Customizing an LLM judge to a specific problem or domain often involves optimizing its prompt across multiple evaluation criteria simultaneously. Textual gradient methods automate this for a single judge criterion, however they produce natural-language critiques, not numerical vectors. Thus, the conflict-resolution toolkit of multi-task learning (PCGrad, MGDA) does not apply to this multi-objective textual gradient setting. We extend TextGrad to the multi-objective setting and test four decomposition modes of textual gradient optimizers by varying how much cross-objective information the loss, gradient and optimizer LLMs share. We find the gradient's task-focus drops by 59% (9.0 to 3.7 out of 10) when the gradient LLM must provide feedback on multiple criteria jointly. Separately, we observe that naively combining single-objective optimized instructions into a single prompt degrades Spearman rho from 0.305 to 0.220 (-0.085). These results identify two separable failure modes: optimization-time gradient dilution and inference-time instruction interference, which together constrain the design space for multi-objective judge optimization using textual feedback.

翻译：将LLM裁判定制到特定问题或领域时，通常需要同时针对多项评估标准优化其提示。文本梯度方法可针对单一裁判标准实现自动化优化，但其输出的是自然语言评述而非数值向量。因此，多任务学习中的冲突解决工具（如PCGrad、MGDA）并不适用于这种多目标文本梯度设定。我们将TextGrad扩展至多目标场景，并通过改变损失函数、梯度及优化器LLM之间共享的跨目标信息量，测试了四种文本梯度优化器的分解模式。研究发现，当梯度LLM需联合处理多项标准的反馈时，其任务聚焦能力从10分中的9.0分骤降至3.7分（降幅达59%）。此外，我们观察到将单目标优化指令简单组合为单条提示，会导致斯皮尔曼相关系数从0.305下降至0.220（降幅0.085）。这些结果揭示了两种可分离的失败模式：优化时的梯度稀释与推理时的指令干扰，二者共同制约了利用文本反馈进行多目标裁判优化的设计空间。