no free-lunch theorem

1. No-free-lunch (NFL) theorem

2. There are so many algorithms for
optimization, so what is the best one?
Answer: NO
Reasons that we cannot answer this question
 Complexity and diversity of real-world problems often
mean that some problems are easier to solve,
 whereas others can be extremely difficult to solve
A single method that can cope with all types of
problems.

3. No-free-lunch (NFL) theorem
 There’s no one model that works for every
problem
 Assumptions of a great model for one problem
may not hold for another problem

4. No-free-lunch (NFL) theorem
 States that there is no universal algorithm for all
problems
 Extremum - any point at which the value of a
function is largest (a maximum) or smallest (a
minimum).
If any algorithm A outperforms another algorithm
B in the search for an extremum of an objective
function, then algorithm B will outperform A over
other objective functions.

5. No-free-lunch (NFL) theorem
 NFL theorems apply to the scenario, either
deterministic or stochastic,
 a set of continuous (or discrete or mixed) parameters θ
maps the objective or cost function into a finite set

19. THANK
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