“We introduce the Fixed Landscape Inference MethOd, a new likelihood-free inference method for continuous state-space stochastic models. It applies deterministic gradient-based optimization algorithms to obtain a point estimate of the parameters, minimizing the difference between the data and some simulations according to some prescribed summary statistics. In this sense, it is analogous to Approximate Bayesian Computation (ABC). Like ABC, it can also provide an approximation of the distribution of the parameters.”
I quickly read this arXival by Monard et al. that is presented as an alternative to ABC, while outside a Bayesian setup. The central concept is that a deterministic gradient descent provides an optimal parameter value when replacing the likelihood with a distance between the observed data and simulated synthetic data indexed by the current value of the parameter (in the descent). In order to operate the descent the synthetic data is assumed to be available as a deterministic transform of the parameter value and of a vector of basic random objects, eg Uniforms. In order to make the target function differentiable, the above Uniform vector is fixed for the entire gradient descent. A puzzling aspect of the paper is that it seems to compare the (empirical) distribution of the resulting estimator with a posterior distribution, unless the comparison is with the (empirical) distribution of the Bayes estimators. The variability due to the choice of the fixed vector of basic random objects does not seem to be taken into account either, apparently. Furthermore, the method is presented as able to handle several models at once, which I find difficult to fathom as (a) the random vectors behind each model necessarily vary and (b) there is no apparent penalisation for complexity.
[Here is an 
