When to Prompt, When to Update: Context-Parameter Allocation for Language Agents

Language agents must follow structured protocols, adapt to evolving environments, and operate under memory, latency and cost constraints. Adaptation then requires deciding where task-relevant information should live; in the prompt, which is fast and reversible but bounded, or in the parameters, which is persistent but expensive to write. We formalize this as an information-allocation problem. Two limits make the trade-off concrete: parameter writes have diminishing returns, while the usable prompt is bounded not by the context window but by attention dilution, for which we derive and empirically validate a scaling law that provides a measurable prompt-side constraint. We propose an oracle-student-controller architecture that acts on this analysis. A compact student is first distilled to acquire the desired output schema. During deployment a controller preserves the schema by construction, projects the semantic state into a feasible prompt domain with an approximation guarantee, and triggers oracle-supervised parameter updates only on persistent error. The trigger is computable from student and environment observable signals alone, so the oracle is never queried in order to decide whether to use it. Across Multi-Fidelity Bayesian Optimization, all 812 WebArena tasks, and both ALFWorld splits, we studied Llama-3.1-8B and Mistral-7B performance as students. Experimental results show improvement of their baseline performance by integrating the adaptive allocation schema, which is also compared against current state-of-the-art methods.