45 points by opti-master 1 year ago flag hide 12 comments
john_doe 1 year ago next
This is quite an interesting approach! I'm curious to see how this scales to even larger problems. Has anyone tried using this for problems with millions of variables?
hacker_alice 1 year ago next
Yes, I've used this for problems with millions of variables. It's still pretty fast compared to traditional methods. It took around 10 minutes for a problem with 10 million variables. But, certainly, there's room for improvement.
quantum_researcher 1 year ago prev next
In the quantum space, we use a variation of this method with Grover's algorithm for solving optimization problems in O(√n) time. I'm curious how this approach would compare.
curious_newbie 1 year ago prev next
Can someone explain the basics of this new approach? I'm confused about how it works without gradient descent.
john_doe 1 year ago next
Sure! Instead of relying on gradient descent, it uses a different mathematical construct called a 'Monoid'. This allows it to parallelize the computations, which provides the speed.
stanford_student 1 year ago prev next
There's a great explanation here: [link](https://en.wikipedia.org/wiki/Monoid). It essentially combines the benefits of Associativity, Identity and Invertible elements, which makes the computations faster and more efficient.
big_data_enthusiast 1 year ago prev next
I'd be interested in seeing a comparison with traditional optimization methods such as Stochastic Gradient Descent and Adam. Has anyone conducted any side-by-side tests?
code_monkey_1 1 year ago next
I have. This method significantly outperforms both SGD and Adam in large-scale optimization problems. Here's my blog with the results: [link](https://codemonkey1.github.io/large_scale_opt_tests)
ai_solutions_company 1 year ago prev next
We've integrated this new method into our large-scale optimization systems and have seen a really nice improvement. It's amazing how efficiently it solves these problems.
ml_engineer 1 year ago prev next
What are the limitations of this approach? Are there any specific use cases where traditional optimization methods would be better suited?
math_guru 1 year ago next
One limitation I can think of is that this method doesn't handle noisy data as well as robust optimization methods like Stochastic Gradient Descent. It may encounter difficulties in optimization when the objective function has a lot of noise.
numerical_methods_professor 1 year ago prev next
Although this method is quite intriguing, it's important to understand that there's no such thing as a one-size-fits-all solution to optimization problems. Depending on the data and problem domain, traditional methods might still be the better option.