We present a formulation of deep learning that aims at producing a large margin classifier. The notion of \emc{margin}, minimum distance to a decision boundary, has served as the foundation of several theoretically profound and empirically successful results for both classification and regression tasks. However, most large margin algorithms are applicable only to shallow models with a preset feature representation; and conventional margin methods for neural networks only enforce margin at the output layer. Such methods are therefore not well suited for deep networks. In this work, we propose a novel loss function to impose a margin on any chosen set of layers of a deep network (including input and hidden layers). Our formulation allows choosing any $l_p$ norm ($p \geq 1$) on the metric measuring the margin. We demonstrate that the decision boundary obtained by our loss has nice properties compared to standard classification loss functions. Specifically, we show improved empirical results on the MNIST, CIFAR-10 and ImageNet datasets on multiple tasks: generalization from small training sets, corrupted labels, and robustness against adversarial perturbations. The resulting loss is general and complementary to existing data augmentation (such as random/adversarial input transform) and regularization techniques such as weight decay, dropout, and batch norm. \footnote{Code for the large margin loss function is released at \url{https://github.com/google-research/google-research/tree/master/large_margin}}

Most frameworks for utility elicitation assume a predefined set of features over which user preferences are expressed. We consider utility elicitation in the presence of subjective or user-defined features, whose definitions are not known in advance. We treat the problem of learning a user's feature definition as one of concept learning, but whose goal is to learn only enough about the concept definition to enable a good decision to be made. This is complicated by the fact that user utility is unknown. We describe computational procedures for identifying optimal alternatives w.r.t minimax regret in the presence of both utility and concept uncertainty; and develop several heuristic query strategies that focus simultaneously on reduction of relevant concept and utility uncertainty.

The precise specification of reward functions for Markov decision processes (MDPs) is often extremely difficult, motivating research into both reward elicitation and the robust solution of MDPs with imprecisely specified reward (IRMDPs). We develop new techniques for the robust optimization of IRMDPs, using the minimax regret decision criterion, that exploit the set of nondominated policies, i.e., policies that are optimal for some instantiation of the imprecise reward function. Drawing parallels to POMDP value functions, we devise a Witness-style algorithm for identifying nondominated policies. We also examine several new algorithms for computing minimax regret using the nondominated set, and examine both practically and theoretically the impact of approximating this set. Our results suggest that a small subset of the nondominated set can greatly speed up computation, yet yield very tight approximations to minimax regret.

Most models of utility elicitation in decision support and interactive optimization assume a predefined set of "catalog" features over which user preferences are expressed. However, users may differ in the features over which they are most comfortable expressing their preferences. In this work we consider the problem of feature elicitation: a user's utility function is expressed using features whose definitions (in terms of "catalog" features) are unknown. We cast this as a problem of concept learning, but whose goal is to identify only enough about the concept to enable a good decision to be recommended. We describe computational procedures for identifying optimal alternatives w.r.t. minimax regret in the presence of concept uncertainty; and describe several heuristic query strategies that focus on reduction of relevant concept uncertainty.

Utility or preference elicitation is a critical component in many recommender and decision support systems. However, most frameworks for elicitation assume a predefined set of features (e.g., as derived from catalog descriptions) over which user preferences are expressed. Just as user preferences vary considerably, so too can the features over which they are most comfortable expressing these preferences. In this work, we consider preference elicitation in the presence of subjective or user-defined features. We treat the problem of learning a user's feature definition as one of concept learning, but whose goal is to learn only enough about the concept definition to enable a good decision to be made. This is complicated by the fact that user preferences are unknown. We describe computational procedures for identifying optimal alternatives w.r.t minimax regret in the presence of both utility and concept uncertainty; and develop several heuristic query strategies that focus on reduction of relevant concept and utility uncertainty. Computational experiments verify the efficacy of these strategies.

Reinforcement learning (RL) was originally proposed as a framework to allow agents to learn in an online fashion as they interact with their environment. Existing RL algorithms come short of achieving this goal because the amount of exploration required is often too costly and/or too time consuming for online learning. As a result, RL is mostly used for offline learning in simulated environments. We propose a new algorithm, called BEETLE, for effective online learning that is computationally efficient while minimizing the amount of exploration. We take a Bayesian model-based approach, framing RL as a partially observable Markov decision process. Our two main contributions are the analytical derivation that the optimal value function is the upper envelope of a set of multivariate polynomials, and an efficient point-based value iteration algorithm that exploits this simple parameterization.