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U-statistics play central roles in many statistical learning tools but facethe haunting issue of scalability. Significant efforts have been devoted intoaccelerating computation by U-statistic reduction. However, existing resultsalmost exclusively focus on power analysis, while little work addresses riskcontrol accuracy -- comparatively, the latter requires distinct and much morechallenging techniques. In this paper, we establish the first statisticalinference procedure with provably higher-order accurate risk control forincomplete U-statistics. The sharpness of our new result enables us to revealhow risk control accuracy also trades off with speed for the first time inliterature, which complements the well-known variance-speed trade-off. Ourproposed general framework converts the long-standing challenge of formulatingaccurate statistical inference procedures for many different designs into asurprisingly routine task. This paper covers non-degenerate and degenerateU-statistics, and network moments. We conducted comprehensive numerical studiesand observed results that validate our theory's sharpness. Our method alsodemonstrates effectiveness on real-world data applications.

U-Statistic Reduction: Higher-Order Accurate Risk Control and Statistical-Computational Trade-Off, with Application to Network Method-of-Moments