Questions tagged [non-convex]

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If $\ell_0$ regularization can be done via the proximal operator, why are people still using LASSO?

I have just learned that a general framework in constrained optimization is called "proximal gradient optimization". It is interesting that the $\ell_0$ "norm" is also associated with a proximal ...
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0answers
73 views

Bayesian interpretation of gradient clipping

In the context of Bayesian interpretations of SGD for neural network training, is there an interpretation for the gradient clipping operation which is often included?
8
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3answers
2k views

Gradient descent on non-convex functions

What situations do we know of where gradient descent can be shown to converge (either to a critical point or to a local/global minima) for non-convex functions? For SGD on non-convex functions, one ...
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0answers
34 views

Solving constrained optimization problems with Adam

The adam algorithm has been very successful for solving non-convex optimization problems that appear in deep learning. Are there ways to extend adam to solve constrained optimization problems? Among ...
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0answers
13 views

Stochastic gradient variance reduced methods

I'm doing stochastic gradient descent on a non-convex optimization problem. Gradient corresponds to an intractable expectation which I approximate via Monte Carlo averaging. I'm trying to infer the ...
2
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0answers
29 views

How to solve a non-convex with equality constraint optimization problem?

I have a non-convex optimization problem with equality constraint, I can derive the KKT conditions, but it seems just one of the KKT conditions is valid. Could you please give some advice on how to ...
0
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1answer
140 views

Is error function always assumed and convex?

While updating weights of the neural network, most of the algorithms use convex optimisation because of the reason that error is a convex function. My doubt is that whether the convex-ness of error ...
3
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0answers
81 views

Optimization textbooks for statistics and data analytics

Any statistical analysis, machine learning or data science involves some sort of optimization at the end of the day. I'm looking for good linear and nonlinear optimization textbooks for self ...
1
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0answers
116 views

How to optimize ratiometric loss function with variance term in it?

I'm training a neural network (or any ML model with non-convex gradient-based optimization) to predict a continuous outcome variable. Currently, I use the mean squared error loss function, i.e., if $y$...
1
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0answers
28 views

Minimal requirement for reaching a feasible solution in non-convex constrained gradient descent

The problem is as follows: $\max_x f(x) \enspace , \enspace \text{s.t.} \enspace g(x) \leq \alpha $ We can not assume that either $f$ nor $g$ are convex, on the contrary - we can assume they are ...
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0answers
48 views

How to solve a DC (Difference of Convex) program?

I have an objective function which is the difference of two convex functions in Tensorflow and I want to minimize it. Formally, I have the following problem: $\text{min}_{x \in \mathcal{X}} \;\;f(x)-...
2
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1answer
553 views

Non-convex optimization without using gradient descent

If we want to optimize a convex function, we could use methods like gradient descent or computing the derivative of the function and equalize to zero so we can obtain the global minimum. But I ...