When Should Agents Build Reusable Tools?

Modern agents can improve over time by turning solved tasks into persistent reusable tools, but building such capabilities requires an upfront investment that may not pay off. We study when an online agent should build a new tool rather than patch the current task or reuse an existing one, under uncertain task recurrence and stochastic tool quality. We formulate this as cost-sensitive capability acquisition and develop Demand-Sensitive Acquisition (DSA), a controller that combines recurrence estimates with uncertainty in current success, durable admission, and future reuse. In a separable model where each tool serves one recurring task type, we derive the exact finite-horizon optimal policy and decompose the cost gap of building when a task type first appears; on an executable API-migration benchmark with 108 LLM-generated candidates, DSA lowers modeled cost by 6.7% over 200 heavy-tailed task sequences, relative to a pattern-level baseline that builds when each pattern first appears. These results frame agent self-improvement as a sequential investment problem over reusable capabilities.