block structure of the problem? How do you solve the coordinate descent subproblems in the block coordinate descent method? In the proximal gradient descent method, how do compute the prox operator? You can't say much without knowing answers to all of these questions.
$endgroup$
– Brian Borchers
Feb 1 at 0:51
$begingroup$
@Brian, it's sum of smooth and non-smooth function. For the non-smooth part, I do have analytical solution for proximal operator.
$endgroup$
– user2806363
Feb 1 at 9:08
$begingroup$
Experimentation is your answer here, in my view.
$endgroup$
– Michael Grant
Feb 3 at 21:09