AlphaZero has demonstrated the effectiveness of integrating reinforcement learning (RL) with search methods in perfect-information games such as chess and Go. However, extending this paradigm to imperfect-information games remains a significant challenge due to the presence of hidden information.Counterfactual Regret Minimization (CFR) provides theoretical convergence guarantees in such settings, recent advances like Recursive Belief-based Learning (ReBeL) have introduced a unified RL+Search framework by transforming imperfect-information games into perfect-information games over public belief states (PBS).Despite its theoretical appeal, ReBeL’s implementation based on multi-layer perceptron (MLP) is limited in its ability to capture the relational structure inherent in PBS. In this paper, we propose GNN-ReBeL, a novel approach that leverages Graph Neural Network (GNN) to explicitly model the strategic relationships among information states by representing PBS as graph-structured data. This graph-based representation enhances information propagation within the belief space while preserving convergence to a Nash equilibrium.Empirical results on benchmark imperfect-information games Liar’s Dice, show that GNN-ReBeL outperforms existing methods by achieving exploitability values that are only 33%-85% of those of the original MLP-based approach under comparable computational budgets. These findings underscore the advantages of structured belief representations for strategic reasoning in complex imperfect-information environments.

The integration of reinforcement learning with search algorithms has revolutionized AI performance in perfect-information games, with AlphaZero demonstrating superhuman abilities in chess, shogi, and Go. Counterfactual Regret Minimization (CFR) has been the traditional approach for imperfect-information games, but requires extensive precomputation of complete game strategies. Recursive Belief-based Learning (ReBeL) represents a breakthrough by combining self-play reinforcement learning with real-time search in imperfect-information settings, enabling superhuman performance in poker and other games with hidden information. A critical hyperparameter in ReBeL’s algorithm is the depth of subgames used during search. While deeper subgames potentially capture more strategic information, they also increase computational complexity. This paper presents a systematic investigation of the impact of subgame depth on ReBeL’s performance, convergence rate, and computational requirements. Through extensive experiments on benchmark imperfect-information games Liar’s Dice, we demonstrate that optimal subgame depth involves a non-trivial trade-off between solution quality and computational efficiency. Our findings provide practical guidance for implementing ReBeL in various game domains and contribute to the broader understanding of search depth parameterization in reinforcement learning algorithms for imperfect-information games.

We describes four scheduling schemes on the predefined path in large-scale wireless networks supported by full-duplex radios. The end-to-end throughput on multi-hop path with these schemes is discussed, indicating the effect of scheduling schemes and the influence of full-duplex radios on multi-hop data transmission. We make a simulator and compare the throughput results in these schemes. Results show that the new scheduling methods may improve end-to-end throughput on multi-hop path in wireless networks moderately.

Achievable capacity in multi-hop wireless networks is seriously lower than single-hop communication. Two full-duplex nodes potentially have 2× capacity in wireless communications, compared to two half-duplex nodes. Organize the two nodes as one unit and reorganize nodes to be the units in multi-hop paths, the capacity can achieve 1× to 2× under space division simultaneous transmission mode, which is verified by analysis and simulation results.

In wireless networks, it is still a challenge to allocate the limited resources among users to meet their specific quality of service (QoS) requirements, especially when the users have different traffic types, i.e., the hard QoS traffic, the best effort traffic, and the soft QoS traffic. In this paper, we develop the utility-based resource allocation algorithms in the following three tasks: 1) resource allocation among the hard QoS traffic and the soft QoS traffic; 2) resource allocation among the best effort traffic and the soft QoS traffic; and 3) finally resource allocation among the hard QoS traffic, the best effort traffic, and the soft QoS traffic, by solving the network utility maximization problem using the Karush-Kuhn-Tucker condition. We develop a number of critical theorems to give the conditions that find the optimal solutions for the above three cases in a unified framework. These theorems then act as design guidelines for the three algorithms. The proposed algorithms take into account the traffic type, the total available resources and the users' channel qualities. We evaluate the time complexity of the proposed algorithms, which comes out to be polynomial, and study the network performance by numerical examples. Numerical results demonstrate the bandwidth allocations, the fairness index and the total maximum utility under different channel qualities and resource situations.

FAST TCP is a promising new transfer control protocol developed for high-speed long-latency networks, whose performance has previously only been studied for data traffic sent in one direction. In this study, the authors propose a mathematical model for bi-directional connections using the FAST TCP protocol, which captures the asymmetric bandwidth dynamics in duplex dumbbell networks, prevalent in ADSL, satellite and other high-speed technologies. Using this model, the authors obtain a powerful result that the queue delays observed by opposite FAST TCP flows only have a time difference in a dumbbell network. Furthermore, the authors establish the conditions under which the bi-directional FAST TCP flows achieve stability, and on this basis the throughput rates of the forward and backward flows at steady-state are deduced. The authors find that, in the case of bandwidth asymmetry and one flow in each direction, in equilibrium the throughput of the bi-directional FAST TCP flows can only achieve the smaller link capacity of the duplex links, and the link with larger capacity is not fully occupied. These theoretical findings are corroborated by NS2 simulations.

For the separation of linear instantaneous mixtures of independent sources, many Independent Component Analysis (ICA) algorithms can learn the separating matrix by optimizing some objective functions derived from various criteria. The Maximum Likelihood (ML) principle, with hypothesized model pdf's, provides an objective function which is commonly used. It is generally considered that the ML approach leads to a separating solution as long as the kurtosis signs of the model pdf's can correspond and equal to those of the sources, respectively, in some order, which is referred to as the one-bit-matching condition. In this letter, we present an experimental analysis on spurious solution of the ML approach and show that spurious maximum of the objective function really exists in certain cases even if the one-bit-matching condition is satisfied.