Convex optimization problems with staged structure appear in several contexts, including optimal control, verification of deep neural networks, and isotonic regression. Off-the-shelf solvers can solve these problems but may scale poorly.

In a seminal paper, Szegedy et al. [Sze+14] observed that deep networks are extremely vulnerable to adversarial examples, namely, very small perturbations to the inputs

In a seminal paper, Szegedy et al. [Sze+14] observed that deep networks are extremely vulnerable to adversarial examples, namely, very small perturbations to the inputs

In this paper, we theoretically and empirically characterize obstructions to training encoders with geometric latent spaces. We show that local optima can arise due to singularities (e.g.

In our method and all the baselines except surrogate-based triage, we use the cross-entropy loss and implement SGD using Adam optimizer [40] with initial learning rate set by cross validation independently foreachmethod andleveloftriageb. Insurrogate-based triage, weusethelossand optimization method used by the authors in their public implementation. Moreover, we use early stopping with the patience parameterep = 10,i.e.,we stop the training process ifno reduction of cross entropy loss is observed on the validation set. This suggests that the humans aremore accurate than thepredictivemodel throughout theentire feature space. This suggests that the humans are less accurate than the predictive model in some regions of the featurespace.

While these algorithms havebeen extensively studied, both theoretically and practically, see, e.g., [10], many questions remain open. In particular, most results are based onthecase where theestimatord V isunbiased.

We introduce a novel policy learning method that integrates analytical gradients from differentiable environments with the Proximal Policy Optimization (PPO) algorithm.