Nested Monte Carlo Search (NMCS) has numerous applications, ranging from chemical retrosynthesis to quantum circuit design. We propose a generalization of NMCS that we named Nested Depth Search (NDS), in which a fixed depth search is used during a higher-level playout to generate the states sent to lower-level exploration. We establish the runtime of NDS and provide algorithms to compute the exact probability distribution of sequences generated by NDS. Experiments with the Set Cover problem and the Multiple Sequence Alignment problem show that NDS outperforms NMCS with the same time budget.

Extensive-form games model strategic interaction between players, with an emphasis on the sequential aspect of decision-making: players take turns to move until an ending is reached, and receive a reward according to which ending is reached. We study the complexity of computing the pure maxmin value for such games, i.e. the maximum reward that a player can guarantee by playing a pure strategy, whatever their opponents play. We focus on two-player and two-team games and perform a systematic study depending on the degree of imperfect information of each player or team: perfect information, perfect recall, or perfect recall for each agent in a team (which we call multi-agent perfect recall). For each combination, we settle the complexity of deciding whether the maxmin value is at least as high as a given threshold. We give a complete complexity picture for three orthogonal settings: games represented explicitly by their game tree; games represented compactly by game rules, for which we propose two new formalisms; games in which the set of strategies of the opponents is restricted to a known set of opponent models.

Games with incomplete information are games that model situations where players do not have common knowledge about the game they play, e.g. card games such as poker or bridge. Opponent models can be of crucial importance for decision-making in such games. We propose algorithms for computing optimal and/or robust strategies in games with incomplete information, given various types of knowledge about opponent models. As an application, we describe a framework for reasoning about an opponent's reasoning in such games, where opponent models arise naturally.

We define a new setting related to the evaluation of AND-OR directed acyclic graphs with partially ordered values. Such graphs arise naturally when solving games with incomplete information (e.g. most card games such as Bridge) or games with multiple criteria. In particular, this setting generalises standard AND-OR graph evaluation and computation of optimal strategies in games with complete information. Under this setting, we propose a new algorithm which uses both alpha-beta pruning and cached values. In this paper, we present our algorithm, prove its correctness, and give experimental results on a card game with incomplete information.

In this paper, a Takenaka-Malmquist (TM) basis function based equivalent data-model is established by an adaptive rational decomposition for the finite-time interval trajectory tracking control and real-time control of a class of nonlinear systems in the frequency domain. This data model can adaptively learn and match the control process of nonlinear systems. As a result, the proposed trajectory tracking as well as real-time control method can reflect the feature of adaptive learning in order-by-order decomposition, and the feasibility of the proposed method is guaranteed by the convergence of adaptive decomposition by TM basis function under the maximum selection principle (MSP) in Hardy space$H^{2}(\mathbb {D})$. Compared with the traditional model-free control method, this data learning model which matches the control process has obvious advantages in the system model expression and control accuracy. Simulation results at the end of this paper show the effectiveness of the proposed method.