Gaussian Process Planning with Lipschitz Continuous Reward Functions: Towards Unifying Bayesian Optimization, Active Learning, and Beyond

TL;DR

This paper introduces a flexible Gaussian process planning framework with Lipschitz continuous rewards, unifying active learning and Bayesian optimization, and proposes an efficient, real-time epsilon-GPP algorithm with performance guarantees.

Contribution

It develops a nonmyopic adaptive GPP framework leveraging Lipschitz continuity to solve complex decision problems and introduces an anytime branch-and-bound algorithm for real-time planning.

Findings

Effective in Bayesian optimization tasks

Demonstrated success in energy harvesting applications

Provides performance guarantees for the planning algorithm

Abstract

This paper presents a novel nonmyopic adaptive Gaussian process planning (GPP) framework endowed with a general class of Lipschitz continuous reward functions that can unify some active learning/sensing and Bayesian optimization criteria and offer practitioners some flexibility to specify their desired choices for defining new tasks/problems. In particular, it utilizes a principled Bayesian sequential decision problem framework for jointly and naturally optimizing the exploration-exploitation trade-off. In general, the resulting induced GPP policy cannot be derived exactly due to an uncountable set of candidate observations. A key contribution of our work here thus lies in exploiting the Lipschitz continuity of the reward functions to solve for a nonmyopic adaptive epsilon-optimal GPP (epsilon-GPP) policy. To plan in real time, we further propose an asymptotically optimal, branch-and-bound anytime variant of epsilon-GPP with performance guarantee. We empirically demonstrate the effectiveness of our epsilon-GPP policy and its anytime variant in Bayesian optimization and an energy harvesting task.