Learning from Acceptance: Cumulative Regret in the Game of Coding

2026-05-10

AI Summary

This work addresses the challenge of minimizing cumulative estimation error in decentralized systems, where a data collector must learn an optimal acceptance rule through repeated interactions without assuming the presence of honest nodes or knowledge of adversarial strategies. The paper introduces, for the first time, a cumulative regret metric within an information-asymmetric coding game framework, formulated as a Stackelberg game with the collector acting as the leader who dynamically adjusts its strategy. To tackle this problem, the authors propose an online learning algorithm that progressively refines high-potential acceptance rules by integrating adaptive search with regret analysis. Theoretical analysis establishes a sublinear cumulative regret bound for the algorithm, and empirical evaluations demonstrate its superior learning efficiency and robustness compared to baseline methods.

Abstract

Classical coding-theoretic guarantees often rely on trust assumptions, such as requiring sufficiently many honest nodes compared with adversarial ones. These assumptions are difficult to enforce in open decentralized systems where participants are not centrally certified. At the same time, such environments often contain incentive mechanisms: participants may be rewarded only when their submitted data are accepted and the system remains functional. This changes the role of an adversary. Rather than acting as a pure saboteur, a strategic adversary may submit data that are consistent enough to be accepted while still degrading the quality of the final estimate. The game-of-coding framework models this strategic interaction between a data collector (DC) and an adversary. Existing works on the game of coding mostly consider the complete-information case, where the DC knows how the adversary trades off acceptance and estimation error. In this paper, we study an incomplete-information version of the game of coding in which the DC, acting as a Stackelberg leader, does not know the adversary's utility trade-off and must learn through repeated interaction. Prior work on the unknown-adversary setting considered an explore-then-commit objective, where only the final selected acceptance rule is evaluated. In contrast, we study the full learning trajectory: every acceptance rule used during the algorithm is executed and contributes to performance. We propose an algorithm that refines its search around promising acceptance rules, prove that it achieves sublinear cumulative regret, and evaluate its performance through numerical experiments.

Problem

• game of coding
• incomplete information
• cumulative regret
• strategic adversary
• acceptance mechanism

Innovation

• incomplete-information game
• cumulative regret
• game of coding
• Stackelberg learning
• adaptive acceptance rule