Vision-driven autonomous river following by Unmanned Aerial Vehicles is critical for applications such as rescue, surveillance, and environmental monitoring, particularly in dense riverine environments where GPS signals are unreliable. These safety-critical navigation tasks must satisfy hard safety constraints while optimizing performance. Moreover, the reward in river following is inherently history-dependent (non-Markovian) by which river segment has already been visited, making it challenging for standard safe Reinforcement Learning (SafeRL). To address these gaps, we propose three contributions. First, we introduce Marginal Gain Advantage Estimation, which refines the reward advantage function by using a sliding window baseline computed from historical episodic returns, aligning the advantage estimate with non-Markovian dynamics. Second, we develop a Semantic Dynamics Model based on patchified water semantic masks offering more interpretable and data-efficient short-term prediction of future observations compared to latent vision dynamics models. Third, we present the Constrained Actor Dynamics Estimator architecture, which integrates the actor, cost estimator, and SDM for cost advantage estimation to form a model-based SafeRL framework. Simulation results demonstrate that MGAE achieves faster convergence and superior performance over traditional critic-based methods like Generalized Advantage Estimation. SDM provides more accurate short-term state predictions that enable the cost estimator to better predict potential violations. Overall, CADE effectively integrates safety regulation into model-based RL, with the Lagrangian approach providing a "soft" balance between reward and safety during training, while the safety layer enhances inference by imposing a "hard" action overlay.

Reinforcement learning (RL) has emerged as an effective approach for enhancing the reasoning capabilities of large language models (LLMs), especially in scenarios where supervised fine-tuning (SFT) falls short due to limited chain-of-thought (CoT) data. Among RL-based post-training methods, group relative advantage estimation, as exemplified by Group Relative Policy Optimization (GRPO), has attracted considerable attention for eliminating the dependency on the value model, thereby simplifying training compared to traditional approaches like Proximal Policy Optimization (PPO). However, we observe that existing group relative advantage estimation method still suffers from training inefficiencies, particularly when the estimated advantage approaches zero. To address this limitation, we propose Advantage-Augmented Policy Optimization (AAPO), a novel RL algorithm that optimizes the cross-entropy (CE) loss using advantages enhanced through a momentum-based estimation scheme. This approach effectively mitigates the inefficiencies associated with group relative advantage estimation. Experimental results on multiple mathematical reasoning benchmarks and model series demonstrate the superior performance of AAPO. Reinforcement learning (RL) has emerged as a powerful approach for enhancing the reasoning and decision-making capabilities of large language models (LLMs). To address this limitation, recent research has explored RL-based training paradigms, which have shown considerable empirical success in specialized domains such as mathematical reasoning.