Optimizing Chance-Constrained Submodular Problems with Variable Uncertainties

• URL: http://arxiv.org/abs/2309.14359v1
• Date: Sat, 23 Sep 2023 04:48:49 GMT
• Title: Optimizing Chance-Constrained Submodular Problems with Variable Uncertainties
• Authors: Xiankun Yan, Anh Viet Do, Feng Shi, Xiaoyu Qin, Frank Neumann
• Abstract summary: We study chance-constrained submodular optimization problems, which capture a wide range of problems with constraints. We present greedy algorithms that can obtain a high-quality solution, i.e., a constant approximation ratio to the given optimal solution.
• Score: 12.095075636344536
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Chance constraints are frequently used to limit the probability of constraint violations in real-world optimization problems where the constraints involve stochastic components. We study chance-constrained submodular optimization problems, which capture a wide range of optimization problems with stochastic constraints. Previous studies considered submodular problems with stochastic knapsack constraints in the case where uncertainties are the same for each item that can be selected. However, uncertainty levels are usually variable with respect to the different stochastic components in real-world scenarios, and rigorous analysis for this setting is missing in the context of submodular optimization. This paper provides the first such analysis for this case, where the weights of items have the same expectation but different dispersion. We present greedy algorithms that can obtain a high-quality solution, i.e., a constant approximation ratio to the given optimal solution from the deterministic setting. In the experiments, we demonstrate that the algorithms perform effectively on several chance-constrained instances of the maximum coverage problem and the influence maximization problem.

Related papers

• Generalization Bounds of Surrogate Policies for Combinatorial Optimization Problems [61.580419063416734]
  A recent stream of structured learning approaches has improved the practical state of the art for a range of optimization problems. The key idea is to exploit the statistical distribution over instances instead of dealing with instances separately. In this article, we investigate methods that smooth the risk by perturbing the policy, which eases optimization and improves the generalization error.
  arXiv  Detail & Related papers  (2024-07-24T12:00:30Z)
• Model-Based Epistemic Variance of Values for Risk-Aware Policy Optimization [59.758009422067]
  We consider the problem of quantifying uncertainty over expected cumulative rewards in model-based reinforcement learning. We propose a new uncertainty Bellman equation (UBE) whose solution converges to the true posterior variance over values. We introduce a general-purpose policy optimization algorithm, Q-Uncertainty Soft Actor-Critic (QU-SAC) that can be applied for either risk-seeking or risk-averse policy optimization.
  arXiv  Detail & Related papers  (2023-12-07T15:55:58Z)
• Likelihood Ratio Confidence Sets for Sequential Decision Making [51.66638486226482]
  We revisit the likelihood-based inference principle and propose to use likelihood ratios to construct valid confidence sequences. Our method is especially suitable for problems with well-specified likelihoods. We show how to provably choose the best sequence of estimators and shed light on connections to online convex optimization.
  arXiv  Detail & Related papers  (2023-11-08T00:10:21Z)
• Margin theory for the scenario-based approach to robust optimization in high dimension [0.0]
  This paper deals with the scenario approach to robust optimization. This relies on a random sampling of the possibly infinite number of constraints induced by uncertainties in a problem.
  arXiv  Detail & Related papers  (2023-03-07T13:33:46Z)
• High-Probability Bounds for Stochastic Optimization and Variational Inequalities: the Case of Unbounded Variance [59.211456992422136]
  We propose algorithms with high-probability convergence results under less restrictive assumptions. These results justify the usage of the considered methods for solving problems that do not fit standard functional classes in optimization.
  arXiv  Detail & Related papers  (2023-02-02T10:37:23Z)
• Fully Stochastic Trust-Region Sequential Quadratic Programming for Equality-Constrained Optimization Problems [62.83783246648714]
  We propose a sequential quadratic programming algorithm (TR-StoSQP) to solve nonlinear optimization problems with objectives and deterministic equality constraints. The algorithm adaptively selects the trust-region radius and, compared to the existing line-search StoSQP schemes, allows us to utilize indefinite Hessian matrices.
  arXiv  Detail & Related papers  (2022-11-29T05:52:17Z)
• Learning to Optimize with Stochastic Dominance Constraints [103.26714928625582]
  In this paper, we develop a simple yet efficient approach for the problem of comparing uncertain quantities. We recast inner optimization in the Lagrangian as a learning problem for surrogate approximation, which bypasses apparent intractability. The proposed light-SD demonstrates superior performance on several representative problems ranging from finance to supply chain management.
  arXiv  Detail & Related papers  (2022-11-14T21:54:31Z)
• Integrated Conditional Estimation-Optimization [6.037383467521294]
  Many real-world optimization problems uncertain parameters with probability can be estimated using contextual feature information. In contrast to the standard approach of estimating the distribution of uncertain parameters, we propose an integrated conditional estimation approach. We show that our ICEO approach is theally consistent under moderate conditions.
  arXiv  Detail & Related papers  (2021-10-24T04:49:35Z)
• Runtime Analysis of Single- and Multi-Objective Evolutionary Algorithms for Chance Constrained Optimization Problems with Normally Distributed Random Variables [11.310502327308575]
  We study the scenario of components that are independent and normally distributed. We introduce a multi-objective formulation of the problem which trades off the expected cost and its variance. We prove that this approach can also be used to compute a set of optimal solutions for the chance constrained minimum spanning tree problem.
  arXiv  Detail & Related papers  (2021-09-13T09:24:23Z)
• A sampling criterion for constrained Bayesian optimization with uncertainties [0.0]
  We consider the problem of chance constrained optimization where it is sought to optimize a function and satisfy constraints, both of which are affected by uncertainties. To tackle such problems, we propose a new Bayesian optimization method. It applies to the situation where the uncertainty comes from some of the inputs, so that it becomes possible to define an acquisition criterion in the joint controlled-uncontrolled input space.
  arXiv  Detail & Related papers  (2021-03-09T20:35:56Z)
• Heuristic Strategies for Solving Complex Interacting Stockpile Blending Problem with Chance Constraints [14.352521012951865]
  In this paper, we consider the uncertainty in material grades and introduce chance constraints that are used to ensure the constraints with high confidence. To address the stockpile blending problem with chance constraints, we propose a differential evolution algorithm combining two repair operators.
  arXiv  Detail & Related papers  (2021-02-10T07:56:18Z)

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.