Atmospheric retrieval of exoplanets from spectroscopic observations requires an extensive exploration of a highly degenerate and high-dimensional parameter space to accurately constrain atmospheric parameters. Retrieval methods commonly conduct Bayesian parameter estimation and statistical inference using sampling algorithms such as Markov Chain Monte Carlo (MCMC) or Nested Sampling. Recently several attempts have been made to use machine learning algorithms either to complement or replace fully Bayesian methods. While much progress has been made, these approaches are still at times unable to accurately reproduce results from contemporary Bayesian retrievals. The goal of our present work is to investigate the efficacy of machine learning for atmospheric retrieval. As a case study, we use the Random Forest supervised machine learning algorithm which has been applied previously with some success for atmospheric retrieval of the hot Jupiter WASP-12b using its near-infrared transmission spectrum. We reproduce previous results using the same approach and the same semi-analytic models, and subsequently extend this method to develop a new algorithm that results in a closer match to a fully Bayesian retrieval. We combine this new method with a fully numerical atmospheric model and demonstrate excellent agreement with a Bayesian retrieval of the transmission spectrum of another hot Jupiter, HD 209458b. Despite this success, and achieving high computational efficiency, we still find that the machine learning approach is computationally prohibitive for high-dimensional parameter spaces that are routinely explored with Bayesian retrievals with modest computational resources. We discuss the trade offs and potential avenues for the future.