Wall Observer BTC/USD - Bitcoin price movement tracking & discussion

[adam.sandler]

Exactly. And it's not just a smart-sounding phrase—it was proven mathematically in 1995 by Wolpert & Macready. I remember referring to their paper when I was doing research back in the late 90s.

[Santa Fe Institute] William Macready, David Wolpert — No Free Lunch Theorems for Search

The full paper in PDF format can be found in the above link.

Hello. I want to give you a simple and concise summary of the article "No Free Lunch Theorems for Search".

If you need to find your key in a cluttered room your starting point depends on where the key most likely rests. No method is always the best.

The article also says that in the world of algorithms, if we examine all problems, no algorithm is better than the others in general. That is, Algorithm A is better in some problems and Algorithm B is better in others. There is no shortcut that always works; each algorithm must be suitable for its own problem.

Each problem requires its unique solution because no algorithm can be the optimal solution across all domains.

In short, there is no "free lunch" here.

Actually, the paper refers to search for maximum or minimum values of an objective function (cost or prize) of the key values f(x[j]), not to search among the keys x[j] themselves. It says that if you average over all functions, no algorithm is better than any other. This is unsurprising, since the objective function can have any general form - in particular, it can be nonlinear, which invalidates the simplest approach: first sort the keys, then the max or min is either at the beginning or at the end. Averaging over ALL possible real functions is not trivial, since it's an uncountable infinity. The proof uses some clever reasoning to avoid actually expressing the average.

On the other hand, if we search among the key values themselves, the simple sort-and-pick-first-or-last algorithm can be used and it IS better than all the others. If the keys are integers, say, we can use a radix sort, which requires a time proportional to the number n of keys. Then we instantly pick either the first or the last. Total: O(n).

If the keys are already sorted, of course, picking first or last is immediate, no matter how many there are. That's O(1). If the keys can't be sorted lexicographically (e.g., real, complex, or aggregated data types), or if you're searching among values of the objective function f(x[j]), then radix sort is no good and you first spend O(n log n) to sort, then you pick first-or-last. So, there can be free lunches if you don't have to evaluate objective functions after all.

Thanks for your detailed explanation. My aim is to discuss the main ideas within your perspective and my overall understanding of the concept.

First, my goal in writing the summary was to simplify the concept of the article for a general audience who may not be familiar with the technical details of algorithms or complex mathematics. I used the example of “finding a key in a room” to make the main idea of ​​the article, which is “no algorithm is always better than the others,” understandable to everyone.

I fully agree that the article is specifically about finding the minimum or maximum of the objective function (f(x[j])), not the keys themselves (x[j]).

 But in my summary, I tried to stay away from these technical details so that the general concept would be applicable to everyone.  Using this strategy proves beneficial for group discussions which contain members who are not experts in the topic.

Now, let’s move on to your last sentence: “There could be a free lunch if we didn’t have to evaluate the objective function.” I think there’s a flaw in your argument here. The article “No Free Lunch Theorems” says exactly that when we consider all possible objective functions (which is a very, very large and uncountable set of functions), no algorithm can be better than the others on average.

 Special sorting of keys alongside radix sort methods do not alter the fundamental operation of the principle. Why? Because when the objective function (f(x[j])) is at work, you can’t always get the best answer by simply sorting the keys or choosing the first and last. The objective function presents itself as a shape that can be highly irregular thus motivating the free lunch perspective. 

For example, suppose the keys are sorted and you can take O(1) the first or last. But if the objective function is something nonlinear and complex, this gives you no guarantee of finding the maximum or minimum. Even in scenarios where you look up keys directly (without an objective function), the paper still says that no algorithm is always better than the others if you consider all possible problems.

So I don't think you can say there is a "free lunch", because the point of the paper is that the average performance of algorithms is equal across all problems.

Thanks again for your comment . For our group a basic summary of the information works better than diving deeper into mathematical aspects of the paper.

[ChartBuddy]

Explanation
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[ChartBuddy]

Explanation
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[Krubster]

My LN node has been very active today, no idea why. I usually see these movements when the price is fluctuating heavily, that's not the case today though.

I had my 2nd biggest forward ever happening today as well. Here's the notification from my telegram bot

💰 Forwarded 0.41071514 bfx-lnd0 → LOOP.

110k sats in profit today. I wish I could keep that pace. Normally, my monthly profits varies between 200 to 300k sats.

well 3300k sats vs 300k is a nice goal.

for a months earnings.

Yeah, I wish. Now, most of my expensive sink channels are drained and need to be rebalanced.

Take that ~0.4btc forward to LOOP that I mentioned earlier. Now my node will try to rebalance that channel with a max-cost of 85% of its profits, every 5 minutes, until all the sats are on my end again.

[ChartBuddy]

Explanation
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[ChartBuddy]

Explanation
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[philipma1957]

My LN node has been very active today, no idea why. I usually see these movements when the price is fluctuating heavily, that's not the case today though.

I had my 2nd biggest forward ever happening today as well. Here's the notification from my telegram bot

💰 Forwarded 0.41071514 bfx-lnd0 → LOOP.

110k sats in profit today. I wish I could keep that pace. Normally, my monthly profits varies between 200 to 300k sats.

well 3300k sats vs 300k is a nice goal.

for a months earnings.

Yeah, I wish. Now, most of my expensive sink channels are drained and need to be rebalanced.

Take that ~0.4btc forward to LOOP that I mentioned earlier. Now my node will try to rebalance that channel with a max-cost of 85% of its profits, every 5 minutes, until all the sats are on my end again.

I think you mentioned you tie up some coins doing all this.

But if you really want access back to the btc how fast does it take to get it back?

[d_eddie]

Actually, the paper refers to <snipped out words way above my head...> So, there can be free lunches if you don't have to evaluate objective functions after all.

Well, I had lunch at the bar last week with my work buddy and he kindly covered the tab, including my Gin and Tonic with a twist...so there is that.

You weren't evaluating objective functions though... were you?
Aha, I didn't think so.
 

[d_eddie]

Hello. I want to give you a simple and concise summary of the article "No Free Lunch Theorems for Search".

So, there can be free lunches if you don't have to evaluate objective functions after all.

my goal in writing the summary was to simplify the concept of the article for a general audience

Explaining something
As simple as possible
No simpler than that




#haiku


(Thanks to A. Einstein, R. Sessions.)

[ChartBuddy]

Explanation
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[xhomerx10]

So you're telling me that if I go to Costco to shop when they have the free samples out and I gorge myself on the offerings by taking a little but of this and a little bit of that as I wander through the aisle picking up the things I went to purchase anyway can't be construed as a free lunch?  Thanks for bursting my bubble!

[ChartBuddy]

Explanation
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[philipma1957]

So you're telling me that if I go to Costco to shop when they have the free samples out and I gorge myself on the offerings by taking a little but of this and a little bit of that as I wander through the aisle picking up the things I went to purchase anyway can't be construed as a free lunch?  Thanks for bursting my bubble!

If you can sneak into Costco while not being a member and eat many snacks that is free lunch.

I do that at BJ's.  

The company not my wife

In New Jersey state of no gas self serve laws. They force all the discounters Costco's BJ's Sam's to sell gas to anyone you do not need to be a member.


They are also 16 cents a gallon cheaper then any gas station in Howell, NJ

SO I drive for a fill up grab 13-14 gallons for the sonata hybrid drive from the BJ's gas station to the parking lot and wonder in carefully eat six or seven  snacks. look at every thing get steps in go to the car.

That is a free lunch a free workout and the cheapest gas you can get for under a  20 mile drive from my house.  The cheapest gas by far.

Plus the hybrid sips gas around 45 miles to the gallon sometimes 50 if the traffic is right.

[d_eddie]

First, my goal in writing the summary was to simplify the concept of the article for a general audience

Mind your tongue, my pal
This is no general audience
The Wall Observer!





#haiku

[goldkingcoiner]

So you're telling me that if I go to Costco to shop when they have the free samples out and I gorge myself on the offerings by taking a little but of this and a little bit of that as I wander through the aisle picking up the things I went to purchase anyway can't be construed as a free lunch?  Thanks for bursting my bubble!

If you can sneak into Costco while not being a member and eat many snacks that is free lunch.

I do that at BJ's.  

Costco is free sample land. I loved going there in my childhood.

As I remember it, back in the day you needed a membership card to get in. And why not buy a 48 pack of chicken pot pies while you're at it?

[ChartBuddy]

Explanation
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[ChartBuddy]

Explanation
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[sirazimuth]

So while we are on the topic of free lunches...
At this point in my life, I derive far more of a reward providing a free lunch, rather than getting one.
Albeit, I will say if the other party insists on treating me, (like last week, as mentioned in previous post)
I let them, because I know they are thinking like me.

[Wonder Work]

My LN node has been very active today, no idea why. I usually see these movements when the price is fluctuating heavily, that's not the case today though.

I had my 2nd biggest forward ever happening today as well. Here's the notification from my telegram bot

💰 Forwarded 0.41071514 bfx-lnd0 → LOOP.

110k sats in profit today. I wish I could keep that pace. Normally, my monthly profits varies between 200 to 300k sats.

This is excellent news, as you can see the change in the market's direction while it is rising. The change is not only small for you; you have revealed that this change has also become the second largest forward.

We can't always keep it like this; market fluctuations don't always lead to such big profits. That is why we cannot achieve anything significant, but we always try to keep it. Like you, am also moving forward through a small change. I gained 700 SATS, unbelievably, during the market fluctuations a few days ago. Seeing the amount of your profit, I realized that my profit is minimal. But I'm holding on, and let's see what kind of change I can bring about in the future.

The time to gain more seats is yet to come. Go ahead, and I hope to hear about more big profits from you.

[ChartBuddy]

Explanation
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