Active Learning for Accurate Estimation of Linear Models
This addresses a sequential decision-making problem for machine learning practitioners needing efficient resource allocation in multi-model estimation, though it appears incremental as it builds on existing active learning and bandit frameworks.
The paper tackles the problem of estimating multiple linear models with a shared budget of random contexts, where noise levels are unknown and model-dependent, by proposing Trace-UCB, an adaptive allocation algorithm that learns noise levels while balancing contexts. Simulations show it outperforms baselines and remains robust even when assumptions are violated.
We explore the sequential decision making problem where the goal is to estimate uniformly well a number of linear models, given a shared budget of random contexts independently sampled from a known distribution. The decision maker must query one of the linear models for each incoming context, and receives an observation corrupted by noise levels that are unknown, and depend on the model instance. We present Trace-UCB, an adaptive allocation algorithm that learns the noise levels while balancing contexts accordingly across the different linear functions, and derive guarantees for simple regret in both expectation and high-probability. Finally, we extend the algorithm and its guarantees to high dimensional settings, where the number of linear models times the dimension of the contextual space is higher than the total budget of samples. Simulations with real data suggest that Trace-UCB is remarkably robust, outperforming a number of baselines even when its assumptions are violated.