Long-term memory systems allow LLM agents to preserve information beyond a single context window, but most systems focus on storing and retrieving facts after extraction, leaving the write decision under-specified. What deserves memory can depend on the user's current task, topic, activity, or interaction partner, while uniform extraction applies one notion of importance across these different situations. We formulate this challenge as preference-conditioned write control and introduce AdaMem, which uses adaptive natural-language Memory Policies to personalize what an agent writes to memory. Each policy represents the user's memory preference for a particular interaction context, is updated from periodic feedback, and controls subsequent memory writing. We evaluate this loop in AdaMem-Bench, which assigns different memory preferences to six concurrent interaction personas across five ten-week stories. Across two extraction models and two feedback modes, AdaMem improves average QA accuracy over Mem0 from 80.0\% to 84.35\% while reducing persistent memory by 9.27\%. Our analyses show that explicit feedback helps models learn better memory policies, but current models still struggle to translate those policies into reliably selective writing behavior. AdaMem thus demonstrates the promise of adaptive write control while exposing policy execution as a central limitation of current memory agents. Our code is publicly available: https://github.com/galaxyChen/AdaMem

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