[lkrubner]

Too much focus on utility functions, not enough focus on novelty functions, even though it's been proven that utility functions decline in usefulness as a search space expands. Given an infinite search space, a utility function can only find local optima, there is no global optima. In such situations, a novelty function that finds a path from one happy local optima to another happy local optima is a better bet than using a utility function.

The above paragraph is rational, and yet people who consider themselves hyper rational often ignore the truth of this. And the irony is that some of them do this for an emotional reason: they want the security that comes from believing that there is an absolute right answer. They are irrationally rational.

[hnaccy]

This feels like an opinion on how to live life dressed up in mathematical language.

[antt]

Do you have some resources on novelty functions? Google, like usual recently, is useless at finding something I haven't found before.

[paulbaumgart]

This is a good book on the subject: "Why Greatness Cannot Be Planned: The Myth of the Objective" https://www.amazon.com/Why-Greatness-Cannot-Planned-Objectiv...

[antt]

Much obliged, that book looks interesting.

[tlb]

How would you prove that?

Here's a simple counterexample to what I understand your theorem to say: consider an infinite search space: 𝕽∞ and a utility function: 1-|x|. There's a single global optimum at (0, ...), and the gradient of the utility function would find it quickly.

[pcmaffey]

You missed the point that there is no global optimum. The GP’s novelty function is optimized for novelty, that’s all.

[antt]

Counter example: R^1 with a random function. There is no algorithm that can find a global maximum other than checking every point in R^1, of which there is an uncountable number.

[salty_biscuits]

Not all cost surfaces are equally likely to occur in real problems... Also depends on the constraints, linear assignment (i.e. one job to one worker with a big matrix of cost for job to worker and you minimize the sum) has a polynomial complexity solution.

[antt]

We are not talking about real problems here. Reality is so far from linear, so path dependent, so temporally dependent that by the time you gather 10 data points to try and match some function to the function is already outdated and error prone.

This is infinitely truer for when you try and find absolute maxima and minima and not just local ones.

[tlb]

Sure, some functions have no global maximum. But the comment I replied to claimed a theorem that every utility function on infinite search space has no global maximum, which isn't true.

[shalmanese]

All models are wrong, some are useful. GP presents an interesting way of framing real life decision making processes. That it happens to not be 100% accurate in all aspects is mostly trivia.

[syndacks]

>given an infinite search space

There's no such thing.

I understand the point you're making, but these gross assumptions aren't how the world works. Reminds me of econ models with ridiculous assumptions that don't pan out when reality is a constraint.

[antt]

Doesn't matter. A 50 dimensional search space with 1000 possible values in each dimension has ~10^1700 possible states. That's a number you can't search exhaustively in the age of the universe even if you turned the whole thing into one computer. And this is not a large problem, you run into similar ones in the average gear wheel design.

[VHRanger]

The point of simplified models is to organize thoughts.

The only perfect model of reality is reality itself. Assumptions are fine if they're reasonable

[HeWhoLurksLate]

> Assumptions are fine if they're reasonable

I would assume so...

[Erlich_Bachman]

This is an interesting line of thinking, certainly valueable in some sense.

It is also a very good example of exactly what the previous post refers to: overthinking stuff.

[mysterEFrank]

ken?

[hitekker]

What an interesting perspective with a great paradoxical conclusion.

Well done.