Author name cluster

Rostislav Horčík

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5 papers

1 author row

AAAI Conference 2022 Conference Paper

Competing for Resources: Estimating Adversary Strategy for Effective Plan Generation

Lukáš Chrpa
Pavel Rytíř
Rostislav Horčík
Stefan Edelkamp

Effective decision making while competing for limited resources in adversarial environments is important for many real-world applications (e. g. two Taxi companies competing for customers). Decision-making techniques such as Automated planning have to take into account possible actions of adversary (or competing) agents. That said, the agent should know what the competitor will likely do and then generate its plan accordingly. In this paper we propose a novel approach for estimating strategies of the adversary (or the competitor), sampling its actions that might hinder agent’s goals by interfering with the agent’s actions. The estimated competitor strategies are used in plan generation such that agent’s actions have to be applied prior to the ones of the competitor, whose estimated times dictate the deadlines. We empirically evaluate our approach leveraging sampling of competitor’s actions by comparing it to the naive approach optimising the make-span (not taking the competing agent into account at all) and to Nash Equilibrium (mixed) strategies.

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AAAI Conference 2022 Conference Paper

Homomorphisms of Lifted Planning Tasks: The Case for Delete-Free Relaxation Heuristics

Rostislav Horčík
Daniel Fišer
Álvaro Torralba

Classical planning tasks are modelled in PDDL which is a schematic language based on first-order logic. Most of the current planners turn this lifted representation into a propositional one via a grounding process. However, grounding may cause an exponential blowup. Therefore it is important to investigate methods for searching for plans on the lifted level. To build a lifted state-based planner, it is necessary to invent lifted heuristics. We introduce maps between PDDL tasks preserving plans allowing us to transform a PDDL task into a smaller one. We propose a novel method for computing lifted (admissible) delete-free relaxed heuristics via grounding of the smaller task and computing the (admissible) delete-free relaxed heuristics there. This allows us to transfer the knowledge about relaxed heuristics from the grounded level to the lifted level.

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AAAI Conference 2021 Conference Paper

Double Oracle Algorithm for Computing Equilibria in Continuous Games

Lukáš Adam
Rostislav Horčík
Tomáš Kasl
Tomáš Kroupa

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.

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AAAI Conference 2021 Conference Paper

Endomorphisms of Classical Planning Tasks

Rostislav Horčík
Daniel Fišer

Detection of redundant operators that can be safely removed from the planning task is an essential technique allowing to greatly improve performance of planners. In this paper, we employ structure-preserving maps on labeled transition systems (LTSs), namely endomorphisms that are well known from model theory, in order to detect redundancy. Computing endomorphisms of an LTS induced by a planning task is typically infeasible, so we show how to compute some of them on concise representations of planning tasks such as finite domain representations and factored LTSs. We formulate the computation of endomorphisms as a constraint satisfaction problem (CSP) that can be solved by an off-the-shelf CSP solver. Finally, we experimentally verify that the proposed method can find a sizable number of redundant operators on the standard benchmark set.

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TCS Journal 2011 Journal Article

Disjunction property and complexity of substructural logics

Rostislav Horčík
Kazushige Terui

We systematically identify a large class of substructural logics that satisfy the disjunction property (DP), and show that every consistent substructural logic with the DP is PSPACE-hard. Our results are obtained by using algebraic techniques. PSPACE-completeness for many of these logics is furthermore established by proof theoretic arguments.

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