Behavior Quotient Learning for Low-Rank Adaptation of LLM Agents

LLM-based agents require diverse interaction capabilities to complete complex tasks. Existing approaches often assign these capabilities to multiple LoRA adapters, increasing storage requirements and routing overhead during inference. A single LoRA adapter simplifies deployment but poses two challenges under a fixed rank budget. First, different training trajectories may still reinforce the same behaviors, making part of the supervision redundant. Second, a low-rank approximation can closely match the desired parameter changes while distorting the intended effects on agent decisions. To address these challenges, we propose BQ-LoRA, which adapts LLM agents through two modules, i.e., behavior quotient balancing (BQB) and decision-preserving compression (DPC). BQB constructs a local quotient manifold from representations used to predict agent decisions. Trajectory gradients are then reweighted by their local density in the quotient tangent space to reduce the dominance of redundant behavioral effects. DPC projects the balanced direction onto the fixed-rank tangent space and compresses the resulting target to fit the original rank budget. This compression jointly controls parameter approximation error and first-order distortion of decision representations. Experimental results demonstrate the effectiveness of BQ-LoRA in improving agent performance.