Learning from Equivalence Queries, Revisited

TL;DR

This paper revisits the classical learning from equivalence queries model, proposing a less adversarial environment called symmetric counterexample generators, and provides tight bounds on learning rounds under full-information and bandit feedback.

Contribution

It introduces the symmetric counterexample generator class, broadening the applicability of the model, and derives tight bounds for learning efficiency in this setting.

Findings

Tight bounds on the number of learning rounds under full-information feedback.

Tight bounds on the number of learning rounds under bandit feedback.

A game-theoretic analysis combining adaptive weighting and minimax methods.

Abstract

Modern machine learning systems, such as generative models and recommendation systems, often evolve through a cycle of deployment, user interaction, and periodic model updates. This differs from standard supervised learning frameworks, which focus on loss or regret minimization over a fixed sequence of prediction tasks. Motivated by this setting, we revisit the classical model of learning from equivalence queries, introduced by Angluin (1988). In this model, a learner repeatedly proposes hypotheses and, when a deployed hypothesis is inadequate, receives a counterexample. Under fully adversarial counterexample generation, however, the model can be overly pessimistic. In addition, most prior work assumes a \emph{full-information} setting, where the learner also observes the correct label of the counterexample, an assumption that is not always natural. We address these issues by restricting the environment to a broad class of less adversarial counterexample generators, which we call \emph{symmetric}. Informally, such generators choose counterexamples based only on the symmetric difference between the hypothesis and the target. This class captures natural mechanisms such as random counterexamples (Angluin and Dohrn, 2017; Bhatia, 2021; Chase, Freitag, and Reyzin, 2024), as well as generators that return the simplest counterexample according to a prescribed complexity measure. Within this framework, we study learning from equivalence queries under both full-information and bandit feedback. We obtain tight bounds on the number of learning rounds in both settings and highlight directions for future work. Our analysis combines a game-theoretic view of symmetric adversaries with adaptive weighting methods and minimax arguments.