[論文レビュー] Straggler-Aware Coded Polynomial Aggregation

Xi Zhong, Jörg Kliewer+1 more|arXiv (Cornell University)|Feb 3, 2026

Stochastic Gradient Optimization Techniques被引用数 0

ひとこと要約

The paper extends coded polynomial aggregation (CPA) to straggler-aware systems with a predefined non-straggler pattern, deriving necessary and sufficient conditions for exact recovery and a threshold on intersection size that guarantees feasibility.

ABSTRACT

Coded polynomial aggregation (CPA) in distributed computing systems enables the master to directly recover a weighted aggregation of polynomial computations without individually decoding each term, thereby reducing the number of required worker responses. However, existing CPA schemes are restricted to an idealized setting in which the system cannot tolerate stragglers. In this paper, we extend CPA to straggler-aware distributed computing systems with a pre-specified non-straggler pattern, where exact recovery is required for a given collection of admissible non-straggler sets. Our main results show that exact recovery of the desired aggregation is achievable with fewer worker responses than that required by polynomial codes based on individual decoding, and that feasibility is characterized by the intersection structure of the non-straggler patterns. In particular, we establish necessary and sufficient conditions for exact recovery in straggler-aware CPA. We identify an intersection-size threshold that is sufficient to guarantee exact recovery. When the number of admissible non-straggler sets is sufficiently large, we further show that this threshold is necessary in a generic sense. We also provide an explicit construction of feasible CPA schemes whenever the intersection size exceeds the derived threshold. Finally, simulations verify our theoretical results by demonstrating a sharp feasibility transition at the predicted intersection threshold.

研究の動機と目的

• Motivate reducing decoding load by aggregating polynomial computations rather than recovering each term.
• Extend CPA to systems with stragglers by enforcing exact recovery for a predefined set of non-straggler patterns.
• Characterize feasibility via the intersection structure of non-straggler patterns and derive threshold bounds.
• Provide explicit scheme constructions and empirical validation of feasibility transitions.

提案手法

• Model CPA over a pre-specified non-straggler pattern with K data matrices and a degree-d polynomial function.
• Encode data via an interpolation polynomial E(z) and distribute E(βn) to N workers.
• Decode by constructing a decoder polynomial D(z) from responses of N−S non-stragglers and evaluate at αk to obtain the weighted sum.
• Derive orthogonality conditions that guarantee zero recovery error: sumk wk Pg(αk) αk^j = 0 for j in a defined range and all g, where Pg(z) depends on the non-straggler sets.
• Show that the intersection I of all non-straggler sets governs feasibility, via a reduced problem on PI(z) = ∏n∈I (z−βn).
• Provide an explicit construction when the intersection size I exceeds an I* threshold.

実験結果

リサーチクエスチョン

• RQ1 What are the exact and necessary conditions to achieve exact recovery of the weighted aggregation under a pre-specified non-straggler pattern?
• RQ2 How does the intersection size I of non-straggler sets influence feasibility and what is the role of the threshold I*?
• RQ3 Can we construct explicit CPA schemes that satisfy the orthogonality conditions for feasible non-straggler patterns?
• RQ4 How do the proposed straggler-aware CPA results compare to traditional CPA and polynomial codes under arbitrary stragglers?
• RQ5 Do simulations exhibit a sharp feasibility transition at the intersection threshold?

主な発見

• A CPA scheme is feasible over a pre-specified non-straggler pattern iff the encoding and evaluation points satisfy orthogonality conditions: sumk wk Pg(αk) αk^j = 0 for j in [C], for all non-straggler sets g.
• There exists a sufficient intersection-size threshold I* (dependent on K and d) such that if I ≥ I*, feasibility is guaranteed by an appropriate choice of evaluation points.
• When the number of admissible non-straggler sets is large, the threshold I* becomes (generically) necessary as well.
• An explicit construction of evaluation points is provided for I ≥ I*, adapting a prior algorithm to the straggler-aware setting, ensuring feasibility.
• Simulations show a sharp feasibility transition at the predicted intersection threshold, validating the theoretical results.