“It is not clear this can be shown to be true. ‘Improvement’ depends on what is valued, and what the context permits. In the real world, the value of an algorithm depends on not only its abstract mathematical properties but the costs of implementing it in an environment for which we have only imperfect knowledge.”
Eliezer specifically noted this in the post:
“Sometimes it is too expensive to take advantage of all the knowledge that we could, in theory, acquire from previous tests. Moreover, a complete enumeration or interval-skipping algorithm would still end up being stupid. In this case, computer scientists often use a cheap pseudo-random algorithm, because the computational cost of using our knowledge exceeds the benefit to be gained from using it. This does not show the power of randomness, but, rather, the predictable stupidity of certain specific deterministic algorithms on that particular problem.”
“It is not clear this can be shown to be true. ‘Improvement’ depends on what is valued, and what the context permits. In the real world, the value of an algorithm depends on not only its abstract mathematical properties but the costs of implementing it in an environment for which we have only imperfect knowledge.”
Eliezer specifically noted this in the post:
“Sometimes it is too expensive to take advantage of all the knowledge that we could, in theory, acquire from previous tests. Moreover, a complete enumeration or interval-skipping algorithm would still end up being stupid. In this case, computer scientists often use a cheap pseudo-random algorithm, because the computational cost of using our knowledge exceeds the benefit to be gained from using it. This does not show the power of randomness, but, rather, the predictable stupidity of certain specific deterministic algorithms on that particular problem.”