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  1. In this paper, a generalized information-theoretic framework for the emergence of multi-resolution hierarchical tree abstractions is developed. By leveraging ideas from information-theoretic signal encoding with side information, this paper develops a tree search problem which considers the generation of multi-resolution tree abstractions when there are multiple sources of relevant and irrelevant, or possibly confidential, information. We rigorously formulate an information-theoretic driven tree abstraction problem and discuss its connections with information-theoretic privacy and resource-limited systems. The problem structure is investigated and a novel algorithm, called G-tree search, is proposed. The proposed algorithm is analyzed and a number of theoretical results are established, including the optimally of the G-tree search algorithm. To demonstrate the utility of the proposed framework, we apply our method to a real-world example and provide a discussion of the results from the viewpoint of designing hierarchical abstractions for autonomous systems. 
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  2. We present a framework that incorporates the principle of bounded rationality into dynamic stochastic pursuit-evasion games. The solution of a stochastic game is generally characterized by its (Nash) equilibria in feedback form, whose calculation may require extensive computational resources. In this paper, the agents are modeled as bounded rational entities with limited computational capabilities. We illustrate the proposed framework by applying it to a pursuit-evasion game between two aerial vehicles in a stochastic wind field. We show how such a game may be discretized and properly analyzed by casting it as an iterative sequence of finite-state Markov Decision Processes (MDPs). Leveraging tools and algorithms from the cognitive hierarchy theory (“level-k thinking”) we compute the solution of the ensuing discrete game, while taking into consideration the rationality level of each agent. We also present an online algorithm for each agent to infer its opponent's rationality level. 
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  3. We explore the use of policy approximations to reduce the computational cost of learning Nash equilibria in zero-sum stochastic games. We propose a new Q-learning type algorithm that uses a sequence of entropy-regularized soft policies to approximate the Nash policy during the Q-function updates. We prove that under certain conditions, by updating the regularized Q-function, the algorithm converges to a Nash equilibrium. We also demonstrate the proposed algorithm’s ability to transfer previous training experiences, enabling the agents to adapt quickly to new environments. We provide a dynamic hyper-parameter scheduling scheme to further expedite convergence. Empirical results applied to a number of stochastic games verify that the proposed algorithm converges to the Nash equilibrium while exhibiting a major speed-up over existing algorithms. 
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