75 citations · 276 across the 23 of their papers we have counts for
24 papers
Synthesizing Resilient Strategies for Infinite-Horizon Objectives in Multi-Agent Systems
David Klaška, Antonín Kučera, Martin Kurečka +3
We consider the problem of synthesizing resilient and stochastically stable strategies for systems of cooperating agents striving to minimize the expected time between consecutive…
Mean Payoff Optimization for Systems of Periodic Service and Maintenance
David Klaška, Antonín Kučera, Vít Musil +1
Consider oriented graph nodes requiring periodic visits by a service agent. The agent moves among the nodes and receives a payoff for each completed service task, depending on the…
Optimality problems in Orlicz spaces
Vít Musil, Luboš Pick, Jakub Takáč
In mathematical modelling, the data and solutions are represented as measurable functions and their quality is oftentimes captured by the membership to a certain function space. On…
Optimal Sobolev embeddings for the Ornstein-Uhlenbeck operator
Andrea Cianchi, Vít Musil, Luboš Pick
A comprehensive analysis of Sobolev-type inequalities for the Ornstein-Uhlenbeck operator in the Gauss space is offered. A unified approach is proposed, providing one with criteria…
On-the-fly Adaptation of Patrolling Strategies in Changing Environments
Tomáš Brázdil, David Klaška, Antonín Kučera +3
We consider the problem of efficient patrolling strategy adaptation in a changing environment where the topology of Defender's moves and the importance of guarded targets change un…
General Optimization Framework for Recurrent Reachability Objectives
David Klaška, Antonín Kučera, Vít Musil +1
We consider the mobile robot path planning problem for a class of recurrent reachability objectives. These objectives are parameterized by the expected time needed to visit one pos…
Backpropagation through Combinatorial Algorithms: Identity with Projection Works
Subham Sekhar Sahoo, Anselm Paulus, Marin Vlastelica +3
Embedding discrete solvers as differentiable layers has given modern deep learning architectures combinatorial expressivity and discrete reasoning capabilities. The derivative of t…
Minimizing Expected Intrusion Detection Time in Adversarial Patrolling
David Klaška, Antonín Kučera, Vít Musil +1
In adversarial patrolling games, a mobile Defender strives to discover intrusions at vulnerable targets initiated by an Attacker. The Attacker's utility is traditionally defined as…
Regstar: Efficient Strategy Synthesis for Adversarial Patrolling Games
David Klaška, Antonín Kučera, Vít Musil +1
We design a new efficient strategy synthesis method applicable to adversarial patrolling problems on graphs with arbitrary-length edges and possibly imperfect intrusion detection.…
CombOptNet: Fit the Right NP-Hard Problem by Learning Integer Programming Constraints
Anselm Paulus, Michal Rolínek, Vít Musil +2
Bridging logical and algorithmic reasoning with modern machine learning techniques is a fundamental challenge with potentially transformative impact. On the algorithmic side, many…
Sharp exponential inequalities for the Ornstein-Uhlenbeck operator
Andrea Cianchi, Vít Musil, Luboš Pick
The optimal constants in a class of exponential type inequalities for the Ornstein-Uhlenbeck operator in the Gauss space are detected. The existence of extremal functions in the re…
Maximal non-compactness of Sobolev embeddings
Jan Lang, Vít Musil, Miroslav Olšák +1
It has been known that sharp Sobolev embeddings into weak Lebesgue spaces are non-compact but the question of whether the measure of non-compactness of such an embedding equals to…
Deep Graph Matching via Blackbox Differentiation of Combinatorial Solvers
Michal Rolínek, Paul Swoboda, Dominik Zietlow +3
Building on recent progress at the intersection of combinatorial optimization and deep learning, we propose an end-to-end trainable architecture for deep graph matching that contai…
On the existence of extremals for Moser type inequalities in Gauss space
Andrea Cianchi, Vít Musil, Luboš Pick
The existence of an extremal in an exponential Sobolev type inequality, with optimal constant, in Gauss space is established. A key step in the proof is an augmented version of the…
Optimal Orlicz domains in Sobolev embeddings into Marcinkiewicz spaces
Vít Musil
In this paper we present a method for determining whether there exists a largest Orlicz space satisfying the Sobolev embedding where stands for…
Optimizing Rank-based Metrics with Blackbox Differentiation
Michal Rolínek, Vít Musil, Anselm Paulus +3
Rank-based metrics are some of the most widely used criteria for performance evaluation of computer vision models. Despite years of effort, direct optimization for these metrics re…
Differentiation of Blackbox Combinatorial Solvers
Marin Vlastelica, Anselm Paulus, Vít Musil +2
Achieving fusion of deep learning with combinatorial algorithms promises transformative changes to artificial intelligence. One possible approach is to introduce combinatorial buil…
Moser inequalities in Gauss space
Andrea Cianchi, Vít Musil, Luboš Pick
The sharp constants in a family of exponential Sobolev type inequalities in Gauss space are exhibited. They constitute the Gaussian analogues of the Moser inequality in the borderl…
Boundedness of classical operators on rearrangement-invariant spaces
David E. Edmunds, Zdeněk Mihula, Vít Musil +1
We study the behaviour on rearrangement-invariant spaces of such classical operators of interest in harmonic analysis as the Hardy-Littlewood maximal operator (including the fracti…
Fractional Maximal Operator in Orlicz spaces
Vít Musil
We study the fractional maximal operator acting between Orlicz spaces. We characterise whether the operator is bounded between two given Orlicz spaces. Also a necessary and suffici…
Strict s-numbers of non-compact Sobolev embeddings into continuous functions
Jan Lang, Vít Musil
For limiting non-compact Sobolev embeddings into continuous functions we study behavior of Approximation, Gelfand, Kolmogorov, Bernstein and Isomorphism s-numbers. In the one dimen…
Optimal domain spaces in Orlicz-Sobolev embeddings
Andrea Cianchi, Vít Musil
We deal with Orlicz-Sobolev embeddings in open subsets of . A necessary and sufficient condition is established for the existence of an optimal, i.e. largest possible…
Strict s-numbers of the Volterra operator
Özlem Bakşi, Taqseer Khan, Jan Lang +1
For Volterra operator and summation operator , we obtain exact values of Approximation, Gelfand, Kolmogorov, Mityagin and Isomor…
Interpolation theorem for Marcinkiewicz spaces with applications to Lorentz gamma spaces
Vít Musil, Rastislav Oľhava
This paper is devoted to the interpolation principle between spaces of weak type. We characterise interpolation spaces between two Marcinkiewicz spaces in terms of Hardy type opera…