Active imitation learning reduces expert effort by allowing a learner to request the demonstrations it needs. Existing methods typically select these requests for their expected information gain about the expert policy. In structured multi-task domains, however, the number of start-goal tasks may grow combinatorially despite their solutions sharing reusable behavior. This makes composable behaviors especially valuable, since a single demonstration may help solve many tasks at once. Prior methods do not explicitly account for this value when selecting which demonstration to request. We introduce Adaptive Agents via Latent Topologies (AALT), which requests demonstrations that maximize expected gains in start-goal connectivity. We further show that this objective is formally tied to information gain about task reachability. AALT organizes existing demonstrations into a topology of latent hub states connected by learned behaviors, identifies high-value bridge demonstrations that are likely to enable many tasks at once, and grounds each to an expert query. At inference, it plans through the resulting topology and conditions a diffusion policy on each successive hub transition. In a simulated UR5e robot ordered-retrieval domain with 72 tasks, AALT improved from 42/72 to 72/72 (100%) successful tasks consistently using only 3 demonstrations totaling 5 transitions beyond the initial dataset. After 20 demonstrations, the strongest baseline averaged 88.6% success using 98 transitions.

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