MENTAL MODEL · M2035

No Free Lunch Theorem

TechnicalHigh supportMathematics

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Version 1.0.0 · Updated 2026-07-30

CORE DEFINITION

In the set of all possible problems, no optimization algorithm (whether evolutionary, gradient descent, or random search) can perform better than any other algorithm. If an algorithm performs well on some problems, it must perform poorly on others. -

SCAFFOLDING EFFECT

psychology

Reduce cognitive load

The crusher of universal remedies. - This is a mathematical proof that negates 'universal methodology'. Do not blindly believe that a single mental model (such as 'first principles' or 'dialectics') can solve all problems. There is no best strategy, only the strategy that best fits the current context. The hallmark of professionalism is having an algorithm for different scenarios.

anchor

Anchor fast decisions

On the average distribution of all possible problems, the expected performance of any two optimization algorithms is equal—if one algorithm excels on some problems, it must be inferior on others. Because there is no universal algorithm that is optimal for all problems, performance comes from matching the problem structure rather than the algorithm itself.

MINIMUM ACTION

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Practice this model in one real situation:

When selecting a method, first diagnose the problem structure (smooth/discrete/noisy), then match the algorithm/model
build a 'method toolbox' rather than believing in a single universal method. When evaluating a new method, ask 'On which type of problems is it better, and on which is it worse?'

Check to track your progress (stored locally)

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Source support: Explicit

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en.wikipedia.orghttps://en.wikipedia.org/wiki/No_free_lunch_theoremZH · Explicit
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