Information abstraction is one of the methods for tackling large extensive-form games (EFGs). Removing some information available to players reduces the memory required for computing and storing strategies. We present novel domain-independent abstraction methods for creating very coarse abstractions of EFGs that still compute strategies that are (near) optimal in the original game. First, the methods start with an arbitrary abstraction of the original game (domain-specific or the coarsest possible). Next, they iteratively detect which information is required in the abstract game so that a (near) optimal strategy in the original game can be found and include this information into the abstract game. Moreover, the methods are able to exploit imperfect-recall abstractions where players can even forget the history of their own actions. We present two algorithms that follow these steps -- FPIRA, based on fictitious play, and CFR+IRA, based on counterfactual regret minimization. The experimental evaluation confirms that our methods can closely approximate Nash equilibrium of large games using abstraction with only 0.9% of information sets of the original game.

Extensive-form games with imperfect recall are an important game-theoretic model that allows a compact representation of strategies in dynamic strategic interactions. Practical use of imperfect recall games is limited due to negative theoretical results: a Nash equilibrium does not have to exist, computing maxmin strategies is NP-hard, and they may require irrational numbers. We present the first algorithm for approximating maxmin strategies in two-player zero-sum imperfect recall games without absentmindedness. We modify the well-known sequence-form linear program to model strategies in imperfect recall games and use a recent technique to approximate bilinear terms. Our main algorithm is a branch-and-bound search over these linear programs that provably reaches a desired approximation after an exponential number of steps in the size of the game. Experimental evaluation shows that the proposed algorithm can approximate maxmin strategies of randomly generated imperfect recall games of sizes beyond toy-problems within few minutes.

We solve large two-player zero-sum extensive-form games with perfect recall. We propose a new algorithm based on fictitious play that significantly reduces memory requirements for storing average strategies. The key feature is exploiting imperfect recall abstractions while preserving the convergence rate and guarantees of fictitious play applied directly to the perfect recall game. The algorithm creates a coarse imperfect recall abstraction of the perfect recall game and automatically refines its information set structure only where the imperfect recall might cause problems. Experimental evaluation shows that our novel algorithm is able to solve a simplified poker game with 7.10^5 information sets using an abstracted game with only 1.8% of information sets of the original game. Additional experiments on poker and randomly generated games suggest that the relative size of the abstraction decreases as the size of the solved games increases.

Learning with deep neural networks forms the state-of-the-art in many tasks such as image classification, image detection, speech recognition, text analysis. We here set out to gain understanding in learning in an `end-to-end' manner for an autonomous vehicle, which refers to directly learning the decision which will result from the perception of the scene. For example, we consider learning a binary `stop'/`go' decision, with respect to pedestrians, given the input image. In this work we propose to use additional information, referred to as `proxy supervision', for improved learning and study its effects on the overall performance. We show that the proxy labels significantly improve the robustness of learning, while achieving as good, or better, accuracy than in the original task of binary classification.

Strong Stackelberg Equilibrium (SSE) is a fundamental solution concept in game theory in which one player commits to a strategy, while the other player observes this commitment and plays a best response. We present a new algorithm for computing SSE for two-player extensive-form general-sum games with imperfect information (EFGs) where computing SSE is an NP-hard problem. Our algorithm is based on a correlated version of SSE, known as Stackelberg Extensive-Form Correlated Equilibrium (SEFCE). Our contribution is therefore twofold: (1) we give the first linear program for computing SEFCE in EFGs without chance, (2) we repeatedly solve and modify this linear program in a systematic search until we arrive to SSE. Our new algorithm outperforms the best previous algorithms by several orders of magnitude.

Stackelberg equilibrium is a solution concept prescribing for a player an optimal strategy to commit to, assuming the opponent knows this commitment and plays the best response. Although this solution concept is a cornerstone of many security applications, the existing works typically do not consider situations where the players can observe and react to the actions of the opponent during the course of the game. We extend the existing algorithmic work to extensive-form games and introduce novel algorithm for computing Stackelberg equilibria that exploits the compact sequence-form representation of strategies. Our algorithm reduces the size of the linear programs from exponential in the baseline approach to linear in the size of the game tree. Experimental evaluation on randomly generated games and a security-inspired search game demonstrates significant improvement in the scalability compared to the baseline approach.

Nash equilibrium (NE) is the best known solution concept used in game theory. It is known that NE is particularly weak even in zero-sum extensive-form games since it can prescribe irrational actions to play that do not exploit mistakes made by an imperfect opponent. These issues are addressed by a number of refinements of NE that strengthen the requirements for equilibrium strategies. However, a thorough experimental analysis of practical performance of the Nash equilibria refinement strategies is, to the best of our knowledge, missing. This paper aims to fill this void and provides the first broader experimental comparison of the quality of refined Nash strategies in zero-sum extensive-form games. The experimental results suggest that (1) there is a significant difference between the best and the worst NE strategy against imperfect opponents, (2) the existing refinements outperform the worst NE strategy, (3) they typically perform close to the best possible NE strategy, and (4) the difference in performance of all compared refinements is very small.