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Active Learning for Accurate Estimation of Linear Models

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Carlos Riquelme
Alessandro Lazaric

Abstract

We explore the sequential decision-making problem where the goal is to estimate a number of linear models uniformly well, given a shared budget of random contexts independently sampled from a known distribution. For each incoming context, the decision-maker selects one of the linear models and receives an observation that is corrupted by the unknown noise level of that model. We present Trace-UCB, an adaptive allocation algorithm that learns the models' noise levels while balancing contexts accordingly across them, and prove bounds for its simple regret in both expectation and high-probability. We extend the algorithm and its bounds to the high dimensional setting , where the number of linear models times the dimension of the contexts is more 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.
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Dates and versions

hal-01538762 , version 1 (14-06-2017)

Identifiers

  • HAL Id : hal-01538762 , version 1

Cite

Carlos Riquelme, Mohammad Ghavamzadeh, Alessandro Lazaric. Active Learning for Accurate Estimation of Linear Models. ICML 2017 - 34th International Conference on Machine Learning, Aug 2017, Sydney, Australia. pp.36. ⟨hal-01538762⟩
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