Gaussian Process Optimization with Mutual Information

TL;DR

This paper introduces a new Gaussian Process-based optimization algorithm, GP-MI, which significantly reduces cumulative regret compared to existing methods like GP-UCB, demonstrated through synthetic and real-world experiments.

Contribution

The paper provides improved theoretical bounds on regret for Gaussian process optimization and introduces the novel GP-MI algorithm that outperforms existing methods.

Findings

GP-MI achieves lower cumulative regret than GP-UCB.

Theoretical bounds on regret are exponentially improved.

Empirical results confirm the efficiency of GP-MI on various tasks.

Abstract

In this paper, we analyze a generic algorithm scheme for sequential global optimization using Gaussian processes. The upper bounds we derive on the cumulative regret for this generic algorithm improve by an exponential factor the previously known bounds for algorithms like GP-UCB. We also introduce the novel Gaussian Process Mutual Information algorithm (GP-MI), which significantly improves further these upper bounds for the cumulative regret. We confirm the efficiency of this algorithm on synthetic and real tasks against the natural competitor, GP-UCB, and also the Expected Improvement heuristic.