Active Learning for Accurate Estimation of Linear Models

TL;DR

This paper introduces Trace-UCB, an adaptive algorithm for efficiently estimating multiple linear models with unknown noise levels, demonstrating robustness and superior performance in high-dimensional and real-data scenarios.

Contribution

The paper proposes Trace-UCB, a novel adaptive allocation method for estimating multiple linear models with unknown noise, extending to high-dimensional settings with theoretical guarantees.

Findings

Trace-UCB outperforms baseline methods in simulations.

The algorithm is robust even when assumptions are violated.

Guarantees are provided for simple regret in expectation and high-probability.

Abstract

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.