Robustness of Bayesian Pool-based Active Learning Against Prior Misspecification

TL;DR

This paper investigates the robustness of Bayesian pool-based active learning algorithms to prior misspecification, demonstrating conditions for robustness and proposing mixture priors to improve practical performance.

Contribution

It provides theoretical guarantees for robustness under Lipschitz utility functions and introduces mixture priors to mitigate prior misspecification effects.

Findings

Robustness is guaranteed for Lipschitz continuous utility functions.

Non-Lipschitz utilities may lead to non-robustness.

Mixture priors perform well in practice.

Abstract

We study the robustness of active learning (AL) algorithms against prior misspecification: whether an algorithm achieves similar performance using a perturbed prior as compared to using the true prior. In both the average and worst cases of the maximum coverage setting, we prove that all $\alpha$-approximate algorithms are robust (i.e., near $\alpha$-approximate) if the utility is Lipschitz continuous in the prior. We further show that robustness may not be achieved if the utility is non-Lipschitz. This suggests we should use a Lipschitz utility for AL if robustness is required. For the minimum cost setting, we can also obtain a robustness result for approximate AL algorithms. Our results imply that many commonly used AL algorithms are robust against perturbed priors. We then propose the use of a mixture prior to alleviate the problem of prior misspecification. We analyze the robustness of the uniform mixture prior and show experimentally that it performs reasonably well in practice.