Sequence prediction under a lying oracle

2026-08-14

AI Summary

This study addresses the computational complexity challenges inherent in m-ary sequence prediction under lying oracles by proposing a novel online learning algorithm based on comparison queries. The proposed method effectively operates within both stochastic and adversarial environments, establishing logarithmic upper bounds on regret through a rigorous theoretical analysis framework. By resolving critical theoretical bottlenecks associated with this setting, the research significantly optimizes prediction performance while preserving essential information integrity. Consequently, this work provides a solution that combines theoretical depth with practical utility for sequence prediction tasks in complex noisy environments, offering robust guarantees against unreliable feedback mechanisms.

Abstract

We consider the problem of sequential prediction of an $m$-ary sequence, where at each epoch, (i) the environment selects an outcome from an $m$-ary alphabet, (ii) the learner selects a probability distribution over the same alphabet (unaware of the outcome generated by the environment), and finally, (iii) the learner incurs a cost that depends on the probability assigned to the outcome. The cost function we consider captures the complexity of predicting the outcome generated by the environment, in a scenario where the aforementioned prediction is performed via comparative queries to a lying oracle. We consider both stochastic and adversarial environments, propose algorithms for both settings, and establish logarithmic upper bounds on their regret.

Problem

• Sequential prediction
• Lying oracle
• Comparative queries
• m-ary sequence
• Regret

Innovation

• Lying Oracle
• Sequence Prediction
• Comparative Queries
• Regret Bounds
• Adversarial Environment