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：我们考虑基于专家建议的二元序列在线预测问题。针对该情境，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，在保持最优最坏情况遗憾界的前提下，相较于标准流程能大幅减少所需标签量。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。对于单个专家期望性能显著优于其他专家的情况，我们证明该标签高效预测器的标签复杂度大致与回合数的平方根成比例。最后，通过数值实验实证表明，该标签高效预测器的归一化遗憾值可渐近匹配已知的池基主动学习极小化极大速率，证明其能在良性环境中实现最优自适应调整。