[Optimization] Recommended line search algorithms for non-convex problems?

So I’m optimizing a non-convex objective by gradient descent, and I’m trying to figure out a good way to adaptively choose a step size.

Right now I’m using a fixed step size, but this ‘dumb’ approach has the advantage of not being as susceptible to being caught in local minima. I tried backtracking, and while backtracking ensures monotonic descent for smooth functions, I get further trapped in local minima.

I was thinking I could try backtracking except still permit a step as long as its <= 150%*currentValue or something like that, but I was curious if you guys had suggestions.

I assumed this was a common obvious problem people have, but my googling / google scholar’ing hasn’t been fruitful.

Thoughts?

Thanks.

submitted by Nevin Manimala Nevin Manimala /u/TissueReligion
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Embarrassing mistakes due to the system 1 thinking

I’m referring to those mistakes which can be avoided IF we pay attention to what we’re saying, not those which occur because of a fundamental misunderstanding. See the following:

https://en.wikipedia.org/wiki/Thinking,_Fast_and_Slow

I’m not going to throw anyone under the bus (neither my peers nor myself!), but here are some real examples:

– Forgetting that you’re working with a field of finite characteristic (and dividing by zero);

– Applying dimension formula for vector spaces to more than two vector spaces, which is formally similar to inclusion-exclusion principle (I haven’t made this mistake myself, but I admit I was very prone to making it!);

– 57 is a prime number (ok, this one is very famous);

– Confusing isomorphism with equality: This can be due a fundamental misunderstanding, but from my experience, this is usually hidden in a more complicated fallacious argument, and can be avoided when we DO pay attention.

I find these kind of mistakes quite interesting, and I’d like to hear about your examples.

submitted by Nevin Manimala Nevin Manimala /u/chasesdiagrams
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Beginner maths student, objects dont speed up with more distance under gravity.

So basically I’m a newb but I’m studying objects under gravity. Here’s the textbook understanding that I disagree with.

“objects speed up as they fall when given more distance + time e.g

in 1 second a ball falls 4.9 metres

in 2 seconds a ball falls 19.6 metres (4.9 x 2 squared metres)

in 3 seconds a ball falls 44.1 metres (4.9 x 3 squared metres)

in 4 seconds a ball falls 78.4 metres (4.9 x 4 squared metres)”

Here’s why I disagree;

I subtracted the 1st second distance from the 2nd seconds distance e.g 19.6-4.9=14.7

I subtracted the distance of the 2nd second 14.7 (removing the 1st second 4.9) from the 3rd second = 44.1-14.7=29.4. I then subtracted the 1st second distance from the distance travelled in the 3rd second= 29.4-4.9=24.5

And I did the same to the 4th second swell giving me the actual distances of the seconds when isolated from the other seconds, e.g

Seconds = distance in metres

1=4.9

2=14.7

3=24.5

4=34.3

There is a constant distance here e.g

4.9+ 9.8=14.7

14.7+9.8=24.5

24.5+9.8=34.3

The constant distance travelled in metres by the ball is 9.8 metres under gravity. So objects dont get faster?

submitted by Nevin Manimala Nevin Manimala /u/Syyrus
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Applications of math in your daily life?

One time I was on a trip with a group of 10 friends, and whenever we moved from one place to another, I’d count them to make sure everyone was there. But I wouldn’t count them explicitly (as in outloud); instead, I’d biject them with my fingers.

E.g. if there were 4 grouped together, I’d point 4 of my fingers towards them, then make a mental note that these fingers were “taken”, then continue counting the others with the remaining fingers. (The bijection needn’t be the same every time)

How do you apply math in your day-to-day life?

submitted by Nevin Manimala Nevin Manimala /u/Sarcon5673
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How to represent the percentage change in a table?

I don’t know if this falls strictly under the statistics about Nevin Manimala, but I have no idea where else to ask. I’ll try to explain this as simple as possible: let’s say that I have the following table

Observed variable Placebo Treatment
Some name 325 108

OK, while i have real data and naming, as well as around 14 rows in the real example, this is enough to ask the question. Now, taking the numbers into the consideration, we can see that there is a 66.77% decrease in the case of the treatment, which is good! I would like now to add that percentage into the table, but I have no idea what’s the correct way to report this data along with the raw numbers. Also, I don’t know how to exactly name the column (percentage change? percentage decrease?)

Thanks for any suggestions!

submitted by Nevin Manimala Nevin Manimala /u/JavascriptFanboy
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Gen-Z Yellow Color blocking Jewellery Trends

It is vibrant. It is cheerful. It’s zesty, fruity and loads of fun. And it is the colour that is perking up chic runways and pages of fashion bibles across the world. If you haven’t guessed already, we are talking about Gen Z’s yellow, the new black!

Click for more: https://blog.voylla.com

submitted by Nevin Manimala Nevin Manimala /u/fashionvoylla
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Free Unit Circle Poster worth printing?

Hey Redditors, I am a poor-ass student and I can’t afford a god damn print-out of a unit circle poster. Are there any free ones out there that are big enough and contain enough info? I need it for my studies, as nothing else is working to help me memorise these pie values.

submitted by Nevin Manimala Nevin Manimala /u/Ravedogga
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Probability: Helping a Game Designer Out

Hey Everyone, I’m working on a game that involves multiple players rolling two six sided dice multiple time and recording the result (Craps like RPG). Currently I’m trying to come up with game mechanics that require a particular combo of numbers or numbers to not be rolled.

My question: When rolling two dice, what’s the chance of rolling a 4, 5, 6, 8, 9, and 10 before a 7 is rolled?

I figure it’s going to be a very low chance, but I just can’t get my mind around complicated sets like this and knowing the exact value will help me balance my game. Thank you very much for any help solving or answering this question.

submitted by Nevin Manimala Nevin Manimala /u/EMD_2
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Sold my s2000 today:(

Got a 178k mile s2000 a few months ago. I put about 2500 miles on it. Drove it a few months, autocrossed it, drove to the top of the highest road in America with it, drove it on some amazing Colorado mountain roads and had a damn blast with it. But, as with every car I’ve owned (Miata (5x), 996, wrangler, vw r32 and boxster) I was able to sell it for a little more than I paid so I let it go to its next owner.

I literally drove it til the wheels fell off and let it go after that

Good times. I’ll miss that car. I’ll get another s2000 when I can afford a low mile example

pics of my beat Honda s2000

submitted by Nevin Manimala Nevin Manimala /u/Creativeusername833
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