Active Value Querying to Minimize Additive Error in Subadditive Set Function Learning

2026-02-26

AI Summary

This work addresses the problem of efficiently approximating an unknown subadditive set function when only a subset of its values can be queried, aiming to minimize additive error and reduce optimization uncertainty caused by missing data. We present the first systematic analysis of the tightest possible lower and upper completion bounds for subadditive functions under additive error. Building on this theoretical foundation, we propose a prior-informed active querying strategy that dynamically selects the most informative subsets to query in both offline and online settings. Our theoretical analysis characterizes the completion error bounds across different function classes, and extensive experiments demonstrate that the proposed algorithm significantly outperforms baseline methods, effectively narrowing the gap in completion error.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Heuristic Search
• Machine Learning: Active Learning

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Subadditive set functions play a pivotal role in computational economics (especially in combinatorial auctions), combinatorial optimization or artificial intelligence applications such as interpretable machine learning. However, specifying a set function requires assigning values to an exponentially large number of subsets in general, a task that is often resource-intensive in practice, particularly when the values derive from external sources such as retraining of machine learning models. A~simple omission of certain values introduces ambiguity that becomes even more significant when the incomplete set function has to be further optimized over. Motivated by the well-known result about inapproximability of subadditive functions using deterministic value queries with respect to a multiplicative error, we study a problem of approximating an unknown subadditive (or a subclass of thereof) set function with respect to an additive error -- i. e., we aim to efficiently close the distance between minimal and maximal completions. Our contributions are threefold: (i) a thorough exploration of minimal and maximal completions of different classes of set functions with missing values and an analysis of their resulting distance; (ii) the development of methods to minimize this distance over classes of set functions with a known prior, achieved by disclosing values of additional subsets in both offline and online manner; and (iii) empirical demonstrations of the algorithms'performance in practical scenarios.

Problem

• subadditive set function
• active value querying
• additive error
• function completion
• incomplete data

Innovation

• subadditive set functions
• active value querying
• additive error minimization
• function completion
• combinatorial optimization