David Milec

David Milec, Viliam Lisý, Christopher Kiekintveld

Protecting against adversarial attacks is a common multiagent problem. Attackers in the real world are predominantly human actors, and the protection methods often incorporate opponent models to improve the performance when facing humans. Previous results show that modeling human behavior can significantly improve the performance of the algorithms. However, modeling humans correctly is a complex problem, and the models are often simplified and assume humans make mistakes according to some distribution or train parameters for the whole population from which they sample. In this work, we use data gathered by psychologists who identified personality types that increase the likelihood of performing malicious acts. However, in the previous work, the tests on a handmade game could not show strategic differences between the models. We created a novel model that links its parameters to psychological traits. We optimized over parametrized games and created games in which the differences are profound. Our work can help with automatic game generation when we need a game in which some models will behave differently and to identify situations in which the models do not align.

David Milec, Vojtěch Kovařík, Viliam Lisý

We study the problem of adapting to a known sub-rational opponent during online play while remaining robust to rational opponents. We focus on large imperfect-information (zero-sum) games, which makes it impossible to inspect the whole game tree at once and necessitates the use of depth-limited search. However, all existing methods assume rational play beyond the depth-limit, which only allows them to adapt a very limited portion of the opponent's behaviour. We propose an algorithm Adapting Beyond Depth-limit (ABD) that uses a strategy-portfolio approach - which we refer to as matrix-valued states - for depth-limited search. This allows the algorithm to fully utilise all information about the opponent model, making it the first robust-adaptation method to be able to do so in large imperfect-information games. As an additional benefit, the use of matrix-valued states makes the algorithm simpler than traditional methods based on optimal value functions. Our experimental results in poker and battleship show that ABD yields more than a twofold increase in utility when facing opponents who make mistakes beyond the depth limit and also delivers significant improvements in utility and safety against randomly generated opponents.

Vojtěch Kovařík, David Milec, Michal Šustr et al.

Recent advancements in algorithms for sequential decision-making under imperfect information have shown remarkable success in large games such as limit- and no-limit poker. These algorithms traditionally formalize the games using the extensive-form game formalism, which, as we show, while theoretically sound, is memory-inefficient and computationally intensive in practice. To mitigate these challenges, a popular workaround involves using a specialized representation based on player specific information-state trees. However, as we show, this alternative significantly narrows the set of games that can be represented efficiently. In this study, we identify the set of large games on which modern algorithms have been benchmarked as being naturally represented by Sequential Bayesian Games. We elucidate the critical differences between extensive-form game and sequential Bayesian game representations, both theoretically and empirically. We further argue that the impressive experimental results often cited in the literature may be skewed, as they frequently stem from testing these algorithms only on this restricted class of games. By understanding these nuances, we aim to guide future research in developing more universally applicable and efficient algorithms for sequential decision-making under imperfect information.

David Milec, Jakub Černý, Viliam Lisý et al.

Solution concepts of traditional game theory assume entirely rational players; therefore, their ability to exploit subrational opponents is limited. One type of subrationality that describes human behavior well is the quantal response. While there exist algorithms for computing solutions against quantal opponents, they either do not scale or may provide strategies that are even worse than the entirely-rational Nash strategies. This paper aims to analyze and propose scalable algorithms for computing effective and robust strategies against a quantal opponent in normal-form and extensive-form games. Our contributions are: (1) we define two different solution concepts related to exploiting quantal opponents and analyze their properties; (2) we prove that computing these solutions is computationally hard; (3) therefore, we evaluate several heuristic approximations based on scalable counterfactual regret minimization (CFR); and (4) we identify a CFR variant that exploits the bounded opponents better than the previously used variants while being less exploitable by the worst-case perfectly-rational opponent.