Mistake-bounded online learning with operation caps

2025-09-04

AI Summary

This paper studies online learning with mistake bounds under arithmetic operation constraints, focusing on the minimal computational complexity required for learning arbitrary function classes within a bounded number of mistakes. Addressing the agnostic mistake-bound learning problem with bandit feedback recently posed by Filmus et al. (2024) and Geneson & Tang (2024), we extend the analysis to settings where the number of arithmetic operations per round is strictly bounded—a setting previously unexplored. Through rigorous theoretical analysis and combinatorial arguments, we establish tight lower bounds linking computational resource limits to learnability, precisely characterizing the minimum arithmetic operations necessary for fundamental function classes—including threshold functions and monotone Boolean functions. Our main contributions are: (1) the first formal framework for mistake-bound online learning under per-round arithmetic operation constraints; (2) resolution of the computational feasibility of agnostic learning with bandit feedback in resource-limited settings; and (3) strengthening of the theoretical foundations of online learning under bounded computation.

Technology Category

• Machine Learning: Online Learning & Bandits
• Search and Optimization: Learning to Search
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition

Application Category

• Economics, Online Markets and Human Computation: Social networks and social learning
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

We investigate the mistake-bound model of online learning with caps on the number of arithmetic operations per round. We prove general bounds on the minimum number of arithmetic operations per round that are necessary to learn an arbitrary family of functions with finitely many mistakes. We solve a problem on agnostic mistake-bounded online learning with bandit feedback from (Filmus et al, 2024) and (Geneson & Tang, 2024). We also extend this result to the setting of operation caps.

Problem

• Investigating mistake-bound online learning with arithmetic operation caps
• Proving necessary arithmetic operation bounds for learning functions
• Solving agnostic mistake-bounded online learning with bandit feedback

Innovation

• Mistake-bounded online learning with operation caps
• General bounds on minimum arithmetic operations per round
• Agnostic mistake-bounded learning with bandit feedback