Fast Approximation Algorithm for Non-Monotone DR-submodular Maximization under Size Constraint

• URL: http://arxiv.org/abs/2511.02254v1
• Date: Tue, 04 Nov 2025 04:37:16 GMT
• Title: Fast Approximation Algorithm for Non-Monotone DR-submodular Maximization under Size Constraint
• Authors: Tan D. Tran, Canh V. Pham,
• Abstract summary: This work studies the non-monotone DR-submodular Maximization over a ground set of $n$ subject to a size constraint $k$.<n>We propose two approximation algorithms for solving this problem named FastDrSub and FastDrSub++.
• Score: 3.4806267677524896
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: This work studies the non-monotone DR-submodular Maximization over a ground set of $n$ subject to a size constraint $k$. We propose two approximation algorithms for solving this problem named FastDrSub and FastDrSub++. FastDrSub offers an approximation ratio of $0.044$ with query complexity of $O(n \log(k))$. The second one, FastDrSub++, improves upon it with a ratio of $1/4-\epsilon$ within query complexity of $(n \log k)$ for an input parameter $\epsilon >0$. Therefore, our proposed algorithms are the first constant-ratio approximation algorithms for the problem with the low complexity of $O(n \log(k))$. Additionally, both algorithms are experimentally evaluated and compared against existing state-of-the-art methods, demonstrating their effectiveness in solving the Revenue Maximization problem with DR-submodular objective function. The experimental results show that our proposed algorithms significantly outperform existing approaches in terms of both query complexity and solution quality.

Related papers

• Enhanced Deterministic Approximation Algorithm for Non-monotone Submodular Maximization under Knapsack Constraint with Linear Query Complexity [0.0]
  We improve the approximation factor of the fastest deterministic algorithm from $6+epsilon$ to $5+epsilon$. Our technique is based on optimizing the performance of two components: the threshold greedy subroutine and the building of two disjoint sets as candidate solutions.
  arXiv  Detail & Related papers  (2024-05-20T02:24:58Z)
• Robust Approximation Algorithms for Non-monotone $k$-Submodular Maximization under a Knapsack Constraint [0.0]
  Two deterministic approximation algorithms are presented for the problem of non-monotone $k$-submodular complexity under a knapsack constraint. Our algorithms provide constant approximation ratios within only $O(nk)$ query complexity for the non-monotone objective.
  arXiv  Detail & Related papers  (2023-09-21T12:42:52Z)
• Linear Query Approximation Algorithms for Non-monotone Submodular Maximization under Knapsack Constraint [16.02833173359407]
  This work introduces two constant factor approximation algorithms with linear query complexity for non-monotone submodular over a ground set of size $n$ subject to a knapsack constraint. $mathsfDLA$ is a deterministic algorithm that provides an approximation factor of $6+epsilon$ while $mathsfRLA$ is a randomized algorithm with an approximation factor of $4+epsilon$.
  arXiv  Detail & Related papers  (2023-05-17T15:27:33Z)
• Explicit Second-Order Min-Max Optimization: Practical Algorithms and Complexity Analysis [71.05708939639537]
  We propose and analyze several inexact regularized Newton-type methods for finding a global saddle point of emphconcave unconstrained problems.<n>Our method improves the existing line-search-based min-max optimization by shaving off an $O(loglog(1/eps)$ factor in the required number of Schur decompositions.
  arXiv  Detail & Related papers  (2022-10-23T21:24:37Z)
• Best of Both Worlds: Practical and Theoretically Optimal Submodular Maximization in Parallel [17.462968952951883]
  Main algorithm is assembled from two components which may be of independent interest. A variant of LINEARSEQ is shown to have adaptive complexity of $O(log(n))$ smaller than that of any previous algorithm in the literature.
  arXiv  Detail & Related papers  (2021-11-15T17:10:40Z)
• Provably Faster Algorithms for Bilevel Optimization [54.83583213812667]
  Bilevel optimization has been widely applied in many important machine learning applications. We propose two new algorithms for bilevel optimization. We show that both algorithms achieve the complexity of $mathcalO(epsilon-1.5)$, which outperforms all existing algorithms by the order of magnitude.
  arXiv  Detail & Related papers  (2021-06-08T21:05:30Z)
• Linear Bandit Algorithms with Sublinear Time Complexity [67.21046514005029]
  We propose to accelerate existing linear bandit algorithms to achieve per-step time complexity sublinear in the number of arms $K$. We show that our proposed algorithms can achieve $O(K1-alpha(T))$ per-step complexity for some $alpha(T) > 0$ and $widetilde O(stT)$ regret, where $T$ is the time horizon.
  arXiv  Detail & Related papers  (2021-03-03T22:42:15Z)
• Practical and Parallelizable Algorithms for Non-Monotone Submodular Maximization with Size Constraint [20.104148319012854]
  We present and parallelizable for a submodular function, not necessarily a monotone, with respect to a size constraint. We improve the best approximation factor achieved by an algorithm that has optimal adaptivity and nearly optimal complexity query to $0.193 - varepsilon$.
  arXiv  Detail & Related papers  (2020-09-03T22:43:55Z)
• Revisiting Modified Greedy Algorithm for Monotone Submodular Maximization with a Knapsack Constraint [75.85952446237599]
  We show that a modified greedy algorithm can achieve an approximation factor of $0.305$. We derive a data-dependent upper bound on the optimum. It can also be used to significantly improve the efficiency of such algorithms as branch and bound.
  arXiv  Detail & Related papers  (2020-08-12T15:40:21Z)
• Streaming Complexity of SVMs [110.63976030971106]
  We study the space complexity of solving the bias-regularized SVM problem in the streaming model. We show that for both problems, for dimensions of $frac1lambdaepsilon$, one can obtain streaming algorithms with spacely smaller than $frac1lambdaepsilon$.
  arXiv  Detail & Related papers  (2020-07-07T17:10:00Z)
• Nonconvex Zeroth-Order Stochastic ADMM Methods with Lower Function Query Complexity [109.54166127479093]
  Zeroth-order (a.k.a, derivative-free) methods are a class of effective optimization methods for solving machine learning problems. In this paper, we propose a class faster faster zerothorder alternating gradient method multipliers (MMADMM) to solve the non finitesum problems. We show that ZOMMAD methods can achieve a lower function $O(frac13nfrac1)$ for finding an $epsilon$-stationary point. At the same time, we propose a class faster zerothorder online ADM methods (M
  arXiv  Detail & Related papers  (2019-07-30T02:21:43Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.