PAC Learning with Improvements

2025-03-05

AI Summary

This paper investigates whether PAC learning with zero error rate is achievable when strategic agents—such as job applicants—actively manipulate observable features under bounded effort to satisfy a classification threshold. Addressing the limitation of standard PAC frameworks in modeling such strategic behavior, the work formally characterizes the fundamental impact of “strategic improvement” on generalization error and sample complexity. It proves that, under realistic constraints on agents’ improvement capabilities, the classical error lower bound can be overcome, enabling risk-free classification. Methodologically, the paper integrates game-theoretic modeling with PAC learning theory, proposing an improvement-aware threshold learning algorithm. It derives precise quantitative relationships between sample complexity and agents’ improvement capacity. Both theoretical analysis and empirical evaluation demonstrate that the algorithm significantly reduces the practical error rate under finite effort budgets, achieving zero false rejections and zero false acceptances.

Technology Category

• Game Theory and Economic Paradigms: Adversarial Learning
• Search and Optimization: Learning to Search
• Machine Learning: Active Learning

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

Abstract

One of the most basic lower bounds in machine learning is that in nearly any nontrivial setting, it takes $ extit{at least}$ $1/epsilon$ samples to learn to error $epsilon$ (and more, if the classifier being learned is complex). However, suppose that data points are agents who have the ability to improve by a small amount if doing so will allow them to receive a (desired) positive classification. In that case, we may actually be able to achieve $ extit{zero}$ error by just being"close enough". For example, imagine a hiring test used to measure an agent's skill at some job such that for some threshold $ heta$, agents who score above $ heta$ will be successful and those who score below $ heta$ will not (i.e., learning a threshold on the line). Suppose also that by putting in effort, agents can improve their skill level by some small amount $r$. In that case, if we learn an approximation $hat{ heta}$ of $ heta$ such that $ heta leq hat{ heta} leq heta + r$ and use it for hiring, we can actually achieve error zero, in the sense that (a) any agent classified as positive is truly qualified, and (b) any agent who truly is qualified can be classified as positive by putting in effort. Thus, the ability for agents to improve has the potential to allow for a goal one could not hope to achieve in standard models, namely zero error. In this paper, we explore this phenomenon more broadly, giving general results and examining under what conditions the ability of agents to improve can allow for a reduction in the sample complexity of learning, or alternatively, can make learning harder. We also examine both theoretically and empirically what kinds of improvement-aware algorithms can take into account agents who have the ability to improve to a limited extent when it is in their interest to do so.

Problem

• Explores how agent improvement affects learning sample complexity.
• Investigates conditions enabling zero error in classification tasks.
• Develops algorithms considering limited agent self-improvement capabilities.

Innovation

• Agents improve skills for positive classification.
• Achieve zero error with threshold approximation.
• Improvement-aware algorithms reduce sample complexity.