Systematic Parameter Decision in Approximate Model Counting

2025-04-08

AI Summary

ApproxMC, a hashing-based approximate model counter, suffers from suboptimal internal parameter configurations that hinder its practical scalability. Method: We propose the first parameter optimization framework for ApproxMC with PAC-correctness guarantees, formalizing parameter selection as a decoupled optimization problem—separating correctness verification from performance maximization—and deriving a minimal, efficiently searchable parameter expression. Our approach integrates PAC learning theory, hash function design, and constrained optimization modeling to maximize runtime efficiency while provably ensuring (ε, δ)-approximation accuracy. Contribution/Results: Experimental evaluation demonstrates that our method accelerates the latest ApproxMC by 1.6–2.4× across diverse ε-tolerance settings, significantly improving real-world scalability without compromising theoretical correctness guarantees.

Technology Category

• Search and Optimization: Learning to Search
• Machine Learning: Optimization
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

This paper proposes a novel approach to determining the internal parameters of the hashing-based approximate model counting algorithm $mathsf{ApproxMC}$. In this problem, the chosen parameter values must ensure that $mathsf{ApproxMC}$ is Probably Approximately Correct (PAC), while also making it as efficient as possible. The existing approach to this problem relies on heuristics; in this paper, we solve this problem by formulating it as an optimization problem that arises from generalizing $mathsf{ApproxMC}$'s correctness proof to arbitrary parameter values. Our approach separates the concerns of algorithm soundness and optimality, allowing us to address the former without the need for repetitive case-by-case argumentation, while establishing a clear framework for the latter. Furthermore, after reduction, the resulting optimization problem takes on an exceptionally simple form, enabling the use of a basic search algorithm and providing insight into how parameter values affect algorithm performance. Experimental results demonstrate that our optimized parameters improve the runtime performance of the latest $mathsf{ApproxMC}$ by a factor of 1.6 to 2.4, depending on the error tolerance.

Problem

• Optimizing internal parameters for ApproxMC algorithm efficiency
• Ensuring PAC correctness in hashing-based model counting
• Replacing heuristic methods with a systematic optimization framework

Innovation

• Formulates parameter decision as optimization problem
• Separates algorithm soundness and optimality concerns
• Uses basic search for simple optimization problem