Optimal discovery with probabilistic expert advice

TL;DR

This paper introduces an algorithm for optimal discovery using probabilistic expert advice, combining the optimistic paradigm and Good-Turing estimator, achieving optimal rates under certain conditions and promising robustness in practical scenarios.

Contribution

It proposes a novel algorithm for optimal discovery with probabilistic advice, leveraging the optimistic paradigm and Good-Turing estimator, and demonstrates its optimality and robustness.

Findings

Achieves uniform optimal discovery rate under certain assumptions.

Numerical experiments suggest robustness under weaker assumptions.

Combines optimistic paradigm with Good-Turing estimator for improved performance.

Abstract

We consider an original problem that arises from the issue of security analysis of a power system and that we name optimal discovery with probabilistic expert advice. We address it with an algorithm based on the optimistic paradigm and the Good-Turing missing mass estimator. We show that this strategy uniformly attains the optimal discovery rate in a macroscopic limit sense, under some assumptions on the probabilistic experts. We also provide numerical experiments suggesting that this optimal behavior may still hold under weaker assumptions.