PoKER: A Probability of Kill Estimation Rate Model for Air-to-Air Missiles Using Machine Learning on Stochastic Targets

Beyond-visual-range (BVR) air combat is a challenging reinforcement-learning domain characterized by partial observability, long-horizon decision making, energy management, and limited weapons. We present BVR Sim, an open-source Gymnasium-style environment designed for heterogeneous air-combat reinforcement learning. BVR Sim supports multiple JSBSim aircraft models, including the F-15, F-16, F/A-18, and F-22, with configurable weapons, sensors, controllers, and opponents. A unified tactical action interface specifies desired heading, altitude, speed, and weapon release above aircraft-specific inner-loop controllers, enabling policies to operate across heterogeneous platforms. The environment provides interchangeable Python and accelerated C++ backends, entity-oriented observations, compositional rewards, scripted opponents, replay and visualization, and adapters for multi-agent learning frameworks. At a 0.4-s decision interval, the C++ backend achieves 104 simulated seconds per wall-clock second in 1-vs-1 and remains practical through 10-vs-10 scenarios. A policy trained only on the F-16 transfers without retraining to four unseen aircraft, reaching a 45.5% mean win rate with aircraft-specific controller adaptation. MAPPO and HAPPO experiments further verify end-to-end compatibility with standard multi-agent reinforcement-learning pipelines.

Multi-Agent Reinforcement Learning (MARL) has emerged as a pivotal paradigm for complex decision-making in autonomous systems and air combat. While MARL has demonstrated significant potential in air combat, achieving sophisticated tactical coordination remains a non-trivial challenge. This difficulty is largely attributed to two primary limitations: (1) the absence of structured relational modeling hinders agents from capturing complex, time-varying interactions among battlefield entities; and (2) conventional flat architectures often lack the capability to explicitly model tactical roles, leading to ambiguous task allocation in highly dynamic environments. To address these challenges, we propose Hierarchical Dynamic Role-Graph Multi-Agent Proximal Policy Optimization (DRG-MAPPO), a novel MARL framework that integrates graph-based relational modeling with dynamic role assignment. Specifically, DRG-MAPPO constructs a graph-based representation of battlefield interactions and leverages graph attention mechanisms to extract critical relational features among allies, enemies, and threats. Subsequently, a high-level policy employs a dynamic role assignment mechanism to determine tactical responsibilities (e.g., leader'' and supporter''). Conditioned on these roles and encoded graph-relational features, a low-level policy executes discrete maneuver actions, facilitating the joint optimization of tactical strategy and collaborative execution. Furthermore, a target-priority auxiliary task is designed to foster the emergence of behaviors such as focus-fire. Experimental results demonstrate that DRG-MAPPO achieves a state-of-the-art win rate of 87%, suggesting that our framework effectively balances relational modeling, interpretability, and optimization stability for cooperative air combat.

As modern air combat evolves toward beyond-visual-range (BVR) multi-aircraft cooperative engagements, autonomous decision-making for unmanned combat aerial vehicles (UCAVs) faces significant challenges due to high-dimensional state spaces, discrete action commands, and strongly adversarial dynamic environments. To overcome the limitations of existing multi-agent reinforcement learning (MARL) methods in such settings, namely insufficient exploration efficiency, low sample utilization, and poor policy generalization, we propose Adversarial Curriculum and Evolutionary-enhanced Multi-agent Proximal Policy Optimization (ACE-MAPPO), a hybrid learning framework that integrates evolutionary algorithms with MAPPO. Specifically, a genetic soft update mechanism is introduced to enhance population diversity and mitigate convergence to local optima. An evolutionary-augmented prioritized trajectory replay strategy is further employed to improve the utilization of sparse high-value samples. In addition, an adversarial evolutionary curriculum learning mechanism is designed to enable adaptive training with progressively increasing difficulty. Extensive experimental results demonstrate that the proposed method outperforms MAPPO and other baseline algorithms in terms of training stability, convergence speed, and win rate, validating its effectiveness in multi-aircraft cooperative air combat scenarios.