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arXiv · 2412.00717

Data-Driven Solution Portfolios

Marina Drygala·Silvio Lattanzi·Andreas Maggiori·Miltiadis Stouras·Ola Svensson·Sergei Vassilvitskii
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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 $\Pi$, a set of value functions $V$ over the solutions of $\Pi$, and a distribution $D$ over $V$, our goal is to select $k$ solutions of $\Pi$ that maximize or minimize the expected value of the {\em 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.

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Marina Drygala, Silvio Lattanzi, Andreas Maggiori, Miltiadis Stouras, Ola Svensson, Sergei Vassilvitskii. 2024-12-01. Data-Driven Solution Portfolios. https://arxiv.org/abs/2412.00717

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