We consider online prediction of a binary sequence with expert advice. For this setting, we devise label-efficient forecasting algorithms, which use a selective sampling scheme that enables collecting much fewer labels than standard procedures, while still retaining optimal worst-case regret guarantees. These algorithms are based on exponentially weighted forecasters, suitable for settings with and without a perfect expert. For a scenario where one expert is strictly better than the others in expectation, we show that the label complexity of the label-efficient forecaster scales roughly as the square root of the number of rounds. Finally, we present numerical experiments empirically showing that the normalized regret of the label-efficient forecaster can asymptotically match known minimax rates for pool-based active learning, suggesting it can optimally adapt to benign settings.

翻译：本文针对专家建议下的二元序列在线预测问题展开研究。在该设定下，我们设计了标签高效预测算法，该算法采用选择性采样方案，在保持最优最坏情形遗憾界的前提下，能够比标准流程采集显著更少的标签。这些算法基于指数加权预测器，适用于存在或不存在完美专家的场景。对于某一专家期望表现严格优于其他专家的情形，我们证明该标签高效预测器的标签复杂度大致随回合数的平方根增长。最后，我们通过数值实验表明，该标签高效预测器的归一化遗憾值能够渐进匹配基于池化主动学习已知的极小极大最优速率，说明其可在良性场景下实现最优自适应。