Switching policies for solving inverse problems

In recent years, inverse problems for black-box simulators have enjoyed increased focus of the machine learning community due to their prevalence in science and engineering domains. Such simulators describe a forward process $f: (\psi, x) \rightarrow y$. Here the intent is to optimise simulator parameters $\psi$ to minimise some observation loss on $y$, under some input distribution on $x$. Optimisation of such objectives is often challenging, since it is not trivial to estimate simulator gradients accurately. In settings where multiple related inverse problems need to be solved simultaneously, from-scratch/ab-initio optimisation of each may be infeasible if the forward model is expensive to evaluate. In this paper, we propose a novel method for solving such families of inverse problems with reinforcement learning. We train a policy to guide the optimisation by selecting between gradients estimated numerically from the simulator and gradients estimated from a pre-trained surrogate model. After training the surrogate and the policy, downstream inverse problem optimisations require 10\%-70\% fewer simulator evaluations. Moreover, the policy does successful optimisations on functions where using just simulator gradient estimates fails.