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Facing Sub-rational Opponent in Imperfect-Information Games
Hraní proti subracionálním protivníkům v hrách s neúplnou informací
(Czech Technical University in Prague) Milec, David; Lisý, Viliam; Loebl, Martin; Wright, James
Strategic decision-making in large imperfect-information games presents a fundamental challenge: how to adapt effectively to suboptimal or boundedly rational opponents while maintaining robustness against unexpected behavior and remaining computationally scalable. Classical game-solving methods based on Nash equilibrium offer strong safety guarantees but cannot adapt to opponent mistakes, while pure adaptation approaches achieve high payoffs only when opponent models are accurate, often at the cost of catastrophic losses when it is not. This thesis addresses this tension by developing scalable algorithms for safe opponent adaptation in large imperfect-information games. The thesis makes three core contributions. First, it addresses the challenge of efficiently solving large-scale imperfect-information games by developing a unified theoretical framework that connects previously used domain-specific optimizations to Sequential Bayesian Games (SBGs). Within this framework, the thesis formalizes and analyzes Public State Counterfactual Regret Minimization (PS-CFR). The thesis proves PS-CFR produces identical solutions to vanilla CFR while reducing per-iteration complexity from the number of histories to the number of information sets, resulting in substantial empirical speedups and memory reductions in poker and related domains. Second, the thesis investigates adaptation to boundedly rational opponents using the quantal response framework. It analyzes quantal Nash equilibrium (QNE) and quantal Stackelberg equilibrium (QSE), establishes computational hardness results and shows that CFR does not guarantee convergence to QSE for widely used quantal functions. To overcome these limitations, the thesis introduces scalable CFR-based heuristics, including restricted quantal response (RQR), which balances exploitation and safety by probabilistically mixing rational and quantal opponent models. Extensive experiments demonstrate that RQR achieves superior trade-offs between gain and exploitability across large games. Third, the thesis develops a suite of depth-limited adaptive algorithms suitable for massive domains where full-game solving is infeasible. These include Continual Depth-limited Best Response (CDBR) for maximal exploitation, Continual Depth-limited Restricted Nash Response (CDRNR) for safe adaptation, and Adapting Beyond Depth-limit (ABD), which enables exploitation of opponent weaknesses occurring outside the search horizon using portfolio-based value functions. The thesis provides theoretical guarantees, analyzes limitations of existing subgame-solving gadgets, and introduces new constructions that ensure correctness under adaptation. Empirical evaluation across normal-form games, extensive-form benchmarks, and heads-up no-limit Texas Holdem demonstrates significant performance improvements over existing methods, including state-of-the-art poker agents. Overall, this thesis advances both the theoretical understanding and practical capabilities of opponent adaptation in large imperfect-information games, showing that effective adaptation is possible at scale without sacrificing essential robustness guarantees.
Elements of Atomistic Simulations
(Czech Technical University in Prague, 2026) Cammarata A.; Pervíz, E.
These lecture notes accompany the course “Elements of atomistic simulations” held at the Department of Control Engineering, Faculty of Electrical Engineering, Czech Technical University in Prague, and are intended to provide a coherent written support to the topics discussed during the lectures. The course develops along a progressive path, starting from classical descriptions of matter and advancing toward quantum-mechanical approaches, with the common goal of understanding, modelling, and predicting the structural, dynamical, and electronic properties of condensed-matter systems from an atomistic perspective. We begin by introducing classical molecular dynamics, where atoms are treated as point particles evolving under Newton’s equations of motion. This framework allows the simulation of large systems over long time scales and provides access to thermodynamic, structural, and dynamical properties through statistical averaging. Within this context, we discuss interatomic potentials, equilibration, computation of observables, and the interpretation of quantities such as radial and pair distribution functions, pressure, and temperature. We then extend the discussion to periodic systems, reciprocal space, Brillouin zones, supercells, and k-point sampling, which are essential concepts for modelling crystalline materials and defects. The course then transitions to a quantum-mechanical description of matter, motivated by the limitations of classical approaches when electronic degrees of freedom play a crucial role. We introduce the fundamental concepts of quantum mechanics, the role of the Schr¨odinger equation, basis sets, and the self-consistent field procedure as a unifying framework underlying several electronic-structure methods. Emphasis is placed on how total energies, forces, and other physical quantities are obtained in practice, and on the general structure of first-principles calculations, independently of the specific level of approximation adopted. Building on this foundation, we address key applications such as geometry optimisation, reaction and transformation paths, and phase stability through formation energies. Particular attention is devoted to lattice dynamics and phonons, including their physical interpretation, computational determination, and connection to measurable properties such as vibrational spectra, thermal stability, and heat transport. Both finite-displacement and linear-response approaches are discussed, together with practical aspects of convergence and numerical accuracy. Finally, the course introduces electron–phonon coupling as a central concept linking electronic structure and lattice dynamics, highlighting its importance for transport phenomena, superconductivity, and temperature-dependent material properties. These notes aim to provide a structured reference that students can consult during and after the course, helping to consolidate definitions, equations, and conceptual links between different topics. However, they are not meant to be a self-contained textbook, nor can they substitute for the oral lectures. Many explanations, physical interpretations, examples, and methodological insights are developed interactively during the lectures and through discussion, and cannot be fully captured in written form. The notes should therefore be regarded as a complementary tool, to be read alongside attentive participation in the lectures and active engagement with exercises and computational examples. Several books exist covering all the topics here discussed; as an example, we suggest the reading of “Understanding Molecular Simulation: From Algorithms to Applications” by D. Frenkel and B. Smit,1 “Molecular Quantum Mechanics” by P. W. Atkins and R. S. Friedman,2 “Quantum Mechanics, Volume 1” by C. Cohen-Tannoudji, B. Diu and F. Laloe,3 and “Electrons and Phonons: The Theory of Transport Phenomena in Solids” by J. M. Ziman.4 Ultimately, the objective of the course is not only to present specific methods, but also to develop a critical understanding of their assumptions, capabilities, and limitations, opening the students the path towards the creation of new materials for target applications
Konstruktivní geometrie
(2016) Kočandrlová, M.; Černý, J.
Didaktika technických odborných předmětů
(2016) Vaněček, D.
Termodynamika vlhkého vzduchu
(2016) Šafařík, P.; Vestfálová, M.