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There has been tremendous interest in designing stimuli (e.g. electrical currents) that produce desired neural responses, e.g., for inducing therapeutic effects for treatments. Traditionally, the design of such stimuli has been model-driven. Due to challenges inherent in modeling neural responses accurately, data-driven approaches offer an attractive alternative. The problem of data-driven stimulus design can be thought of as estimating an inverse of a non-linear ``forward" mapping, which takes in as inputs the stimulus parameters and outputs the corresponding neural responses. In most cases of interest, the forward mapping is many-to-one, and hence difficult to invert using traditional methods. Existing methods estimate the inverse by using conditional density estimation methods or numerically inverting an estimated forward mapping, but both approaches tend to perform poorly at small sample sizes. In this work, we develop a new optimization framework called PATHFINDER, which allows us to use regression methods for estimating an inverse mapping. We use toy examples to illustrate key aspects of PATHFINDER, and show, on computational models of biological neurons, that PATHFINDER can outperform existing methods at small sample sizes. The data-efficiency of PATHFINDER is especially valuable in stimulus design as collecting data is expensive in this domain.