Active inference agents choose actions by minimising expected free energy (EFE), a score that balances reaching goals against gathering information. To scale these agents to structured models, inference is usually done by message passing on factor graphs, which minimises a different objective: the Bethe free energy. The two don’t fit together. EFE averages over observations the agent hasn’t made yet, so it lacks the structure that lets the Bethe free energy split into local messages. The Bethe free energy on its own gives a purely goal-seeking agent with no drive to explore. This talk keeps the Bethe free energy and brings exploration back as a constraint. The agent’s expected information gain about states and parameters must be at least as large as the entropy of its goal prior. The resulting policy combines a goal-seeking term and an information-seeking term, weighted by the constraint’s Karush–Kuhn–Tucker multiplier. When the multiplier equals one, the policy is exactly the EFE policy. The multiplier is solved, not tuned. It drops to zero when goal-directed actions already give enough information, so the drive to explore switches off when it isn’t needed. In a grid-world task where the goal’s location is uncertain, the constrained agent detours to an informative cue that a standard EFE agent skips.