Accurate Byzantine Agreement with Feedback

Abstract

The standard Byzantine Agreement (BA) problem requires non-faulty processes to agree on a common value. In many real-world applications, it is important that the processes agree on the correct value rather than any value. In this paper, we present a problem called Accurate Byzantine Agreement (ABA) in which all processes get a common feedback (or payoff) from the environment indicating if the value they agreed upon was correct or not. The solution to this problem, referred to as the ABA algorithm, requires the non-faulty processes to incorporate the feedback so that their chance of choosing the correct value improves over subsequent iterations of the algorithm. We present an algorithm that solves the ABA problem based on two key ingredients: a standard solution to the BA problem and a multiplicative method to maintain and update process weights indicative of how often they are correct. We give guarantees on the accuracy of the algorithm based on assumptions on the accuracy of the processes and the proportion of faulty and non-faulty processes in the system. For each iteration, if the weight of accurate processes is at least 3/4th the weight of the non-faulty processes, the algorithm always decides on the correct value. When the non-faulty processes are accurate with probability greater than 1/2, the algorithm decides on the correct value with very high probability after some initial number of mistakes. In fact, among n processes, if there exists even one process which is accurate for all iterations, the algorithm is wrong only O(log n) times for any large number of iterations of the algorithm.KeywordsByzantine AgreementWeighted MajorityMultiplicative Update