Talk:No free lunch theorem

Why exactly is it called "no free lunch" - theorem?? Just curious... Nils Sens —Preceding unsigned comment added by 121.1.48.2 (talk) 18:08, 27 February 2009 (UTC) Reply

Because the proponents wanted a fancy name for a theorem easy proven and obvious.

The short section that gives the equation doesn't define all the variables. This is terrible practice. In fact, the whole article reads like a student wrote it who didn't have more than 1 hr to try to read/understand the published papers, then had to "whip together" something in another 30min to 1 hr before turning in the research assignment. This should really be labelled as a "stub" or something that needs more work for now. -jp — Preceding unsigned comment added by 99.69.54.49 (talk) 18:49, 2 January 2012 (UTC) Reply

so what is the free lunch theorem? the article should put a Definition on top! — Preceding unsigned comment added by 80.171.6.253 (talk) 11:12, 19 December 2012 (UTC) Reply

Endorsed, the article says "the folkloric theorem is easily stated" but nowhere states it!: Noyster (talk), 13:50, 22 September 2014 (UTC) Reply

I think it's very important to define what they mean by "superiority" of one method over another. When it comes to practical considerations, in plain English most people would declare one optimization software implementation of an algorithm "superior" if it implements the same algorithm but much faster than another implementation. Similarly, if it reports when it is performing poorly and the other implementation does not, the practical minded person who just is an end user of the algorithm would claim that one implementation is "superior" over the other, and very few would challenge this. Therefore, the NFL theorems are genuinely using a definition of "superiority" in a different manner than is often used in common language, so it is important to clearly emphasize what is meant by this.

The lead currently reads:

In mathematical folklore, the "no free lunch" theorem (sometimes pluralized) of David Wolpert and William Macready appears in the 1997 "No Free Lunch Theorems for Optimization". Wolpert had previously derived no free lunch theorems for machine learning (statistical inference).

There are a couple of problems with this:

• The lead should concisely say what the NFL theorem is, not where it was published.
• According to the definition in the mathematical folklore article, if a result is published, it is not "folklore". Perhaps this article formalized and extended some pre-existing piece of mathematical folklore?

Later, we read:

The folkloric "no free lunch" (NFL) theorem is an easily stated and easily understood consequence of theorems Wolpert and Macready actually prove. It is weaker than the proven theorems, and thus does not encapsulate them.

But the folkloric NFL theorem, even if it is "easily stated", is actually never stated in this article! Can someone fix these problems? I'm afraid this is really out of my area of expertise. --Macrakis (talk) 18:28, 22 July 2016 (UTC) Reply

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Algorithm includes many deterministic proven methods to which this theorem does not apply. This theorem only applies to heuristics in specific domains. The language should be clarified to explicitly say "heuristic" rather than generic "algorithm".

For example, binary addition is an algorithm. Constant folding is an optimization algorithm. "No free lunch" applies to neither of these algorithms. 2607:5380:1240:F801:0:0:0:109 (talk) 19:31, 15 July 2025 (UTC) Reply