Long-horizon language agents accumulate observations, reasoning traces, and retrieved facts exceeding context windows, making memory retention a fundamental resource-allocation problem. Existing systems treat retention as local and do not model long-term consequences under observability constraints. To fill this gap, we formulate memory retention as a constrained stochastic optimization with budget feasibility, evidence utility, and delayed costs including miss, reacquisition, and stale penalties. We show this multi-step problem is NP-hard, making exact solution intractable. Moreover, deployment decisions must be made under partial observability. To address these challenges, we propose OSL-MR (Observability-Safe Learning for Memory Retention), a learning-augmented framework that enforces a strict separation between online-observable features and offline-available supervision. OSL-MR combines an evidence learner trained from realized evidence with a Mixed-Score heuristic that serves as a deployable online-safe baseline and an inductive prior. The policy learns query-conditioned evidence from interaction data and remains deployable under the same constraints. Experiments on LoCoMo and LongMemEval show OSL-MR outperforms recency-based, Generative Agents-style, and other heuristic baselines, especially under tight budgets. The Mixed-Score prior improves precision and recall, and sensitivity analysis shows robustness across cost settings. On small solvable instances, single-step optimization is insufficient to anticipate future demand shifts, while OSL-MR stays significantly closer to the dynamic-programming optimum, confirming the necessity of the sequential formulation and reinforcing our learning-guided approximation. These results establish constrained stochastic optimization and optimization-guided learning as a principled foundation for memory management in long-horizon agents.

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