When should an expert make a prediction?

TL;DR

This paper studies the optimal timing for an expert to reveal information in a prediction setting, characterizing the optimal policy, analyzing expected rewards, and providing an efficient algorithm.

Contribution

It introduces a threshold-based optimal policy for expert information revelation, links rewards to the Law of the Iterated Logarithm, and offers a dynamic programming solution.

Findings

Optimal policy is threshold-based.

Expected reward relates to the Law of the Iterated Logarithm.

Efficient algorithm computes the optimal policy.

Abstract

We consider a setting where in a known future time, a certain continuous random variable will be realized. There is a public prediction that gradually converges to its realized value, and an expert that has access to a more accurate prediction. Our goal is to study {\em when} should the expert reveal his information, assuming that his reward is based on a logarithmic market scoring rule (i.e., his reward is proportional to the gain in log-likelihood of the realized value). Our contributions are: (1) we characterize the expert's optimal policy and show that it is threshold based. (2) we analyze the expert's asymptotic expected optimal reward and show a tight connection to the Law of the Iterated Logarithm, and (3) we give an efficient dynamic programming algorithm to compute the optimal policy.