LIPIcs.ITCS.2025.46.pdf
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Data-Driven Solution Portfolios
Authors
Marina Drygala 
,
Silvio Lattanzi ,
Andreas Maggiori ,
Miltiadis Stouras ,
Ola Svensson ,
Sergei Vassilvitskii
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Volume:
16th Innovations in Theoretical Computer Science Conference (ITCS 2025)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: Innovations in Theoretical Computer Science Conference (ITCS) - License:
Creative Commons Attribution 4.0 International license
- Publication Date: 2025-02-11
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Marina Drygala, Silvio Lattanzi, Andreas Maggiori, Miltiadis Stouras, Ola Svensson, and Sergei Vassilvitskii. Data-Driven Solution Portfolios. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 46:1-46:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)
https://doi.org/10.4230/LIPIcs.ITCS.2025.46
Abstract
In this paper, we consider a new problem of portfolio optimization using stochastic information. In a setting where there is some uncertainty, we ask how to best select k potential solutions, with the goal of optimizing the value of the best solution. More formally, given a combinatorial problem Π, a set of value functions 𝒱 over the solutions of Π, and a distribution 𝒟 over 𝒱, our goal is to select k solutions of Π that maximize or minimize the expected value of the best of those solutions. For a simple example, consider the classic knapsack problem: given a universe of elements each with unit weight and a positive value, the task is to select r elements maximizing the total value. Now suppose that each element’s weight comes from a (known) distribution. How should we select k different solutions so that one of them is likely to yield a high value? In this work, we tackle this basic problem, and generalize it to the setting where the underlying set system forms a matroid. On the technical side, it is clear that the candidate solutions we select must be diverse and anti-correlated; however, it is not clear how to do so efficiently. Our main result is a polynomial-time algorithm that constructs a portfolio within a constant factor of the optimal.
Subject Classification
ACM Subject Classification
- Theory of computation → Design and analysis of algorithms
Keywords
- solution portfolios
- data-driven algorithm design
- matroids
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References
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