5 ms·

no such thing as free lunch - https://en.m.wikipedia.org/wiki/No_free_lunch_theorem https://en.m.wikipedia.org/wiki/No_free_lunch_theorem

tomrod 4y ago
We really need to revise this to say "there is no global free lunch." You can and often do get local free lunches.
- medo-bear 4y ago
  the question was about "objective that works well in practice for any task". thats pretty global in my books
  - karpierz 4y ago
    If you take "any task" to mean literally any conceivable task, then sure. If you take "any task" to mean "any practical task" or "any task a human would conceivably want to have done", then no free lunch doesn't apply.
  - tbalsam 4y ago
    Another way of looking at karpierz's comment is through the incompressibility of pure noise at scale. As soon as some infinitely generated sort of noise is from some subset of possible noise, there is indeed (AFAIK) some kind of an ideal estimator that appropriately compresses that noise source with no bias and less entropy that the full space of possible noise. I hope this shines an additional alternative light on the topic.
    - mitthrowaway2 4y ago
      I deeply suspect that this has more than surface similarities with the observation that you cannot extract work from a uniform heat bath, but you can extract work from a temperature gradient. There's probably not much an intelligence could learn to predict about its future environment living inside the core of the sun, even if it could withstand those temperatures -- just randomness everywhere in every direction. But on Earth, with the sun shining in and the coolness of space behind us, there are a lot of causal relationships that can be compressed to make useful predictions.
      - tbalsam 4y ago
        The flow of entropy is a marvelous, strange, bizarre, and beautiful thing.
  - nl 4y ago
    The "in practice" thing is pretty important. In the no-free-lunch version of the world memory is infinite, all mathematical operations are the same performance wise and things the size of your floating point numbers are ignored. But "in practice" these things matter a lot. For practical purposes the no-free-lunch theorem is a distraction, or at best something to encourage people to try alternate approaches.
    - tbalsam 4y ago
      A bumpy landscape indeedy.
tbalsam 4y ago
The most common statement I make is about the misapplication of the NFL. This is not an appropriate use of the NFL. The original commenter is asking about a general solution that will work well for all problems presented at it. The NFL details fine-grained tradeoffs in _ideal solutions_ for specific traits in certain areas. Additionally, we're not operating in an unbiased space here, so trivially there is a best estimator without bias. So by that very fact alone the NFL is invalidated in terms of the method it is being applied in here. This is something I feel frustrated seeing a lot of younger people entering the field do (not saying you are young or new, it's just the trend). If this was the case in this kind of a way we never would have gotten beyond MLPs. Yes, indeed there is in fact a set of general solutions that works roughly well over everything and is biased towards the situations where people will need it the most. No, it will likely not be the technically best performing solution. What the OP is looking for I believe is convenience, stability, and reliably good performance. Hence, the NFL is not applicable or relevant to this matter in the way it is being used.
- medo-bear 4y ago
  > The original commenter is asking about a general solution that will work well for all problems presented at it solution of what? nfl is actually pretty simple. it says that if you have a black box optimization technique then it will perform no better than a random function. a black box function is one that assumes no domain knowledge on the problem it is being applied to. since the op used the term 'any task' im pretty sure it applies to his statement otherwise, please give me an example of an algorithm that goes against what im saying
  - tbalsam 4y ago
    The primary poster with a high degree of likelihood means "an reasonable human task". Unless in the future we need models that make summarized briefs from hyperintelligent dogs that communicate only in a language embedded in the Fourier Domain with an XOR-like mapping and zero redundancy as well as summarize a news article _with exactly equal probability to each other in the same model_, then the NFL theorem does not generally apply. Because there's bias. If it helps, put another way, the previous poster isn't being literal. They're using vernacular meaning most expected outcomes, i e. Generally whatever minimizes the empirical risk via a log likelihood criterion. The expected nonliterality of English at all of the wrong times can be quite bizzare.

tomrod 4y ago

We really need to revise this to say "there is no global free lunch." You can and often do get local free lunches.

medo-bear 4y ago
the question was about "objective that works well in practice for any task". thats pretty global in my books
- karpierz 4y ago
  If you take "any task" to mean literally any conceivable task, then sure. If you take "any task" to mean "any practical task" or "any task a human would conceivably want to have done", then no free lunch doesn't apply.
- tbalsam 4y ago
  Another way of looking at karpierz's comment is through the incompressibility of pure noise at scale. As soon as some infinitely generated sort of noise is from some subset of possible noise, there is indeed (AFAIK) some kind of an ideal estimator that appropriately compresses that noise source with no bias and less entropy that the full space of possible noise. I hope this shines an additional alternative light on the topic.
  - mitthrowaway2 4y ago
    I deeply suspect that this has more than surface similarities with the observation that you cannot extract work from a uniform heat bath, but you can extract work from a temperature gradient. There's probably not much an intelligence could learn to predict about its future environment living inside the core of the sun, even if it could withstand those temperatures -- just randomness everywhere in every direction. But on Earth, with the sun shining in and the coolness of space behind us, there are a lot of causal relationships that can be compressed to make useful predictions.
    - tbalsam 4y ago
      The flow of entropy is a marvelous, strange, bizarre, and beautiful thing.
- nl 4y ago
  The "in practice" thing is pretty important. In the no-free-lunch version of the world memory is infinite, all mathematical operations are the same performance wise and things the size of your floating point numbers are ignored. But "in practice" these things matter a lot. For practical purposes the no-free-lunch theorem is a distraction, or at best something to encourage people to try alternate approaches.
  - tbalsam 4y ago
    A bumpy landscape indeedy.

tbalsam 4y ago

The most common statement I make is about the misapplication of the NFL. This is not an appropriate use of the NFL. The original commenter is asking about a general solution that will work well for all problems presented at it. The NFL details fine-grained tradeoffs in _ideal solutions_ for specific traits in certain areas. Additionally, we're not operating in an unbiased space here, so trivially there is a best estimator without bias. So by that very fact alone the NFL is invalidated in terms of the method it is being applied in here. This is something I feel frustrated seeing a lot of younger people entering the field do (not saying you are young or new, it's just the trend). If this was the case in this kind of a way we never would have gotten beyond MLPs. Yes, indeed there is in fact a set of general solutions that works roughly well over everything and is biased towards the situations where people will need it the most. No, it will likely not be the technically best performing solution. What the OP is looking for I believe is convenience, stability, and reliably good performance. Hence, the NFL is not applicable or relevant to this matter in the way it is being used.

medo-bear 4y ago
> The original commenter is asking about a general solution that will work well for all problems presented at it solution of what? nfl is actually pretty simple. it says that if you have a black box optimization technique then it will perform no better than a random function. a black box function is one that assumes no domain knowledge on the problem it is being applied to. since the op used the term 'any task' im pretty sure it applies to his statement otherwise, please give me an example of an algorithm that goes against what im saying
- tbalsam 4y ago
  The primary poster with a high degree of likelihood means "an reasonable human task". Unless in the future we need models that make summarized briefs from hyperintelligent dogs that communicate only in a language embedded in the Fourier Domain with an XOR-like mapping and zero redundancy as well as summarize a news article _with exactly equal probability to each other in the same model_, then the NFL theorem does not generally apply. Because there's bias. If it helps, put another way, the previous poster isn't being literal. They're using vernacular meaning most expected outcomes, i e. Generally whatever minimizes the empirical risk via a log likelihood criterion. The expected nonliterality of English at all of the wrong times can be quite bizzare.