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.

研究了顺序决策问题，提出了Trace-UCB自适应分配算法，用于评估多个线性模型，同时学习噪声，实现在不同线性函数之间平衡样本预算，扩展了算法到高维度设置，并在现实数据上进行了模拟，表明Trace-UCB具有良好的鲁棒性。

精确估计线性模型的主动学习