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Active Learning for Accurate Estimation of Linear Models

Carlos Riquelme 1 Mohammad Ghavamzadeh 2, 3 Alessandro Lazaric 2
2 SEQUEL - Sequential Learning
Inria Lille - Nord Europe, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189
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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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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