scholarly journals The Price of Usability: Designing Operationalizable Strategies for Security Games

2018 ◽  
Author(s):  
Sara Marie Mc Carthy ◽  
Corine M. Laan ◽  
Kai Wang ◽  
Phebe Vayanos ◽  
Arunesh Sinha ◽  
...  
Keyword(s):  
Optimization Problem ◽  
Mixed Strategy ◽  
Static Solution ◽  
Mixed Integer ◽  
Integer Optimization ◽  
Security Personnel ◽  
Security Games ◽  
Game Theoretic ◽  
Pure Strategies ◽  
Security Game

We consider the problem of allocating scarce security resources among heterogeneous targets to thwart a possible attack. It is well known that deterministic solutions to this problem being highly predictable are severely suboptimal. To mitigate this predictability, the game-theoretic security game model was proposed which randomizes over pure (deterministic) strategies, causing confusion in the adversary. Unfortunately, such mixed strategies typically involve randomizing over a large number of strategies, requiring security personnel to be familiar with numerous protocols, making them hard to operationalize. Motivated by these practical considerations, we propose an easy to use approach for computing  strategies that are easy to operationalize and that bridge the gap between the static solution and the optimal mixed strategy. These strategies only randomize over an optimally chosen subset of pure strategies whose cardinality is selected by the defender, enabling them to conveniently tune the trade-off between ease of operationalization and efficiency using a single design parameter. We show that the problem of computing such operationalizable strategies is NP-hard, formulate it as a mixed-integer optimization problem, provide an algorithm for computing epsilon-optimal equilibria, and an efficient heuristic. We evaluate the performance of our approach on the problem of screening for threats at airport checkpoints and show that the Price of Usability, i.e., the loss in optimality to obtain a strategy that is easier to operationalize, is typically not high.

Loss reduction as a Mixed Integer optimization problem

2009 ◽  
Author(s):  
Stephane Fliscounakis ◽  
Fabrice Zaoui ◽  
Marie-Pierre Houry ◽  
Emilie Milin
Keyword(s):  
Optimization Problem ◽  
Mixed Integer ◽  
Loss Reduction ◽  
Integer Optimization ◽  
Mixed Integer Optimization

scholarly journals Multistage Attack Graph Security Games: Heuristic Strategies, with Empirical Game-Theoretic Analysis

2018 ◽  
Vol 2018 ◽  
pp. 1-28 ◽  
Author(s):  
Thanh H. Nguyen ◽  
Mason Wright ◽  
Michael P. Wellman ◽  
Satinder Singh
Keyword(s):  
Cyber Attacks ◽  
Attack Graphs ◽  
Game Analysis ◽  
Attack Graph ◽  
Game Theoretic Analysis ◽  
Security Environment ◽  
Heuristic Strategies ◽  
Security Games ◽  
Game Theoretic ◽  
Security Game

We study the problem of allocating limited security countermeasures to protect network data from cyber-attacks, for scenarios modeled by Bayesian attack graphs. We consider multistage interactions between a network administrator and cybercriminals, formulated as a security game. This formulation is capable of representing security environments with significant dynamics and uncertainty and very large strategy spaces. We propose parameterized heuristic strategies for the attacker and defender and provide detailed analysis of their time complexity. Our heuristics exploit the topological structure of attack graphs and employ sampling methods to overcome the computational complexity in predicting opponent actions. Due to the complexity of the game, we employ a simulation-based approach and perform empirical game analysis over an enumerated set of heuristic strategies. Finally, we conduct experiments in various game settings to evaluate the performance of our heuristics in defending networks, in a manner that is robust to uncertainty about the security environment.

scholarly journals An Algorithm for Rescheduling of Trains under Planned Track Closures

2021 ◽  
Vol 11 (5) ◽  
pp. 2334
Author(s):  
Grzegorz Filcek ◽  
Dariusz Gąsior ◽  
Maciej Hojda ◽  
Jerzy Józefczyk
Keyword(s):  
Optimization Problem ◽  
Broad Class ◽  
Mixed Integer ◽  
Time Shift ◽  
Integer Optimization ◽  
Train Rescheduling ◽  
Feasible Solutions ◽  
The Given ◽  
Np Hardness

This work considered a joint problem of train rescheduling and closure planning. The derivation of a new train run schedule and the determination of a closure plan not only must guarantee the satisfaction of all the given constraints but also must optimize the number of accepted closures, the number of approved train runs, and the total time shift between the resultant and the original schedule. Presented is a novel nonlinear mixed integer optimization problem which is valid for a broad class of railway networks. A multi-level hierarchical heuristic algorithm is introduced due to the NP-hardness of the considered optimization problem. The algorithm is able, on an iterative basis, to jointly select closures and train runs, along with the derivation of a train schedule. Results obtained by the algorithm, launched for the conducted experiments, confirm its ability to provide acceptable and feasible solutions in a reasonable amount of time.

scholarly journals Stability by the vector criterion of a mixed integer optimization problem with quadratic criterial fun ctions

2020 ◽  
pp. 15-21
Author(s):  
Т.Т. Lebedeva ◽  
◽  
N.V. Semenova ◽  
T.I. Sergienko ◽  
◽  
...  
Keyword(s):  
Initial Data ◽  
Optimization Problem ◽  
Sufficient Conditions ◽  
Mixed Integer ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Integer Optimization ◽  
Mixed Integer Optimization ◽  
Vector Criterion

The article is devoted to the study of qualitative characteristics of different concepts of stability of vector problems of mixed-integer optimization, namely, to identifying the conditions under which the set of Pareto-optimal solutions of the problem possesses some property of invariance defined in advance in relation to the external influences on initial data of the problem. We investigate the questions of stability with respect to data perturbations in a vector criterion of mixed-integer optimization problem. The necessary and sufficient conditions of stability of three types for a problem of finding the solutions of the Pareto set are found. Such conditions guarantee that the small variations of initial data of vector criterion: 1) do not result in new Paretooptimal solutions, 2) save all Pareto-optimal solutions of the problem and can admit new solutions, 3) do not change the set of Pareto-optimal solutions of the initial problem.

scholarly journals Mixed-Integer Convex Nonlinear Optimization with Gradient-Boosted Trees Embedded

2020 ◽  
Author(s):  
Miten Mistry ◽  
Dimitrios Letsios ◽  
Gerhard Krennrich ◽  
Robert M. Lee ◽  
Ruth Misener
Keyword(s):  
Large Scale ◽  
Optimization Problem ◽  
Regression Tree ◽  
Penalty Functions ◽  
Discrete Models ◽  
Mixed Integer ◽  
Integer Optimization ◽  
Data Set ◽  
Chemical Catalysis ◽  
Feasible Solutions

Decision trees usefully represent sparse, high-dimensional, and noisy data. Having learned a function from these data, we may want to thereafter integrate the function into a larger decision-making problem, for example, for picking the best chemical process catalyst. We study a large-scale, industrially relevant mixed-integer nonlinear nonconvex optimization problem involving both gradient-boosted trees and penalty functions mitigating risk. This mixed-integer optimization problem with convex penalty terms broadly applies to optimizing pretrained regression tree models. Decision makers may wish to optimize discrete models to repurpose legacy predictive models or they may wish to optimize a discrete model that accurately represents a data set. We develop several heuristic methods to find feasible solutions and an exact branch-and-bound algorithm leveraging structural properties of the gradient-boosted trees and penalty functions. We computationally test our methods on a concrete mixture design instance and a chemical catalysis industrial instance.

FREQUENCY-RESPONSE MASKING BASED FIR FILTER DESIGN WITH POWER-OF-TWO COEFFICIENTS AND SUBOPTIMUM PWR

2003 ◽  
Vol 12 (05) ◽  
pp. 591-599 ◽  
Author(s):  
W. R. LEE ◽  
V. REHBOCK ◽  
K. L. TEO ◽  
L. CACCETTA
Keyword(s):  
Frequency Response ◽  
Optimization Problem ◽  
Filter Design ◽  
Mixed Integer ◽  
Discrete Optimization Problem ◽  
Linear Phase ◽  
Integer Optimization ◽  
Scaling Parameters ◽  
Frequency Response Masking ◽  
Fir Filter Design

This paper presents a new method for designing sharp linear phase FIR filters with power-of-two coefficients. The method is based on a frequency-response masking technique. In this method, the power-of-two coefficients and continuous scaling parameters of the subfilters are taken to be decision variables, and minimizing peak weighted ripple (PWR) is taken to be the design objective. The resulting nonlinear mixed integer optimization problem for each subfilter is first reduced to an equivalent discrete optimization problem whose search region is then cropped for efficiency of computation, similar to the approach in Ref. 1, although a different cropping strategy is used here. The effectiveness of the method is demonstrated through a lowpass linear phase sharp FIR digital filter example.

Generalized Replicator Dynamics as a Model of Specialization and Diversity in Societies

1998 ◽  
Vol 01 (04) ◽  
pp. 325-359 ◽  
Author(s):  
Vivek S. Borkar ◽  
Sanjay Jain ◽  
Govindan Rangarajan
Keyword(s):  
Mixed Strategy ◽  
Replicator Dynamics ◽  
Pure Strategy ◽  
Evolutionary Game ◽  
Payoff Matrix ◽  
Theoretic Model ◽  
Final States ◽  
Game Theoretic ◽  
Game Theoretic Model ◽  
Pure Strategies

We consider a generalization of replicator dynamics as a non-cooperative evolutionary game-theoretic model of a community of N agents. All agents update their individual mixed strategy profiles to increase their total payoff from the rest of the community. The properties of attractors in this dynamics are studied. Evidence is presented that under certain conditions the typical attractors of the system are corners of state space where each agent has specialized to a pure strategy, and/or the community exhibits diversity, i.e., all strategies are represented in the final states. The model suggests that new pure strategies whose payoff matrix elements satisfy suitable inequalities with respect to the existing ones can destabilize existing attractors if N is sufficiently large, and be regarded as innovations that enhance the diversity of the community.

scholarly journals Smart “Predict, then Optimize”

2021 ◽  
Author(s):  
Adam N. Elmachtoub ◽  
Paul Grigas
Keyword(s):  
Prediction Model ◽  
Loss Function ◽  
Optimization Problem ◽  
Linear Models ◽  
Prediction Models ◽  
Optimization Problems ◽  
Mixed Integer ◽  
Complex Nature ◽  
Integer Optimization ◽  
Highly Nonlinear

Many real-world analytics problems involve two significant challenges: prediction and optimization. Because of the typically complex nature of each challenge, the standard paradigm is predict-then-optimize. By and large, machine learning tools are intended to minimize prediction error and do not account for how the predictions will be used in the downstream optimization problem. In contrast, we propose a new and very general framework, called Smart “Predict, then Optimize” (SPO), which directly leverages the optimization problem structure—that is, its objective and constraints—for designing better prediction models. A key component of our framework is the SPO loss function, which measures the decision error induced by a prediction. Training a prediction model with respect to the SPO loss is computationally challenging, and, thus, we derive, using duality theory, a convex surrogate loss function, which we call the SPO+ loss. Most importantly, we prove that the SPO+ loss is statistically consistent with respect to the SPO loss under mild conditions. Our SPO+ loss function can tractably handle any polyhedral, convex, or even mixed-integer optimization problem with a linear objective. Numerical experiments on shortest-path and portfolio-optimization problems show that the SPO framework can lead to significant improvement under the predict-then-optimize paradigm, in particular, when the prediction model being trained is misspecified. We find that linear models trained using SPO+ loss tend to dominate random-forest algorithms, even when the ground truth is highly nonlinear. This paper was accepted by Yinyu Ye, optimization.

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