Norms have been extensively studied to coordinate multi-agent systems, and the literature has investigated two general approaches to norm synthesis: off-line (synthesising norms at design-time) and on-line (run-time synthesis). On-line synthesis is generally recognised to be appropriate for open systems, where aspects of the system remain unknown at design-time. In this paper we present LION, an algorithm aimed at synthesising liberal normative systems. LION’s normative systems respect the agents’ autonomy to the greatest possible extent, constraining their behaviour when only necessary to avoid undesirable system states. LION’s norm synthesis is also driven by the need to construct compact normative systems. The key to the success of LION in this multi-objective synthesis process is that it learns about and exploits norm synergies. More precisely, LION can learn when norms are either substitutable or complementary. We show empirically that LION significantly outperforms the st...