Indirect Active Learning
This work addresses a limitation in active learning for complex systems where direct manipulation is not possible, though it appears incremental as it extends existing frameworks with new theoretical analysis.
The paper tackles the problem of active learning when covariates can only be indirectly influenced via control variables, establishing minimax convergence rates for estimating relationships locally and showing that a simple two-stage passive learner often achieves the full asymptotic benefit of active learning.
Traditional models of active learning assume a learner can directly manipulate or query a covariate $X$ in order to study its relationship with a response $Y$. However, if $X$ is a feature of a complex system, it may be possible only to indirectly influence $X$ by manipulating a control variable $Z$, a scenario we refer to as Indirect Active Learning. Under a nonparametric model of Indirect Active Learning with a fixed budget, we study minimax convergence rates for estimating the relationship between $X$ and $Y$ locally at a point, obtaining different rates depending on the complexities and noise levels of the relationships between $Z$ and $X$ and between $X$ and $Y$. We also identify minimax rates for passive learning under comparable assumptions. In many cases, our results show that, while there is an asymptotic benefit to active learning, this benefit is fully realized by a simple two-stage learner that runs two passive experiments in sequence.