Offline preference optimization aligns reasoning models from fixed chosen-rejected pairs, yet standard methods apply gradient updates from every pair regardless of its training value under the current policy. We argue that this uniform treatment is wasteful and potentially harmful. From the perspective of gradient utility, we show that a pair’s contribution depends jointly on informativeness and stability. Pair utility drifts as the policy evolves, high-gradient samples can coincide with high-curvature regions, leading to noisy and destabilizing updates, and the most effective supervision comes from stable confident errors where the model is reliably wrong yet curvature remains low. These findings motivate **SAGE** (Stability-Aware Gradient Efficiency), which maintains difficulty-stratified candidate pools refreshed during training and selects pairs within each pool by a forward-pass signal-to-curvature score. Only pairs with high current utility receive gradient computation; the rest are excluded from backpropagation. On mathematical reasoning benchmarks across multiple model scales, SAGE outperforms full-data and size-matched baselines while producing substantially smoother optimization trajectories.

Embodied agents in open-ended environments such as Minecraft increasingly adopt planner–controller architectures, with large language models acting as high-level planners. While planning has advanced rapidly, control remains underexplored. Existing systems commonly rely on a monolithic policy to execute subgoals across varying contexts, forcing incompatible behaviors into a shared parameter space and causing interference that scaling only partially mitigates. To address this, we propose MoEC, a Memory-Routed Mixture-of-Experts Controller for Adaptive Minecraft Control. MoEC routes via a subgoal-indexed, non-parametric expert memory and regulates capacity through failure-triggered expert growth and redundancy-aware consolidation. This design enables continual adaptation without full retraining, while maintaining parameter efficiency and with bounded inference cost. We evaluate MoEC on diverse and compositional Minecraft tasks, demonstrating significant gains in adaptability, robustness, and execution consistency over strong baselines, yielding a scalable and efficient alternative for open-ended control.