Random sample consensus (RANSAC), which is based on a repetitive sampling from a given dataset, is one of the most popular robust estimation methods. In this study, an energy-based model (EBM) for robust estimation that has a similar scheme to RANSAC, energy-based RANSAC (EB-RANSAC), is proposed. EB-RANSAC is applicable to a wide range of estimation problems similar to RANSAC. However, unlike RANSAC, EB-RANSAC does not require a troublesome sampling procedure and has only one hyperparameter. The effectiveness of EB-RANSAC is numerically demonstrated in two applications: a linear regression and maximum likelihood estimation.

Markov decision processes (MDPs) often suffer from the sensitivity issue under model ambiguity. In recent years, robust MDPs have emerged as an effective framework to overcome this challenge. Distributionally robust MDPs extend the robust MDP framework by incorporating distributional information of the uncertain model parameters to alleviate the conservative nature of robust MDPs.

When releasing outputs from confidential data, agencies need to balance the analytical usefulness of the released data with the obligation to protect data subjects'

Error bound conditions (EBC) are properties that characterize the growth of an objectivefunction when apoint ismovedawayfrom theoptimal set.

However, the optimization aspect is not sufficient to achieve the success of stochastic minimax optimizationinmachinelearning.

(Bertsekas, 1999). Algorithm 1. Furthermore, we call ˆ f (), X We can show that | f () ˆ f () |, 8 2 [, ] . Besides, computing the upper bound claimed in Proposition 4.2 requires finding The second equality is from the fact that the objective function is affine w.r.t. Finally, we verify the rest two components. Finally, we verify the rest two components. This finishes the proof of our claim.