While Large Language Models (LLMs) demonstrate remarkable zero-shot generalization, adapting them to downstream tasks or shifting data distributions often requires continual fine-tuning—a process prone to catastrophic forgetting and limited knowledge transfer. This challenge is especially pronounced in online Incremental Learning (IL) settings, where task boundaries are blurred, and data arrives in a non-stationary stream. To address these issues, we propose GROLE (Group Relative Optimization for LoRA Experts), a novel approach that incrementally constructs a pool of frozen, task-specific Low-Rank Adaptation (LoRA) experts. At its core, GROLE employs a lightweight, instance-level expert selector optimized through a group relative reinforcement learning objective, which dynamically combines relevant experts to maximize adaptability without compromising stability. Extensive experiments across diverse incremental learning benchmarks show that GROLE consistently outperforms state-of-the-art methods, particularly in task-free and blurred-boundary settings, achieving an optimal balance between plasticity and robustness.