A Unified Approach to Submodular Maximization Under Noise

2025-10-23

AI Summary

This paper studies submodular function maximization under noisy value oracles—where function evaluations are accessible only via noisy queries—and addresses how to preserve approximation guarantees in such settings. We propose the first unified meta-algorithmic framework that automatically transforms any robust algorithm designed for exact oracles into a noise-resilient variant retaining its original approximation ratio. The framework is constraint-agnostic, supporting diverse settings including matroid and unconstrained constraints, without relying on specific algorithmic structures. Leveraging a synergistic design of continuous greedy and double greedy methods, our approach achieves strong robustness under persistent noise: it attains a $(1-1/e)$-approximation for monotone submodular functions, and $1/e$ (under matroid constraints) or $1/2$ (in the unconstrained setting) for non-monotone cases—substantially improving upon prior results.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Mixed Discrete/Continuous Search
• Intelligent Robots: Learning & Optimization for ROB

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

We consider the problem of maximizing a submodular function with access to a noisy value oracle for the function instead of an exact value oracle. Similar to prior work, we assume that the noisy oracle is persistent in that multiple calls to the oracle for a specific set always return the same value. In this model, Hassidim and Singer (2017) design a $(1-1/e)$-approximation algorithm for monotone submodular maximization subject to a cardinality constraint, and Huang et al (2022) design a $(1-1/e)/2$-approximation algorithm for monotone submodular maximization subject to any arbitrary matroid constraint. In this paper, we design a meta-algorithm that allows us to take any "robust" algorithm for exact submodular maximization as a black box and transform it into an algorithm for the noisy setting while retaining the approximation guarantee. By using the meta-algorithm with the measured continuous greedy algorithm, we obtain a $(1-1/e)$-approximation (resp. $1/e$-approximation) for monotone (resp. non-monotone) submodular maximization subject to a matroid constraint under noise. Furthermore, by using the meta-algorithm with the double greedy algorithm, we obtain a $1/2$-approximation for unconstrained (non-monotone) submodular maximization under noise.

Problem

• Maximizing submodular functions using noisy value oracles
• Developing meta-algorithm for noisy optimization with approximation guarantees
• Extending robust algorithms to handle persistent noise in evaluations

Innovation

• Meta-algorithm transforms robust exact algorithms for noise
• Uses measured continuous greedy for matroid-constrained optimization
• Applies double greedy for unconstrained non-monotone maximization