Related papers: Optimizing Chance-Constrained Submodular Problems …
We study the correlated stochastic knapsack problem of a submodular target function, with optional additional constraints. We utilize the multilinear extension of submodular function, and bundle it with an adaptation of the relaxed linear…
We study a stochastic variant of monotone submodular maximization problem as follows. We are given a monotone submodular function as an objective function and a feasible domain defined on a finite set, and our goal is to find a feasible…
The subspace selection problem seeks a subspace that maximizes an objective function under some constraint. This problem includes several important machine learning problems such as the principal component analysis and sparse dictionary…
While techniques have been developed for chance constrained stochastic optimal control using sample disturbance data that provide a probabilistic confidence bound for chance constraint satisfaction, far less is known about how to use sample…
A number of discrete and continuous optimization problems in machine learning are related to convex minimization problems under submodular constraints. In this paper, we deal with a submodular function with a directed graph structure, and…
When dealing with real-world optimization problems, decision-makers usually face high levels of uncertainty associated with partial information, unknown parameters, or complex relationships between these and the problem decision variables.…
Chance-constrained programming (CCP) is one of the most difficult classes of optimization problems that has attracted the attention of researchers since the 1950s. In this survey, we focus on cases when only a limited information on the…
In black-box function optimization, we need to consider not only controllable design variables but also uncontrollable stochastic environment variables. In such cases, it is necessary to solve the optimization problem by taking into account…
Constrained maximization of submodular functions poses a central problem in combinatorial optimization. In many realistic scenarios, a number of agents need to maximize multiple submodular objectives over the same ground set. We study such…
In this paper, we study the classic submodular maximization problem subject to a group equality constraint under both non-adaptive and adaptive settings. It has been shown that the utility function of many machine learning applications,…
Optimization of complex functions, such as the output of computer simulators, is a difficult task that has received much attention in the literature. A less studied problem is that of optimization under unknown constraints, i.e., when the…
Solving stochastic optimization problems under partial observability, where one needs to adaptively make decisions with uncertain outcomes, is a fundamental but notoriously difficult challenge. In this paper, we introduce the concept of…
An algorithm is proposed, analyzed, and tested experimentally for solving stochastic optimization problems in which the decision variables are constrained to satisfy equations defined by deterministic, smooth, and nonlinear functions. It is…
Submodularity is a key property in discrete optimization. Submodularity has been widely used for analyzing the greedy algorithm to give performance bounds and providing insight into the construction of valid inequalities for mixed-integer…
Uncertainties from deepening penetration of renewable energy resources have posed critical challenges to the secure and reliable operations of future electric grids. Among various approaches for decision making in uncertain environments,…
This article presents a constrained policy optimization approach for the optimal control of systems under nonstationary uncertainties. We introduce an assumption that we call Markov embeddability that allows us to cast the stochastic…
Submodular maximization constitutes a prominent research topic in combinatorial optimization and theoretical computer science, with extensive applications across diverse domains. While substantial advancements have been achieved in…
We study the worst-case adaptive optimization problem with budget constraint that is useful for modeling various practical applications in artificial intelligence and machine learning. We investigate the near-optimality of greedy algorithms…
Evolutionary algorithms have been applied to a wide range of stochastic problems. Motivated by real-world problems where constraint violations have disruptive effects, this paper considers the chance-constrained knapsack problem (CCKP)…
A method is developed to numerically solve chance constrained optimal control problems. The chance constraints are reformulated as nonlinear constraints that retain the probability properties of the original constraint. The reformulation…