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Large Language Models (LLMs) are powerful but limited by static parametric knowledge that becomes outdated once pretraining ends. Knowledge editing addresses this problem by updating model behavior on target facts without full retraining. In particular, in-context knowledge editing has gained attention because it is training-free and readily applicable to black-box LLMs. Recent reinforcement learning (RL)-based approaches improve over fixed retrieval strategies by adapting prompt construction to the quantity-quality trade-off. Despite initial success, they fail to model the prompt as a structured entity under the distinct and often competing objectives of reliability, generality, and specificity. Previous methods largely optimize a single objective and make decisions over only part of the prompt construction process, thereby overlooking both the balance of different objectives and the global organization of demonstrations. We propose Multi-Objective In-context Knowledge Editing (MO-IKE), a multi-objective RL algorithm that formulates prompt construction for in-context knowledge editing as a Constrained Markov Decision Process. MO-IKE trains a dynamic retriever to optimize competing objectives in knowledge editing, enabling more balanced and globally coherent prompt construction. On Llama-3.2, MO-IKE improves edit success (reliability) from 85.0% to 92.0%, paraphrase consistency (generality) from 77% to 79%, while increasing retention rate (specificity) by 23.0% compared to prior RL-based methods.