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Fast pareto-front calculation for 2D #687

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merged 14 commits into from
Dec 21, 2023
Merged

Fast pareto-front calculation for 2D #687

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bd69232
Fast pareto-front calculation for 2D
contramundum53 Nov 8, 2023
e3c1d74
Fix bug in getIsDominatedTrialND
contramundum53 Nov 10, 2023
aba648e
Code fix
contramundum53 Nov 10, 2023
becaff1
Update optuna_dashboard/ts/components/GraphParetoFront.tsx
contramundum53 Nov 29, 2023
4ef4aa1
Update optuna_dashboard/ts/components/GraphParetoFront.tsx
contramundum53 Nov 29, 2023
b0f66b3
Update optuna_dashboard/ts/components/GraphParetoFront.tsx
contramundum53 Nov 29, 2023
5b4f0bb
Update optuna_dashboard/ts/components/GraphParetoFront.tsx
contramundum53 Nov 29, 2023
8ebed9b
fix pareto-front
contramundum53 Dec 14, 2023
422ffd2
rename variables
contramundum53 Dec 14, 2023
01ecc55
rename functions
contramundum53 Dec 14, 2023
a9b23ae
remove unnecessary condition
contramundum53 Dec 14, 2023
29d44ab
Fix bug
contramundum53 Dec 14, 2023
4315c9d
Update optuna_dashboard/ts/components/GraphParetoFront.tsx
contramundum53 Dec 20, 2023
1203501
Rename variable
contramundum53 Dec 20, 2023
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65 changes: 53 additions & 12 deletions optuna_dashboard/ts/components/GraphParetoFront.tsx
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Original file line number Diff line number Diff line change
Expand Up @@ -165,6 +165,58 @@ const makeMarker = (
}
}

const getIsDominatedTrialND = (normalizedValues: number[][]) => {
// Fallback for straight-forward pareto front algorithm (O(N^2) complexity).
const dominatedTrials: boolean[] = []
normalizedValues.forEach((values0: number[]) => {
const dominated = normalizedValues.some((values1: number[]) => {
if (values0.every((value0: number, k: number) => values1[k] === value0)) {
return false
}
return values0.every((value0: number, k: number) => values1[k] <= value0)
})
dominatedTrials.push(dominated)
})
return dominatedTrials
}

const getIsDominatedTrial2D = (normalizedValues: number[][]) => {
// Fast pareto front algorithm (O(N log N) complexity).
const sorted = normalizedValues
.map((values, i) => [values[0], values[1], i])
.sort()
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@nabenabe0928 nabenabe0928 Dec 13, 2023 •
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const values = [[2, 2], [3, 2], [10, 2]]
const sortedValues = values.map((v, i) => [v[0], v[1], i]).sort()
console.log(sortedValues)

Output

[ [ 10, 2, 2 ], [ 2, 2, 0 ], [ 3, 2, 1 ] ]

So you still need to change the comparator inside sort().

Suggested change
.sort()
.sort((a, b) => a[0] !== b[0] ? a[0] - b[0] : a[1] - b[1])

Output after the change:

[ [ 2, 2, 0 ], [ 3, 2, 1 ], [ 10, 2, 2 ] ]

let minValue1 = sorted[0][1]
const dominatedTrials: boolean[] = new Array(normalizedValues.length).fill(
true
)

sorted.forEach((values) => {
if (values[1] <= minValue1) {
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This condition is buggy when the values between trials are the same.

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In that case, both trials should be considered undominated.

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@nabenabe0928 nabenabe0928 Dec 13, 2023 •
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Now given a sequence of 2D vectors $\{(a_n, b_n)\}_{n=1}^N$ such that $a_1 \leq a_2 \leq \dots \leq a_N$ and $b_i \leq b_j$ for all $\{(i, j) \in [N] \times [N] \mid a_i = a_j, i &lt; j\}$ where $[N] \coloneqq \{1,2,\dots,N\}$, the condition here is a bit strange when the equality holds.

For example, $a_i \leq a_j$ holds from the assumption and we now assume that $b_i = b_j$.
As mentioned above, let's assume that $a_i = a_j$ and $b_i = b_j$ do not dominate each other.
However, $a_i &lt; a_j$ and $\min_{n \in [i]} b_i = b_j$ could still hold.
It means that there could exist $(a_i, b_i)$ such that $a_i &lt; a_j$ and $b_i \leq b_j$, which weakly dominates $(a_j, b_j)$.

Btw, I guessed you are trying to get "weak dominance" from getIsDominatedTrialND.

Maybe I am wrong, if so, correct me please!

const normalizedValues = [[0, 1], [1, 1], [2, 1]]

const getIsDominatedTrial2D = (normalizedValues: number[][]) => {
    const sortedValues = normalizedValues
      .map((values, i) => [values[0], values[1], i])
      .sort((a, b) => a[0] !== b[0] ? a[0] - b[0] : a[1] - b[1])
    let minValue1 = sortedValues[0][1]
    const dominatedTrials: boolean[] = new Array(normalizedValues.length).fill(
      true
    )
    sortedValues.forEach((values) => {
      if (values[1] <= minValue1) {
        dominatedTrials[values[2]] = false
        minValue1 = values[1]
      }
    })
    return dominatedTrials
}

console.log(getIsDominatedTrial2D(normalizedValues))

Output

[ false, false, false ]

I guess (if we need weakly dominated trials) what we want is:

[ false, true, true ]

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@nabenabe0928 nabenabe0928 Dec 13, 2023 •
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Quick solution to this is the following:

const normalizedValues = [[0, 1], [1, 1], [2, 1]]

const getIsDominatedTrial2D = (normalizedValues: number[][]) => {
    const sortedValues = normalizedValues
      .map((values, i) => [values[0], values[1], i])
      .sort((a, b) => a[0] !== b[0] ? a[0] - b[0] : a[1] - b[1])
    let minValue1 = sortedValues[0][1]
    let latestParetoSolution = sortedValues[0].slice(0, 2)
    const dominatedTrials: boolean[] = new Array(normalizedValues.length).fill(
      true
    )
    sortedValues.forEach((values) => {
      if (values[1] < minValue1 || latestParetoSolution.every((v, i) => v === values[i])) {
        dominatedTrials[values[2]] = false
        minValue1 = values[1]
        latestParetoSolution = values.slice(0, 2)
      }
    })
    return dominatedTrials
}

console.log(getIsDominatedTrial2D(normalizedValues))

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See https://github.com/optuna/optuna/blob/master/optuna/study/_multi_objective.py#L101. Optuna uses weakly dominates for comparison. It seems that @nabenabe0928 is correct.

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Thank you for pointing out. My statement is incorrect and @nabenabe0928's one is correct, I think.

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@nabenabe0928 nabenabe0928 Dec 14, 2023 •
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The new modification fails with the following case.

const normalizedValues = [[0, 1], [1, 2], [2, 1], [3, 0], [3, 0]]

We get:

[ false, true, false, false, false ]

But we would like to have:

[ false, true, true, false, false ]

I think the suggestion here is sufficient.

dominatedTrials[values[2]] = false
minValue1 = values[1]
}
})
return dominatedTrials
}

const getIsDominatedTrial1D = (normalizedValues: number[][]) => {
const best_value = Math.min(...normalizedValues.map((values) => values[0]))
return normalizedValues.map((value) => value[0] !== best_value)
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Suggested change
return normalizedValues.map((value) => value[0] !== best_value)
return normalizedValues.map((values) => values[0] !== best_value)

}

const getIsDominatedTrial = (normalizedValues: number[][]) => {
if (normalizedValues.length === 0) {
return []
}
if (normalizedValues[0].length === 1) {
return getIsDominatedTrial1D(normalizedValues)
} else if (normalizedValues[0].length === 2) {
return getIsDominatedTrial2D(normalizedValues)
} else {
return getIsDominatedTrialND(normalizedValues)
}
}

const plotParetoFront = (
study: StudyDetail,
objectiveXId: number,
Expand Down Expand Up @@ -218,18 +270,7 @@ const plotParetoFront = (
}
})

const dominatedTrials: boolean[] = []
normalizedValues.forEach((values0: number[], i: number) => {
const dominated = normalizedValues.some((values1: number[], j: number) => {
if (i === j) {
return false
}
return values0.every((value0: number, k: number) => {
return values1[k] <= value0
})
})
dominatedTrials.push(dominated)
})
const dominatedTrials: boolean[] = getIsDominatedTrial(normalizedValues)

const plotData: Partial<plotly.PlotData>[] = [
makeScatterObject(
Expand Down