scholarly journals Fast Pareto Optimization for Subset Selection with Dynamic Cost Constraints

2021 ◽  
Author(s):  
Chao Bian ◽  
Chao Qian ◽  
Frank Neumann ◽  
Yang Yu
Keyword(s):  
Objective Function ◽  
Greedy Algorithm ◽  
Real World ◽  
Fundamental Problem ◽  
Subset Selection ◽  
Selection Strategy ◽  
Cost Constraints ◽  
Approximation Guarantee ◽  
Changes Over Time ◽  
Over Time

Subset selection with cost constraints is a fundamental problem with various applications such as influence maximization and sensor placement. The goal is to select a subset from a ground set to maximize a monotone objective function such that a monotone cost function is upper bounded by a budget. Previous algorithms with bounded approximation guarantees include the generalized greedy algorithm, POMC and EAMC, all of which can achieve the best known approximation guarantee. In real-world scenarios, the resources often vary, i.e., the budget often changes over time, requiring the algorithms to adapt the solutions quickly. However, when the budget changes dynamically, all these three algorithms either achieve arbitrarily bad approximation guarantees, or require a long running time. In this paper, we propose a new algorithm FPOMC by combining the merits of the generalized greedy algorithm and POMC. That is, FPOMC introduces a greedy selection strategy into POMC. We prove that FPOMC can maintain the best known approximation guarantee efficiently.

scholarly journals On Subset Selection with General Cost Constraints

2017 ◽  
Author(s):  
Chao Qian ◽  
Jing-Cheng Shi ◽  
Yang Yu ◽  
Ke Tang
Keyword(s):  
Objective Function ◽  
Greedy Algorithm ◽  
Subset Selection ◽  
Approximation Ratio ◽  
Selection Problem ◽  
Iterative Approach ◽  
Cost Constraints ◽  
General Approximation ◽  
Approximation Guarantee

This paper considers the subset selection problem with a monotone objective function and a monotone cost constraint, which relaxes the submodular property of previous studies. We first show that the approximation ratio of the generalized greedy algorithm is $\frac{\alpha}{2}(1 \textendash \frac{1}{e^{\alpha}})$ (where $\alpha$ is the submodularity ratio); and then propose POMC, an anytime randomized iterative approach that can utilize more time to find better solutions than the generalized greedy algorithm. We show that POMC can obtain the same general approximation guarantee as the generalized greedy algorithm, but can achieve better solutions in cases and applications.

scholarly journals Pareto Optimization for Subset Selection with Dynamic Cost Constraints

2019 ◽  
Vol 33 ◽  
pp. 2354-2361 ◽  
Author(s):  
Vahid Roostapour ◽  
Aneta Neumann ◽  
Frank Neumann ◽  
Tobias Friedrich
Keyword(s):  
Greedy Algorithms ◽  
Subset Selection ◽  
Pareto Optimization ◽  
Experimental Investigations ◽  
Optimization Approach ◽  
Submodular Optimization ◽  
Approximation Quality ◽  
Cost Constraints ◽  
Changes Over Time ◽  
Over Time

In this paper, we consider the subset selection problem for function f with constraint bound B which changes over time. We point out that adaptive variants of greedy approaches commonly used in the area of submodular optimization are not able to maintain their approximation quality. Investigating the recently introduced POMC Pareto optimization approach, we show that this algorithm efficiently computes a φ = (αf/2)(1− α1f )-approximation, where αf is the sube modularity ratio of f, for each possible constraint bound b ≤ B. Furthermore, we show that POMC is able to adapt its set of solutions quickly in the case that B increases. Our experimental investigations for the influence maximization in social networks show the advantage of POMC over generalized greedy algorithms.

scholarly journals Subset Selection by Pareto Optimization with Recombination

2020 ◽  
Vol 34 (03) ◽  
pp. 2408-2415
Author(s):  
Chao Qian ◽  
Chao Bian ◽  
Chao Feng
Keyword(s):  
Feature Selection ◽  
Objective Function ◽  
Fundamental Problem ◽  
Subset Selection ◽  
Optimal Solution ◽  
Sparse Regression ◽  
Unsupervised Feature Selection ◽  
Optimal Polynomial ◽  
Approximation Guarantee ◽  
The Given

Subset selection, i.e., to select a limited number of items optimizing some given objective function, is a fundamental problem with various applications such as unsupervised feature selection and sparse regression. By employing a multi-objective evolutionary algorithm (EA) with mutation only to optimize the given objective function and minimize the number of selected items simultaneously, the recently proposed POSS algorithm achieves state-of-the-art performance for subset selection. In this paper, we propose the PORSS algorithm by incorporating recombination, a characterizing feature of EAs, into POSS. We prove that PORSS can achieve the optimal polynomial-time approximation guarantee as POSS when the objective function is monotone, and can find an optimal solution efficiently in some cases whereas POSS cannot. Extensive experiments on unsupervised feature selection and sparse regression show the superiority of PORSS over POSS. Our analysis also theoretically discloses that recombination from diverse solutions can be more likely than mutation alone to generate various variations, thereby leading to better exploration; this may be of independent interest for understanding the influence of recombination.

scholarly journals Lifelong Learning with a Changing Action Set

2020 ◽  
Vol 34 (04) ◽  
pp. 3373-3380
Author(s):  
Yash Chandak ◽  
Georgios Theocharous ◽  
Chris Nota ◽  
Philip Thomas
Keyword(s):  
Lifelong Learning ◽  
Real World ◽  
Large Scale ◽  
Learning Problems ◽  
Sequential Decision Making ◽  
Sequential Decision ◽  
Transition Dynamics ◽  
Unknown Structure ◽  
Changes Over Time ◽  
Over Time

In many real-world sequential decision making problems, the number of available actions (decisions) can vary over time. While problems like catastrophic forgetting, changing transition dynamics, changing rewards functions, etc. have been well-studied in the lifelong learning literature, the setting where the size of the action set changes remains unaddressed. In this paper, we present first steps towards developing an algorithm that autonomously adapts to an action set whose size changes over time. To tackle this open problem, we break it into two problems that can be solved iteratively: inferring the underlying, unknown, structure in the space of actions and optimizing a policy that leverages this structure. We demonstrate the efficiency of this approach on large-scale real-world lifelong learning problems.

scholarly journals Concept Drift Detection in Dynamic Probabilistic Relational Models

2021 ◽  
Vol 34 (1) ◽  
Author(s):  
Nils Finke ◽  
Tanya Braun ◽  
Marcel Gehrke ◽  
Ralf Möller
Keyword(s):  
Real World ◽  
Joint Distribution ◽  
Concept Drift ◽  
Probability Distributions ◽  
Real World Data ◽  
Relational Models ◽  
World Data ◽  
Probabilistic Relational Models ◽  
Changes Over Time ◽  
Over Time

Dynamic probabilistic relational models, which are factorized w.r.t. a full joint distribution, are used to cater for uncertainty and for relational and temporal aspects in real-world data. While these models assume the underlying temporal process to be stationary, real-world data often exhibits non-stationary behavior where the full joint distribution changes over time. We propose an approach to account for non-stationary processes w.r.t. to changing probability distributions over time, an effect known as concept drift. We use factorization and compact encoding of relations to efficiently detect drifts towards new probability distributions based on evidence.

Approximation Guarantees of Stochastic Greedy Algorithms for Subset Selection

2018 ◽  
Author(s):  
Chao Qian ◽  
Yang Yu ◽  
Ke Tang
Keyword(s):  
Real World ◽  
Large Scale ◽  
Fundamental Problem ◽  
Greedy Algorithms ◽  
Subset Selection ◽  
Objective Functions ◽  
General Constraint ◽  
Real World Applications ◽  
General Stochastic

Subset selection is a fundamental problem in many areas, which aims to select the best subset of size at most $k$ from a universe. Greedy algorithms are widely used for subset selection, and have shown good approximation performances in deterministic situations. However, their behaviors are stochastic in many realistic situations (e.g., large-scale and noisy). For general stochastic greedy algorithms, bounded approximation guarantees were obtained only for subset selection with monotone submodular objective functions, while real-world applications often involve non-monotone or non-submodular objective functions and can be subject to a more general constraint than a size constraint. This work proves their approximation guarantees in these cases, and thus largely extends the applicability of stochastic greedy algorithms.

scholarly journals Sequence Selection by Pareto Optimization

2018 ◽  
Author(s):  
Chao Qian ◽  
Chao Feng ◽  
Ke Tang
Keyword(s):  
Objective Function ◽  
Real World ◽  
Superior Performance ◽  
Sequence Length ◽  
Iterative Approach ◽  
Reasonable Time ◽  
Sequence Selection ◽  
Real World Applications ◽  
Approximation Guarantee ◽  
The Given

The problem of selecting a sequence of items from a universe that maximizes some given objective function arises in many real-world applications. In this paper, we propose an anytime randomized iterative approach POSeqSel, which maximizes the given objective function and minimizes the sequence length simultaneously. We prove that for any previously studied objective function, POSeqSel using a reasonable time can always reach or improve the best known approximation guarantee. Empirical results exhibit the superior performance of POSeqSel.

scholarly journals Controlling transient gas flow in real-world pipeline intersection areas

2020 ◽  
Author(s):  
Felix Hennings ◽  
Lovis Anderson ◽  
Kai Hoppmann-Baum ◽  
Mark Turner ◽  
Thorsten Koch
Keyword(s):  
Real World ◽  
Gas Flow ◽  
Mixed Integer ◽  
Real World Data ◽  
Operation Modes ◽  
Intersection Area ◽  
Demand Scenario ◽  
Changes Over Time ◽  
Ongoing Project ◽  
Over Time

Abstract Compressor stations are the heart of every high-pressure gas transport network. Located at intersection areas of the network, they are contained in huge complex plants, where they are in combination with valves and regulators responsible for routing and pushing the gas through the network. Due to their complexity and lack of data compressor stations are usually dealt with in the scientific literature in a highly simplified and idealized manner. As part of an ongoing project with one of Germany’s largest transmission system operators to develop a decision support system for their dispatching center, we investigated how to automatize the control of compressor stations. Each station has to be in a particular configuration, leading in combination with the other nearby elements to a discrete set of up to 2000 possible feasible operation modes in the intersection area. Since the desired performance of the station changes over time, the configuration of the station has to adapt. Our goal is to minimize the necessary changes in the overall operation modes and related elements over time while fulfilling a preset performance envelope or demand scenario. This article describes the chosen model and the implemented mixed-integer programming based algorithms to tackle this challenge. By presenting extensive computational results on real-world data, we demonstrate the performance of our approach.

scholarly journals An Optimal Approximation for Submodular Maximization Under a Matroid Constraint in the Adaptive Complexity Model

2021 ◽  
Author(s):  
Eric Balkanski ◽  
Aviad Rubinstein ◽  
Yaron Singer
Keyword(s):  
Greedy Algorithm ◽  
Fundamental Problem ◽  
Constant Factor ◽  
Optimal Approximation ◽  
Approximation Guarantee ◽  
Adaptive Complexity ◽  
Submodular Maximization ◽  
The Greedy Algorithm ◽  
Novel Algorithm

An Exponentially Faster Algorithm for Submodular Maximization Under a Matroid Constraint This paper studies the problem of submodular maximization under a matroid constraint. It is known since the 1970s that the greedy algorithm obtains a constant-factor approximation guarantee for this problem. Twelve years ago, a breakthrough result by Vondrák obtained the optimal 1 − 1/e approximation. Previous algorithms for this fundamental problem all have linear parallel runtime, which was considered impossible to accelerate until recently. The main contribution of this paper is a novel algorithm that provides an exponential speedup in the parallel runtime of submodular maximization under a matroid constraint, without loss in the approximation guarantee.

Introduction

2020 ◽  
pp. 1-20
Author(s):  
Ioana Emy Matesan
Keyword(s):  
Theoretical Framework ◽  
Selection Strategy ◽  
Case Selection ◽  
Nonviolent Resistance ◽  
Recent Developments ◽  
Changes Over Time ◽  
Over Time

Research shows that repression can lead to both radicalization and deradicalization. When does it drive groups to pick up arms, and under what conditions does it foster disengagement from violence? To answer these questions, it is important to trace tactical changes over time, and to parse the factors that push groups toward or away from violence. The introduction outlines some conventional explanations for understanding tactical choices and shows that recent developments in terrorism studies and in the research on nonviolent resistance leave several puzzles unanswered. It introduces a theoretical framework through which we can understand both escalation and de-escalation, and provides a typology of engagement with violence that can guide the investigation of tactical change. After considering whether Islamist groups are distinctive, the chapter outlines the case-selection strategy and the methodology employed in the book, and then concludes with an outline of the remaining chapters.

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