Agent-based models (ABMs) are a valuable tool for simulating complex systems. However, ABMs have limitations such as manual rule specification, lack of adaptation, intractability, and computational cost, limiting wide scale adoption. Recently, ADAGE was introduced to address the first two issues with a bi-level optimisation framework. However, this framework exacerbates the latter two issues. To help remedy these concerns, in this work, the bi-level framework is integrated with a differentiable simulator, resulting in tractable parameter updates and improved computational efficiency. The applicability of the framework is demonstrated for automated policy design, showing how taxation policies can be learnt to maximise fairness in a canonical multi-agent market entrance game with adaptive agents.