Pareto optimization

Skill cxcscmu/SkillLearnBench/skills/b1-one-shot-claude-opus-4-6/dbscan-parameter-tuning/pareto-optimization

[COLM'26] SkillLearnBench is the first benchmark for evaluating continual learning methods that automatically generate agent skills.

Install

npx -y skills add cxcscmu/SkillLearnBench --skill pareto-optimization

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Multi-objective optimization with Pareto frontiers for finding trade-off solutions between conflicting objectives.

SKILL.md

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Pareto Frontier Computation

Definition

A point is Pareto-optimal if no other point is better in ALL objectives simultaneously.

For Maximize F1, Minimize Delta

import numpy as np

def pareto_frontier(results):
    """Find Pareto-optimal points.
    results: list of (f1, delta, ...) tuples
    Maximize f1, minimize delta.
    """
    arr = np.array([(r[0], r[1]) for r in results])
    is_pareto = np.ones(len(arr), dtype=bool)
    for i in range(len(arr)):
        if not is_pareto[i]:
            continue
        for j in range(len(arr)):
            if i == j or not is_pareto[j]:
                continue
            # j dominates i if j has >= f1 AND <= delta, with at least one strict
            if arr[j, 0] >= arr[i, 0] and arr[j, 1] <= arr[i, 1]:
                if arr[j, 0] > arr[i, 0] or arr[j, 1] < arr[i, 1]:
                    is_pareto[i] = False
                    break
    return [r for r, p in zip(results, is_pareto) if p]

Key Points