Abstract Classification with costly features (CwCF) is a classification problem that includes the cost of features in the optimization criteria. Individually for each sample, its features are sequentially acquired to maximize accuracy while minimizing the acquired features’ cost. However, existing approaches can only process data that can be expressed as vectors of fixed length. In real life, the data often possesses rich and complex structure, which can be more precisely described with formats such as XML or JSON. The data is hierarchical and often contains nested lists of objects. In this work, we extend an existing deep reinforcement learning-based algorithm with hierarchical deep sets and hierarchical softmax, so that it can directly process this data. The extended method has greater control over which features it can acquire and, in experiments with seven datasets, we show that this leads to superior performance. To showcase the real usage of the new method, we apply it to a real-life problem of classifying malicious web domains, using an online service.

Multiagent decision-making in partially observable environments is usually modelled as either an extensive-form game (EFG) in game theory or a partially observable stochastic game (POSG) in multiagent reinforcement learning (MARL). One issue with the current situation is that while most practical problems can be modelled in both formalisms, the relationship of the two models is unclear, which hinders the transfer of ideas between the two communities. A second issue is that while EFGs have recently seen significant algorithmic progress, their classical formalization is unsuitable for efficient presentation of the underlying ideas, such as those around decomposition. To solve the first issue, we introduce factored-observation stochastic games (FOSGs), a minor modification of the POSG formalism which distinguishes between private and public observation and thereby greatly simplifies decomposition. To remedy the second issue, we show that FOSGs and POSGs are naturally connected to EFGs: by "unrolling" a FOSG into its tree form, we obtain an EFG. Conversely, any perfect-recall timeable EFG corresponds to some underlying FOSG in this manner. Moreover, this relationship justifies several minor modifications to the classical EFG formalization that recently appeared as an implicit response to the model's issues with decomposition. Finally, we illustrate the transfer of ideas between EFGs and MARL by presenting three key EFG techniques -- counterfactual regret minimization, sequence form, and decomposition -- in the FOSG framework.

Standard machine learning (ML) problems are formulated on data converted into a suitable tensor representation. However, there are data sources, for example in cybersecurity, that are naturally represented in a unifying hierarchical structure, such as XML, JSON, and Protocol Buffers. Converting this data to a tensor representation is usually done by manual feature engineering, which is laborious, lossy, and prone to bias originating from the human inability to correctly judge the importance of particular features. JsonGrinder.jl is a library automating various ML tasks on these difficult sources. Starting with an arbitrary set of JSON samples, it automatically creates a differentiable ML model (called hmilnet), which embeds raw JSON samples into a fixed-size tensor representation. This embedding network can be naturally extended by an arbitrary ML model expecting tensor inputs in order to perform classification, regression, or clustering.

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.

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.

Stackelberg security games (SSGs) have been deployed in many real-world situations to optimally allocate scarce resource to protect targets against attackers. However, actual human attackers are not perfectly rational and there are several behavior models that attempt to predict subrational behavior. Quantal response is among the most commonly used such models and Quantal Stackelberg Equilibrium (QSE) describes the optimal strategy to commit to when facing a subrational opponent. Non-concavity makes computing QSE computationally challenging and while there exist algorithms for computing QSE for SSGs, they cannot be directly used for solving an arbitrary game in the normal form. We (1) present a transformation of the primal problem for computing QSE using a Dinkelbach's method for any general-sum normal-form game, (2) provide a gradient-based and a MILP-based algorithm, give the convergence criteria, and bound their error, and finally (3) we experimentally demonstrate that using our novel transformation, a QSE can be closely approximated several orders of magnitude faster.

We study a classification problem where each feature can be acquired for a cost and the goal is to optimize a trade-off between the expected classification error and the feature cost. We revisit a former approach that has framed the problem as a sequential decision-making problem and solved it by Q-learning with a linear approximation, where individual actions are either requests for feature values or terminate the episode by providing a classification decision. On a set of eight problems, we demonstrate that by replacing the linear approximation with neural networks the approach becomes comparable to the state-of-the-art algorithms developed specifically for this problem. The approach is flexible, as it can be improved with any new reinforcement learning enhancement, it allows inclusion of pre-trained high-performance classifier, and unlike prior art, its performance is robust across all evaluated datasets.

Moving target defense (MTD) strategies have been widely studied for securing computer systems. We consider using MTD strategies to provide long-term cryptographic security for message transmission against an eavesdropping adversary who has access to a quantum computer. In such a setting, today’s widely used cryptographic systems including Diffie-Hellman key agreement protocol and RSA cryptosystem will be insecure and alternative solutions are needed. We will use a physical assumption, existence of multiple communication paths between the sender and the receiver, as the basis of security, and propose a cryptographic system that uses this assumption and an MTD strategy to guarantee efficient long-term information theoretic security even when only a single path is not eavesdropped. Following the approach of Maleki et al., we model the system using a Markov chain, derive its transition probabilities, propose two security measures, and prove results that show how to calculate these measures using transition probabilities. We define two types of attackers that we call risk-taking and risk-averse and compute our proposed measures for the two types of adversaries for a concrete MTD strategy. We will use numerical analysis to study tradeoffs between system parameters, discuss our results, and propose directions for future research.

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.

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.

Many real world security problems can be modelled as finite zero-sum games with structured sequential strategies and limited interactions between the players. An abstract class of games unifying these models are the normal-form games with sequential strategies (NFGSS). We show that all games from this class can be modelled as well-formed imperfect-recall extensive-form games and consequently can be solved by counterfactual regret minimization. We propose an adaptation of the CFR+ algorithm for NFGSS and compare its performance to the standard methods based on linear programming and incremental game generation. We validate our approach on two security-inspired domains. We show that with a negligible loss in precision, CFR+ can compute a Nash equilibrium with five times less computation than its competitors.

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.

Developing scalable solution algorithms is one of the central problems in computational game theory. We present an iterative algorithm for computing an exact Nash equilibrium for two-player zero-sum extensive-form games with imperfect information. Our approach combines two key elements: (1) the compact sequence-form representation of extensive-form games and (2) the algorithmic framework of double-oracle methods. The main idea of our algorithm is to restrict the game by allowing the players to play only selected sequences of available actions. After solving the restricted game, new sequences are added by finding best responses to the current solution using fast algorithms. We experimentally evaluate our algorithm on a set of games inspired by patrolling scenarios, board, and card games. The results show significant runtime improvements in games admitting an equilibrium with small support, and substantial improvement in memory use even on games with large support. The improvement in memory use is particularly important because it allows our algorithm to solve much larger game instances than existing linear programming methods. Our main contributions include (1) a generic sequence-form double-oracle algorithm for solving zero-sum extensive-form games; (2) fast methods for maintaining a valid restricted game model when adding new sequences; (3) a search algorithm and pruning methods for computing best-response sequences; (4) theoretical guarantees about the convergence of the algorithm to a Nash equilibrium; (5) experimental analysis of our algorithm on several games, including an approximate version of the algorithm.

In this paper, we study Monte Carlo tree search (MCTS) in zero-sum extensive-form games with perfect information and simultaneous moves. We present a general template of MCTS algorithms for these games, which can be instantiated by various selection methods. We formally prove that if a selection method is $\epsilon$-Hannan consistent in a matrix game and satisfies additional requirements on exploration, then the MCTS algorithm eventually converges to an approximate Nash equilibrium (NE) of the extensive-form game. We empirically evaluate this claim using regret matching and Exp3 as the selection methods on randomly generated and worst case games. We confirm the formal result and show that additional MCTS variants also converge to approximate NE on the evaluated games.

Mobile robot localization is taken into account as one of the most important topics in robotics. In this paper, the localization problem is extended to the cases in which estimating the position of multi robots is considered. To do so, the joint probabilistic data association filter (JPDAF) approach is applied for tracking the position of multiple robots. To characterize the motion of each robot, two models are used. First, a simple near constant velocity model is considered and then a variable velocity model is applied for tracking. This improves the performance when the robots change their velocity and conduct maneuvering movements. This issue gives an advantage to explore the movement of the manoeuvring objects which is common in many robotics problems such as soccer or rescue robots. Simulation results show the efficiency of the JPDAF algorithm in tracking multiple mobile robots with maneuvering movements.