Lidé

doc. Ing. Tomáš Kroupa, Ph.D.

Všechny publikace

Catch Me if You Can: Improving Adversaries in Cyber-Security with Q-Learning Algorithms

  • DOI: 10.5220/0011684500003393
  • Odkaz: https://doi.org/10.5220/0011684500003393
  • Pracoviště: Katedra počítačů, Centrum umělé inteligence
  • Anotace:
    The ongoing rise in cyberattacks and the lack of skilled professionals in the cybersecurity domain to combat these attacks show the need for automated tools capable of detecting an attack with good performance. Attackers disguise their actions and launch attacks that consist of multiple actions, which are difficult to detect. Therefore, improving defensive tools requires their calibration against a well-trained attacker. In this work, we propose a model of an attacking agent and environment and evaluate its performance using basic Q-Learning, Naive Q-learning, and DoubleQ-Learning, all of which are variants of Q-Learning. The attacking agent is trained with the goal of exfiltrating data whereby all the hosts in the network have a non-zero detection probability. Results show that the DoubleQ-Learning agent has the best overall performance rate by successfully achieving the goal in 70% of the interactions.

Multiple Oracle Algorithm to Solve Continuous Games

  • DOI: 10.1007/978-3-031-26369-9_8
  • Odkaz: https://doi.org/10.1007/978-3-031-26369-9_8
  • Pracoviště: Katedra počítačů, Centrum umělé inteligence
  • Anotace:
    Continuous games are multiplayer games in which strategy sets are compact and utility functions are continuous. These games typically have a highly complicated structure of Nash equilibria, and numerical methods for the equilibrium computation are known only for particular classes of continuous games, such as two-player polynomial games or games in which pure equilibria are guaranteed to exist. This contribution focuses on the computation and approximation of a mixed strategy equilibrium for the whole class of multiplayer general-sum continuous games. We vastly extend the scope of applicability of the double oracle algorithm, initially designed and proved to converge only for two-player zero-sum games. Specifically, we propose an iterative strategy generation technique, which splits the original problem into the master problem with only a finite subset of strategies being considered, and the subproblem in which an oracle finds the best response of each player. This simple method is guaranteed to recover an approximate equilibrium in finitely many iterations. Further, we argue that the Wasserstein distance (the earth mover’s distance) is the right metric for the space of mixed strategies for our purposes. Our main result is the convergence of this algorithm in the Wasserstein distance to an equilibrium of the original continuous game. The numerical experiments show the performance of our method on several classes of games including randomly generated examples.

Values of games over Boolean player sets

  • DOI: 10.1016/j.ijar.2023.108925
  • Odkaz: https://doi.org/10.1016/j.ijar.2023.108925
  • Pracoviště: Katedra počítačů, Centrum umělé inteligence
  • Anotace:
    In this paper, we study new classes of value operators for coalitional games with players organized into a boolean algebra. Coalitional games are cooperative models in which players can form coalitions to maximize profit. The basic solution concepts in such game scenarios are value operators, which assign a unique real value to every player, reflecting thus selected principles of economic rationality. Some value concepts were extended beyond the classic coalitional model where every coalition of players can form. In particular, the extension of Shapley value exists for coalitional games in which players are partially ordered, and the feasible coalitions are the corresponding down-sets. Interestingly, this game-theoretic framework was employed in the method called Information Attribution. This method aims to solve the information decomposition problem, which asks for a particular additive decomposition of the mutual information between the input and target random variables. In such information-theoretic games, the players are predictors, and their set has the natural structure of a boolean algebra. Motivated by the original problem, we consider coalitional games where the players form a boolean algebra, and the coalitions are the corresponding down-sets. This more general approach enables us to study various value solution concepts in detail. Namely, we focus on the classes of values that can represent alternatives to the solution of the information decomposition problem, such as random-order values or sharing values. We extend the axiomatic characterization of some classes of values that were known only for the standard coalitional games.

A finite axiomatization of positive MV-algebras

  • DOI: 10.1007/s00012-022-00776-3
  • Odkaz: https://doi.org/10.1007/s00012-022-00776-3
  • Pracoviště: Centrum umělé inteligence
  • Anotace:
    Positive MV-algebras are the subreducts of MV-algebras with respect to the signature containing Lukasiewicz sum and multiplication, the join and meet, together with the zero and unit constants. We provide a finite quasi-equational axiomatization for the class of such algebras.

Double Oracle Algorithm for Computing Equilibria in Continuous Games

  • Autoři: Adam, L., Ing. Rostislav Horčík, Ph.D., Kasl, T., doc. Ing. Tomáš Kroupa, Ph.D.,
  • Publikace: Proceedings of the Thirty-Fifth AAAI Conference on Artificial Intelligence. Palo Alto, California: Association for the Advancement of Artificial Intelligence (AAAI), 2021. p. 5070-5077. 35. ISSN 2374-3468. ISBN 978-1-57735-866-4.
  • Rok: 2021
  • Pracoviště: Centrum umělé inteligence
  • Anotace:
    Many efficient algorithms have been designed to recover Nash equilibria of various classes of finite games. Special classes of continuous games with infinite strategy spaces, such as polynomial games, can be solved by semidefinite programming. In general, however, continuous games are not directly amenable to computational procedures. In this contribution, we develop an iterative strategy generation technique for finding a Nash equilibrium in a whole class of continuous two-person zero-sum games with compact strategy sets. The procedure, which is called the double oracle algorithm, has been successfully applied to large finite games in the past. We prove the convergence of the double oracle algorithm to a Nash equilibrium. Moreover, the algorithm is guaranteed to recover an approximate equilibrium in finitely-many steps. Our numerical experiments show that it outperforms fictitious play on several examples of games appearing in the literature. In particular, we provide a detailed analysis of experiments with a version of the continuous Colonel Blotto game.

Separable Network Games with Compact Strategy Sets

  • DOI: 10.1007/978-3-030-90370-1_3
  • Odkaz: https://doi.org/10.1007/978-3-030-90370-1_3
  • Pracoviště: Katedra počítačů, Centrum umělé inteligence
  • Anotace:
    A separable network game is a multiplayer finite strategic game in which each player interacts only with adjacent players in a simple undirected graph. The utility of each player results from the aggregation of utilities in the corresponding two-player games. In our contribution, we extend this model to infinite games whose strategy sets are compact subsets of the Euclidean space. We show that Nash equilibria of a zero-sum continuous network game can be characterized as optimal solutions to a specific infinite-dimensional linear optimization problem. In particular, when the utility functions are multivariate polynomials, this optimization formulation enables us to approximate the equilibria using a hierarchy of semidefinite relaxations. We present a security game over a complete bipartite graph in which the nodes are attackers and defenders, who compete for control over given targets.

The two-sorted algebraic theory of states, and the universal states of MV-algebras

  • DOI: 10.1016/j.jpaa.2021.106771
  • Odkaz: https://doi.org/10.1016/j.jpaa.2021.106771
  • Pracoviště: Centrum umělé inteligence
  • Anotace:
    States of unital Abelian lattice-groups provide an abstraction of expected-value operators. A well-known theorem due to Mundici asserts that the category of unital lattice-groups is equivalent to the algebraic category of MV-algebras, and their homomorphisms. Through this equivalence, states of lattice-groups correspond to certain [0,1]-valued functionals on MV-algebras, which are also known as states. In this paper we allow states to take values in any unital lattice-group (or in any MV-algebra) rather than just in R (or just in [0,1], respectively). We introduce a two-sorted algebraic theory whose models are precisely states of MV-algebras. We extend Mundici's equivalence to one between the category of MV-algebras with states as morphisms, and the category of unital Abelian lattice-groups with, again, states as morphisms. Thus, the models of our two-sorted theory may also be regarded as states between unital Abelian lattice-groups. As our first main result, we derive the existence of the universal state of any MV-algebra from the existence of free algebras in multi-sorted algebraic categories. In the remaining part of the paper, we seek concrete representations of such universal states. We begin by clarifying the relationship of universal states with the theory of affine representations: the universal state A→B of the MV-algebra A coincides with a certain modification of Choquet's affine representation (of the lattice-group corresponding to A) if, and only if, B is semisimple. Locally finite MV-algebras are semisimple, and Boolean algebras are instances of locally finite MV-algebras. Our second main result is then that the universal state of any locally finite MV-algebra has semisimple codomain, and can thus be described through our adaptation of Choquet's affine representation.

Core of Coalition Games on MV-algebras

  • DOI: 10.1093/logcom/exp015
  • Odkaz: https://doi.org/10.1093/logcom/exp015
  • Pracoviště: Katedra matematiky
  • Anotace:
    Coalition games are generalized to semisimple MV-algebras. Coalitions are viewed as [0,1]-valued functions on a set of players, which enables to express a degree of membership of a player in a coalition. Every game is a real-valued mapping on a semisimple MV-algebra. The goal is to recover the so-called core: a set of final distributions of payoffs, which are represented by measures on the MV-algebra. A class of sublinear games are shown to have a non-empty core and the core is completely characterized in certain special cases. The interpretation of games on propositional formulas in Lukasiewicz logic is introduced.

Affinity and Continuity of Credal Set Operator

  • Autoři: doc. Ing. Tomáš Kroupa, Ph.D.,
  • Publikace: Proceedings of the 6th International Symposium on Imprecise Probability: Theories and Applications. Durham: SIPTA, 2009. pp. 269-277.
  • Rok: 2009
  • Pracoviště: Katedra matematiky
  • Anotace:
    The credal set operator is studied as a set-valued mapping that assigns the set of dominating probabilities to a coherent lower prevision on some set of gambles. In particular, the conditions guaranteeing its affinity and continuity are identified.

Enlarged Cores and Bargaining Schemes in Games with Fuzzy Coalitions

  • DOI: 10.1016/j.fss.2008.06.001
  • Odkaz: https://doi.org/10.1016/j.fss.2008.06.001
  • Pracoviště: Katedra matematiky
  • Anotace:
    In this paper we introduce a new concept of solution for games with fuzzy coalitions, which we call ail enlarged core. The enlarged core captures an idea that various groups of fuzzy coalitions can have different bargaining power or influence on the final distribution of wealth resulting from the cooperation process. We study a bargaining scheme for the enlarged core, which is ail iterative procedure for generating sequences converging to elements of the enlarged core. It is shown that the enlarged core coincides with Aubin's core For a specific class of games with fuzzy coalitions. (C) 2008 Elsevier B.V. All rights reserved.

Representation of States on MV-algebras by Probabilities on R-generated Boolean Algebras

  • Autoři: doc. Ing. Tomáš Kroupa, Ph.D., Brunella, G.
  • Publikace: Proceedings of IFSA/EUSFLAT 2009. Lisabon: International Fuzzy Systems Associations, 2009. pp. 713-718. ISBN 978-989-95079-6-8.
  • Rok: 2009
  • Pracoviště: Katedra matematiky
  • Anotace:
    Any MV-algebra M can be embedded as a lattice in the Boolean algebra B(M) that is R-generated by M. We relate the study of states on an MV-algebra M to the study of finitely additive probabilities on B(M).

Geometry of Cores of Submodular Coherent Upper Probabilities

  • Autoři: doc. Ing. Tomáš Kroupa, Ph.D.,
  • Publikace: SOFT METHODS FOR HANDLING VARIABILITY AND IMPRECISION. Berlin: Springer, 2008. pp. 306-312. ADVANCES IN SOFT COMPUTING. ISSN 1615-3871. ISBN 978-3-540-85026-7.
  • Rok: 2008
  • Pracoviště: Katedra matematiky
  • Anotace:
    We study and review geometrical properties of the set of the prob- abilities dominated by a submodular coherent upper probability (a possibility measure, in particular) on a finite set. We mention that there exists a polynomial algorithm for vertex enumeration. A new upper bound for the number of vertices in case of possibility measures is derived.

Shapley mappings and the cumulative value for n-person games with fuzzy coalitions

  • Autoři: Butnariu, D., doc. Ing. Tomáš Kroupa, Ph.D.,
  • Publikace: European Journal of Operational Research. 2007, 186(1), 288-299. ISSN 0377-2217.
  • Rok: 2007
  • DOI: 10.1016/j.ejor.2007.01.033
  • Odkaz: https://doi.org/10.1016/j.ejor.2007.01.033
  • Pracoviště: Katedra matematiky
  • Anotace:
    In this paper we prove existence and uniqueness of the so-called Shapley mapping, which is a solution concept for a class of n-person games with fuzzy coalitions whose elements are defined by the specific structure of their characteristic functions. The Shapley mapping, when it exists, associates to each fuzzy coalition in the game an allocation of the coalitional worth satisfying the efficiency, the symmetry, and the null-player conditions. It determines a ''cumulative value'' that is the ''sum'' of all coalitional allocations for whose computation we provide an explicit formula.

Application of the Choquet Integral to Measures of Information in Possibility Theory

  • Pracoviště: Katedra matematiky
  • Anotace:
    The main result of the article is a representation theorem for the nonspecificity of possibility distribution and a new definition of divergence for possibility measures. An application of the divergence to construction of possibilistic models is outlined.

Every state on semisimple MV-algebra is integral

  • DOI: 10.1016/j.fss.2006.06.015
  • Odkaz: https://doi.org/10.1016/j.fss.2006.06.015
  • Pracoviště: Katedra matematiky
  • Anotace:
    Integral representation theorem will be established for finitely additive probability measures (states) on semisimple MV-algebras. This result generalizes the well-known theorem of Butnariu and Klement in case of -order continuous states on tribes of fuzzy sets. Precisely, it will be demonstrated that every state on a separating clan of continuous fuzzy sets arises as an integral with respect to a unique Borel probability measure. The key technique leading to this result exploits the geometrical-topological properties of the state space: the set of all states on every MV-algebra forms a Bauer simplex.

Representation and Extension of States on MV-Algebras

  • DOI: 10.1007/s00153-005-0286-y
  • Odkaz: https://doi.org/10.1007/s00153-005-0286-y
  • Pracoviště: Katedra matematiky
  • Anotace:
    In the presented paper, an integral representation theorem for finitely-additive states on semisimple MV-algebra will be proven. Further, we shall prove extension theorems concerning states defined on sub-MV-algebras and normal partitions of unity generalizing in this way the well-known Horn-Tarski theorem for Boolean algebras.

Conditional Probability on MV-algebras

  • Pracoviště: Katedra kybernetiky
  • Anotace:
    A definition of conditional probability on an MV-algebra is proposed and its basic properties are demonstrated.

Conditional probability on MV-algebras

  • DOI: 10.1016/j.fss.2004.04.010
  • Odkaz: https://doi.org/10.1016/j.fss.2004.04.010
  • Pracoviště: Katedra matematiky
  • Anotace:
    An appropriate definition of a conditional probability on an MV-algebra was an open problem mentioned in Riecan and Mundici (Handbook of Measure Theory, North-Holland, Amsterdam, 2002). We propose some concept of conditional probability (state) on a a-complete MV-algebra with product. Its basic properties will be proven and it will also be demonstrated that the conditional probability in classical probability theory is a special case of this definition. Moreover, the paper contains also a discussion of the interpretation of fuzzy sets and conditioning in fuzzy probability theory.

Conditional Independence in Probability Theory on MV-algebras

  • Pracoviště: Katedra kybernetiky
  • Anotace:
    Conditional independence relation of observables on an MV-algebra with product is formulated and basic properties are proven. An analogy with a classical definition of conditional independence of random variables is discussed and the MV-algebraic concept of conditioning is further explored

Conditional Probability on MV-algebras

  • Autoři: doc. Ing. Tomáš Kroupa, Ph.D.,
  • Publikace: ISCAM 2004. Bratislava: Slovak University of Technology, Faculty of Civil Engineering, 2004, pp. 20.
  • Rok: 2004
  • Pracoviště: Katedra kybernetiky
  • Anotace:
    The contribution proposes an appropriate definition of conditional probability in MV-algebraic probability theory. Its properties are further studied

Copulas and Characterization of T-product Possibility Measures

  • Pracoviště: Katedra kybernetiky
  • Anotace:
    The aim of the contribution is a partial characterization of T-product possibility measures, where T is a t-norm satisfying the Lipschitz property with the constant1. Any possibility measure can be assigned a set of distribution functions which are dominated by this possibility measure. It is demonstrated that the set of all joint distribution functions dominated by a T-product possibility measure contains each joint distribution function obtained by an application of a copula C to some marginal distribution functions dominated by marginal possibility measures

Information Theory for Possibility Measures

  • Autoři: doc. Ing. Tomáš Kroupa, Ph.D.,
  • Publikace: Workshop 2004. Praha: České vysoké učení technické v Praze, 2004, pp. 34-35. ISBN 80-01-02945-X.
  • Rok: 2004
  • Pracoviště: Katedra kybernetiky
  • Anotace:
    The contribution summarizes results of the project whose aim was to develop and study some information quantities in the uncertainty calculus of possibility theory

On Extension of Mappings from Partitions of Unity in MV-algebra

  • Autoři: doc. Ing. Tomáš Kroupa, Ph.D.,
  • Publikace: Proceedings of the 3rd International Workshop on Nonstandard Logics. Praha: ČVUT v Praze, FEL, 2004, pp. 6-8. ISBN 80-01-03003-2.
  • Rok: 2004
  • Pracoviště: Katedra kybernetiky
  • Anotace:
    An extension of state from a given finite partition of unity in a Boolean algebra is uniquely solvable task. A formulation of this problem in MV-algebraic setting is discussed and its solution is outlined

On Interpretation of Possibility Distributions as Sets of Dominated Distribution Functions

  • Autoři: doc. Ing. Tomáš Kroupa, Ph.D.,
  • Publikace: Information Processing and Management of Uncertainty in Knowledge-Based Systems. Roma: University of Roma, 2004,
  • Rok: 2004
  • Pracoviště: Katedra kybernetiky
  • Anotace:
    Possibility distributions are studied using a set of dominated probability distribution functions. This approach enables to characterize T-product possibility distributions with corresponding lower-dimensional distribution functions and certain collection of copulas

Probability Theory of Fuzzy Events and Its Applications

  • Autoři: doc. Ing. Tomáš Kroupa, Ph.D.,
  • Publikace: Workshop 2004. Praha: České vysoké učení technické v Praze, 2004, pp. 32-33. ISBN 80-01-02945-X.
  • Rok: 2004
  • Pracoviště: Katedra kybernetiky
  • Anotace:
    The technical report summarizes results of the project whose aim was to develop both theoretical and practical tools in probability theory of fuzzy events.

Copulas and Characterization of Independence in Possibility Theory

  • Autoři: doc. Ing. Tomáš Kroupa, Ph.D.,
  • Publikace: Abstracts of the FLLL/SCCH Master and PhD Seminar. Hagenberg: Software Competence Center Hagenberg, 2003, pp. 6-10.
  • Rok: 2003
  • Pracoviště: Katedra kybernetiky
  • Anotace:
    The contribution aims at an interpretation of the general independence concept in possibility theory, which is based on a continuous t-norm T instead of considering only the minimum or product to construct the T-product possibility measure. Any possibility measure can be assigned a set of distribution functions which are dominated by this possibility measure. By means of copulas, we can then partially characterize the set of distribution functions that is dominated by the T-product possibility measure

Improved Possibilistic Classifier as a Recommender System

  • Pracoviště: Katedra kybernetiky
  • Anotace:
    Článek popisuje návrh řešení el. obchodu, které by se dalo označit jako inteligentní, neboť si klade za cíl plně provázet uživatele v procesu výběru produktu. Navržený přístup usnadní prohlížení katalogu produktů, nabízí doporučení produktu na základě preference zákazníka a jeho profilu. Technickým základem řešení je possibilistická síť a vylepšený klasifikační algoritmus.

On Application of Choquet integral in possibilistic information theory

  • Pracoviště: Katedra kybernetiky
  • Anotace:
    The aim of this paper is to introduce the Choquet integral representation of some information quantities in the possibility theory. A possibilistic T-independence concept is further analysed with respect to its information-theoretic properties. The main results is then the introduction of a so called general measure of T-dependence. It is further proven that the general measure of T-dependence exhibits significant properties from an information-theoretic point of view and can be conceived as an apt analogy of the well-known probabilistic mutual information.

On Construction of Joint Observable on Lukasiewicz Tribe

  • Autoři: doc. Ing. Tomáš Kroupa, Ph.D.,
  • Publikace: EUSFLAT 2003. Aachen: University of Applied Sciences Aachen, 2003, pp. 665-668. ISBN 3-9808089-4-7.
  • Rok: 2003
  • Pracoviště: Katedra kybernetiky
  • Anotace:
    Analogie mezi konstrukcí náhodného vektoru a sdružené pozorovatelné na Lukasiewiczově kmenu je popsána a diskutována. Je navržena jednoduchá metoda umožňující konstrukci sdružené pozorovatelné. Hodnota sdružené pozorovatelné je interpretována jako fuzzy relace. Technika je ilustrována na příkladu

Information Measures in Possibility Theory

  • Autoři: doc. Ing. Tomáš Kroupa, Ph.D.,
  • Publikace: Proceedings of Seminar on Data Analysis and Decision Making under Uncerrtainty. Sendai: A. A. Balkema Publisher, 2002, pp. 143-148.
  • Rok: 2002
  • Pracoviště: Katedra kybernetiky
  • Anotace:
    Příspěvek pojednává o informačně-teoretických veličinách (nespecificitě a agregátní neurčitosti-AU) definovaných pro neaditvní míry neurčitosti, tzv. possibilistické míry. Nespecificita a AU byly původně definovány v kontextu Dempsterovy-Shaferovy teorie. Pozornost je věnována zejména objasnění jejich vzájemného vztahu, je dokázána základní nerovnost mezi nespecificitou a AU, která platí i v Dempsterově-Shaferově teorii. Dále je zkoumána aditivita obou informačních měr vzhledem k possibilistickému konceptu nezávislosti definovaného pomocí t-normy.

Information Quantities and Possibility Measures

  • Pracoviště: Katedra kybernetiky
  • Anotace:
    Článek shrnuje a analyzuje vlastnosti základních měr informace v teorii možnosti: agregátní neurčitosti a nespecificity, které mohou být studovány v rámci teorie posibility jako speciální případ D-S teorie. Základním výsledkem je nerovnost mezi agregátní neurčitostí a nespecifitou, která objasňuje jejich vzájemný vztah. Dále je studována souvislost mezi posibilistickou nezávislostí parametrizovanou libovolnou t-normou a aditivitou informačních měr.

WISECON - an Intelligent Assistant for Buying Computers on the Internet

  • Autoři: doc. Ing. Tomáš Kroupa, Ph.D., Berka, P., Kočka, T.
  • Publikace: Foundations of Intelligent Systems. Berlin: Springer, 2002, pp. 167-175. ISBN 3-540-43785-1.
  • Rok: 2002
  • Pracoviště: Katedra kybernetiky
  • Anotace:
    Elektronické obchodování se v současné době těší nebývalému rozvoji. Článek popisuje návrh řešení el. obchodu, které by se dalo označit jako inteligentní, neboť si klade za cíl plně provázet uživatele v procesu výběru produktu. Navržený přístup usnadní prohlížení katalogu produktů, nabízí doporučení produktu na základě preference zákazníka a jeho profilu. Technickým základem řešení je Bayesovská síť, která umožňuje využít klasický klasifikační algoritmus k doporučovaní produktů. Ke zrychlení konzultace uživatele se systémem slouží speciální heuristika.

WISECON: The Intelligent Support for E-Commerce

  • Autoři: doc. Ing. Tomáš Kroupa, Ph.D., Berka, P.
  • Publikace: Symposium "Intelligent Systems". Sofia: IEEE, 2002, pp. 210-214. ISBN 0-7803-7601-3.
  • Rok: 2002
  • Pracoviště: Katedra kybernetiky
  • Anotace:
    Elektronické obchodování se v současné době těší nebývalému rozvoji. Článek popisuje návrh řešení el. obchodu, které by se dalo označit jako inteligentní, neboť si klade za cíl plně provázet uživatele v procesu výběru produktu. Navržený přístup usnadní prohlížení katalogu produktů, nabízí doporučení produktu na základě preference zákazníka a jeho profilu. Technickým základem řešení je possibilistická síť, která umožňuje využít klasický klasifikační algoritmus k doporučovaní produktů.

Za stránku zodpovídá: Ing. Mgr. Radovan Suk