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In this paper, we study reinforcement learning (RL) algorithms to solve real-world decision problems with the objective of maximizing the long-term reward as well as satisfying cumulative constraints. We propose a novel first-order policy optimization method, Interior-point Policy Optimization (IPO), which augments the objective with logarithmic barrier functions, inspired by the interior-point method. Our proposed method is easy to implement with performance guarantees and can handle general types of cumulative multiconstraint settings. We conduct extensive evaluations to compare our approach with state-of-the-art baselines. Our algorithm outperforms the baseline algorithms, in terms of reward maximization and constraint satisfaction. 

Deep neural networks are vulnerable to adversarial examples. Prior defenses attempted to make deep networks more robust by either changing the network architecture or augmenting the training set with adversarial examples, but both have inherent limitations. Motivated by recent research that shows outliers in the training set have a high negative influence on the trained model, we studied the relationship between model robustness and the quality of the training set. We first show that outliers give the model better generalization ability but weaker robustness. Next, we propose an adversarial example detection framework, in which we design two methods for removing outliers from training set to obtain the sanitized model and then detect adversarial example by calculating the difference of outputs between the original and the sanitized model. We evaluated the framework on both MNIST and SVHN. Based on the difference measured by Kullback-Leibler divergence, we could detect adversarial examples with accuracy between 94.67% to 99.89%.