Expensive combinatorial optimization of choice of subset from a large finite space
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I have a fairly general question -- what's a good (gradient-free) approach to optimizing an expensive function whose input is a choice of subset from a large finite population?
That is, I have a set $X$, an integer $n$, and a function $F: Y tomathbb{R}$, where $Y$ is the set of all $n$-element subsets of $X$ (and $|X| >> n$). Knowing nothing about F (in fact, assume it's expensive and free of any helpful structure. In the actual use case it's noisy as well, though I'm interested in a non-noisy answer too), what are good options to maximize $F$ on $Y$?
I'm in the process of doing this using a random search-style approach, where the choice of next subset is made by fixing some $m<n$ and redrawing $m$ elements of the subset at each step; I think that "number of elements not in common" constitutes a metric on $Y$, so it seems like this is sound, but it also looks naive to me. This problem seems pretty general and useful, so I'd love to be pointed to some other ideas.
combinatorics discrete-mathematics optimization numerical-methods discrete-optimization
asked Jan 18 at 21:37
rwgprwgp
12
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add a comment |
$begingroup$
I have a fairly general question -- what's a good (gradient-free) approach to optimizing an expensive function whose input is a choice of subset from a large finite population?
That is, I have a set $X$, an integer $n$, and a function $F: Y tomathbb{R}$, where $Y$ is the set of all $n$-element subsets of $X$ (and $|X| >> n$). Knowing nothing about F (in fact, assume it's expensive and free of any helpful structure. In the actual use case it's noisy as well, though I'm interested in a non-noisy answer too), what are good options to maximize $F$ on $Y$?
I'm in the process of doing this using a random search-style approach, where the choice of next subset is made by fixing some $m<n$ and redrawing $m$ elements of the subset at each step; I think that "number of elements not in common" constitutes a metric on $Y$, so it seems like this is sound, but it also looks naive to me. This problem seems pretty general and useful, so I'd love to be pointed to some other ideas.
combinatorics discrete-mathematics optimization numerical-methods discrete-optimization
asked Jan 18 at 21:37
rwgprwgp
12
$endgroup$
add a comment |
$begingroup$
I have a fairly general question -- what's a good (gradient-free) approach to optimizing an expensive function whose input is a choice of subset from a large finite population?
That is, I have a set $X$, an integer $n$, and a function $F: Y tomathbb{R}$, where $Y$ is the set of all $n$-element subsets of $X$ (and $|X| >> n$). Knowing nothing about F (in fact, assume it's expensive and free of any helpful structure. In the actual use case it's noisy as well, though I'm interested in a non-noisy answer too), what are good options to maximize $F$ on $Y$?
I'm in the process of doing this using a random search-style approach, where the choice of next subset is made by fixing some $m<n$ and redrawing $m$ elements of the subset at each step; I think that "number of elements not in common" constitutes a metric on $Y$, so it seems like this is sound, but it also looks naive to me. This problem seems pretty general and useful, so I'd love to be pointed to some other ideas.
combinatorics discrete-mathematics optimization numerical-methods discrete-optimization
asked Jan 18 at 21:37
rwgprwgp
12
$endgroup$
I have a fairly general question -- what's a good (gradient-free) approach to optimizing an expensive function whose input is a choice of subset from a large finite population?
That is, I have a set $X$, an integer $n$, and a function $F: Y tomathbb{R}$, where $Y$ is the set of all $n$-element subsets of $X$ (and $|X| >> n$). Knowing nothing about F (in fact, assume it's expensive and free of any helpful structure. In the actual use case it's noisy as well, though I'm interested in a non-noisy answer too), what are good options to maximize $F$ on $Y$?
I'm in the process of doing this using a random search-style approach, where the choice of next subset is made by fixing some $m<n$ and redrawing $m$ elements of the subset at each step; I think that "number of elements not in common" constitutes a metric on $Y$, so it seems like this is sound, but it also looks naive to me. This problem seems pretty general and useful, so I'd love to be pointed to some other ideas.
combinatorics discrete-mathematics optimization numerical-methods discrete-optimization
combinatorics discrete-mathematics optimization numerical-methods discrete-optimization
asked Jan 18 at 21:37
rwgprwgp
12
asked Jan 18 at 21:37
rwgprwgp
12
asked Jan 18 at 21:37
rwgprwgp
12
asked Jan 18 at 21:37
rwgprwgp
12
asked Jan 18 at 21:37
rwgprwgp
12
12
add a comment |
add a comment |
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