Parallel algorithms for select and partition with noisy comparisons

Braverman, Mark; Mao, Jieming; Weinberg, S. Matthew

doi:10.1145/2897518.2897642

Cited by 31 publications

(54 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Adaptivity. The concept of adaptivity is generally well-studied in computer science, largely due to the role it plays in parallel computing, such as in sorting and selection [Val75, Col88,BMW16], communication complexity [PS84, DGS84, NW91], multi-armed bandits [AAAK17], sparse recovery [HNC09, IPW11, HBCN09], and property testing [CG17, BGSMdW12, CST + 17]. Beyond being a fundamental concept, adaptivity is important for applications where sequentiality is the main runtime bottleneck.…”

Section: Related Workmentioning

confidence: 99%

An Exponential Speedup in Parallel Running Time for Submodular Maximization without Loss in Approximation

Balkanski¹,

Rubinstein²,

Singer³

2019

Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms

View full text Add to dashboard Cite

In this paper we study the adaptivity of submodular maximization. Adaptivity quantifies the number of sequential rounds that an algorithm makes when function evaluations can be executed in parallel. Adaptivity is a fundamental concept that is heavily studied across a variety of areas in computer science, largely due to the need for parallelizing computation. For the canonical problem of maximizing a monotone submodular function under a cardinality constraint, it is well known that a simple greedy algorithm achieves a 1 − 1/e approximation [NWF78] and that this approximation is optimal for polynomial-time algorithms [NW78]. Somewhat surprisingly, despite extensive efforts on submodular optimization for large-scale datasets, until very recently there was no known algorithm that achieves a constant factor approximation for this problem whose adaptivity is sublinear in the size of the ground set n.Recent work by [BS18] describes an algorithm that obtains an approximation arbitrarily close to 1/3 in O(log n) adaptive rounds and shows that no algorithm can obtain a constant factor approximation inõ(log n) adaptive rounds. This approach achieves an exponential speedup in adaptivity (and parallel running time) at the expense of approximation quality.In this paper we describe a novel approach that yields an algorithm whose approximation is arbitrarily close to the optimal 1 − 1/e guarantee in O(log n) adaptive rounds. This algorithm therefore achieves an exponential speedup in parallel running time for submodular maximization at the expense of an arbitrarily small loss in approximation quality. This guarantee is optimal in both approximation and adaptivity, up to lower order terms. 0

show abstract

Section: Related Workmentioning

confidence: 99%

An Exponential Speedup in Parallel Running Time for Submodular Maximization without Loss in Approximation

Balkanski¹,

Rubinstein²,

Singer³

2019

Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms

View full text Add to dashboard Cite

show abstract

“…Similar bounds hold for rank-k in the comparison model (Theorem 2.16). This generalizes the 4-round O(n log n) algorithm of Braverman, Mao, and Weinberg [BMW16]. On the other hand, the query complexity is O(n + k log n) in the value model (Theorem 4.1).…”

Section: Introductionmentioning

confidence: 54%

“…Recently, Braverman, Mao, and Weinberg [BMW16] showed that for n strictly ordered (krank) elements the required query complexity is Ω(n log n) queries to find the maximum w.p. at least 1 − 1/poly(n).…”

Section: Previous Workmentioning

confidence: 99%

See 1 more Smart Citation

Instance-Optimality in the Noisy Value-and Comparison-Model

Cohen-Addad¹,

Mallmann-Trenn²,

Mathieu³

2020

Proceedings of the Fourteenth Annual ACM-SIAM Symposium on Discrete Algorithms

View full text Add to dashboard Cite

Motivated by crowdsourced computation, peer-grading, and recommendation systems, Braverman, Mao and Weinberg [STOC'16] studied the query and round complexity of fundamental problems such as finding the maximum (max), finding all elements above a certain value (threshold-v) or computing the top−k elements (Top-k) in a noisy environment.For example, consider the task of selecting papers for a conference. This task is challenging due the crowdsourcing nature of peer reviews: the results of reviews are noisy and it is necessary to parallelize the review process as much as possible. We study the noisy value model and the noisy comparison model: In the noisy value model, a reviewer is asked to evaluate a single element: "What is the value of paper i?" (e.g. accept). In the noisy comparison model (introduced in the seminal work of Feige, Peleg, Raghavan and Upfal [SICOMP'94]) a reviewer is asked to do a pairwise comparison: "Is paper i better than paper j?"In this paper, we show optimal worst-case query complexity for the max,threshold-v and Top-k problems. For max and Top-k, we obtain optimal worst-case upper and lower bounds on the round vs query complexity in both models. For threshold-v, we obtain optimal query complexity and nearly-optimal round complexity (i.e., optimal up to a factor O(log log k), where k is the size of the output) for both models.We then go beyond the worst-case and address the question of the importance of knowledge of the instance by providing, for a large range of parameters, instance-optimal algorithms with respect to the query complexity. We complement these results by showing that for some family of instances, no instance-optimal algorithm can exist. Furthermore, we show that the value-and comparison-model are for most practical settings asymptotically equivalent (for all the above mentioned problems); on the other hand, in the special case where the papers are totally ordered, we show that the value model is strictly easier than the comparison model.

show abstract

“…Dwork et al [11] and Ailon et al [2] considered a related Kemeny optimization problem, where the goal is to determine the total ordering that minimizes the sum of the distances to different permutations. For top-k identification, Braverman et al [4] initiated the study of how round complexity of active algorithms can affect the sample complexity. Szörényi et al [27] studied the case of k = 1 under the BTL model.…”

Section: Related Workmentioning

confidence: 99%

A Nearly Instance Optimal Algorithm for Top-k Ranking under the Multinomial Logit Model

Chen

Mao

2018

Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms

Self Cite

View full text Add to dashboard Cite

We study the active learning problem of top-k ranking from multi-wise comparisons under the popular multinomial logit model. Our goal is to identify the topk items with high probability by adaptively querying sets for comparisons and observing the noisy output of the most preferred item from each comparison. To achieve this goal, we design a new active ranking algorithm without using any information about the underlying items' preference scores. We also establish a matching lower bound on the sample complexity even when the set of preference scores is given to the algorithm. These two results together show that the proposed algorithm is nearly instance optimal (similar to instance optimal [12], but up to polylog factors). Our work extends the existing literature on rank aggregation in three directions. First, instead of studying a static problem with fixed data, we investigate the top-k ranking problem in an active learning setting. Second, we show our algorithm is nearly instance optimal, which is a much stronger theoretical guarantee. Finally, we extend the pairwise comparison to the multi-wise comparison, which has not been fully explored in ranking literature.

show abstract

Parallel algorithms for select and partition with noisy comparisons

Cited by 31 publications

References 19 publications

An Exponential Speedup in Parallel Running Time for Submodular Maximization without Loss in Approximation

An Exponential Speedup in Parallel Running Time for Submodular Maximization without Loss in Approximation

Instance-Optimality in the Noisy Value-and Comparison-Model

A Nearly Instance Optimal Algorithm for Top-k Ranking under the Multinomial Logit Model

Contact Info

Product

Resources

About