While many works have studied statistical data fusion, they typically assume that the various datasets are given in advance. However, in practice, estimation requires difficult data collection decisions like determining the available data sources, their costs, and how many samples to collect from each source. Moreover, this process is often sequential because the data collected at a given time can improve collection decisions in the future. In our setup, given access to multiple data sources and budget constraints, the agent must sequentially decide which data source to query to efficiently estimate a target parameter. We formalize this task using Online Moment Selection, a semiparametric framework that applies to any parameter identified by a set of moment conditions. Interestingly, the optimal budget allocation depends on the (unknown) true parameters. We present two online data collection policies, Explore-then-Commit and Explore-then-Greedy, that use the parameter estimates at a given time to optimally allocate the remaining budget in the future steps. We prove that both policies achieve zero regret (assessed by asymptotic MSE) relative to an oracle policy. We empirically validate our methods on both synthetic and real-world causal effect estimation tasks, demonstrating that the online data collection policies outperform their fixed counterparts.

翻译：尽管已有诸多研究关注统计数据融合问题，但通常假设各类数据集已预先给定。然而在实际应用中，估计过程需要面对困难的数据收集决策，例如确定可用数据源、其采集成本以及从各数据源应收集的样本量。此外，这一过程往往是序贯进行的，因为当前收集的数据能够改进未来的收集决策。在我们的研究框架中，给定多数据源访问权限与预算约束，智能体必须序贯决定查询哪个数据源以高效估计目标参数。我们通过在线矩选择形式化该任务——这是一个适用于任何由矩条件组识别的参数的半参数框架。值得注意的是，最优预算分配取决于（未知的）真实参数。我们提出两种在线数据收集策略：探索后确定策略与探索后贪婪策略，这两种策略利用当前时刻的参数估计值来优化未来步骤的剩余预算分配。我们证明两种策略均能实现相对于先知策略的零遗憾（以渐近均方误差评估）。我们在合成数据与真实世界因果效应估计任务上实证验证了所提方法，证明在线数据收集策略优于固定分配策略。