Abstract: In recent years, solving inverse problems for black-box simulators has become a point of focus for the machine learning community due to their ubiquity in science and engineering scenarios. In such settings, the simulator describes a forward process $f: (\psi, x) \rightarrow y$ from simulator parameters $\psi$ and input data $x$ to observations $y$, and the goal of the inverse problem is to optimise $\psi$ to minimise some observation loss. Simulator gradients are often unavailable or prohibitively expensive to obtain, making optimisation of these simulators particularly challenging. Moreover, in many applications, the goal is to solve a family of related inverse problems. Thus, starting optimisation ab-initio/from-scratch may be infeasible if the forward model is expensive to evaluate. In this paper, we propose a novel method for solving classes of similar inverse problems. We learn an active learning policy that guides the training of a surrogate and use the gradients of this surrogate to optimise the simulator parameters with gradient descent. After training the policy, downstream inverse problem optimisations require up to 90\% fewer forward model evaluations than the baseline.