Near Optimal Bayesian Active Learning for Decision Making
This work addresses the problem of efficient decision-making under uncertainty for researchers and practitioners in machine learning and robotics, offering a novel algorithmic approach with proven competitive performance.
The paper tackles the problem of Bayesian active learning for decision making by sequentially selecting tests to reduce uncertainty about hypotheses, aiming to drive uncertainty into a single decision region quickly. It introduces the Hyperedge Cutting (HEC) algorithm, proving it is competitive with the optimal policy, and demonstrates effectiveness in applications like approximate comparison-based learning and active localization with a robot manipulator.
How should we gather information to make effective decisions? We address Bayesian active learning and experimental design problems, where we sequentially select tests to reduce uncertainty about a set of hypotheses. Instead of minimizing uncertainty per se, we consider a set of overlapping decision regions of these hypotheses. Our goal is to drive uncertainty into a single decision region as quickly as possible. We identify necessary and sufficient conditions for correctly identifying a decision region that contains all hypotheses consistent with observations. We develop a novel Hyperedge Cutting (HEC) algorithm for this problem, and prove that is competitive with the intractable optimal policy. Our efficient implementation of the algorithm relies on computing subsets of the complete homogeneous symmetric polynomials. Finally, we demonstrate its effectiveness on two practical applications: approximate comparison-based learning and active localization using a robot manipulator.