Neural Information Processing Systems http://nips.cc/

An accurate environment dynamics model is crucial for various downstream tasks in sequential decision-making, such as counterfactual prediction, off-policy evaluation, and offline reinforcement learning. Currently, these models were learned through empirical risk minimization (ERM) by step-wise fitting of historical transition data. This way was previously believed unreliable over long-horizon rollouts because of the compounding errors, which can lead to uncontrollable inaccuracies in predictions. In this paper, we find that the challenge extends beyond just longterm prediction errors: we reveal that even when planning with one step, learned dynamics models can also perform poorly due to the selection bias of behavior policies during data collection.

Offset Rademacher complexities have been shown to provide tight upper bounds for the square loss in a broad class of problems including improper statistical learning and online learning. We show that the offset complexity can be generalized to any loss that satisfies a certain general convexity condition. Further, we show that this condition is closely related to both exponential concavity and self-concordance, unifying apparently disparate results. By a novel geometric argument, many of our bounds translate to improper learning in a non-convex class with Audibert's star algorithm. Thus, the offset complexity provides a versatile analytic tool that covers both convex empirical risk minimization and improper learning under entropy conditions. Applying the method, we recover the optimal rates for proper and improper learning with the p-loss for 1

We develop an approach to risk minimization and stochastic optimization that provides a convex surrogate for variance, allowing near-optimal and computationally efficient trading between approximation and estimation error. Our approach builds off of techniques for distributionally robust optimization and Owen's empirical likelihood, and we provide a number of finite-sample and asymptotic results characterizing the theoretical performance of the estimator. In particular, we show that our procedure comes with certificates of optimality, achieving (in some scenarios) faster rates of convergence than empirical risk minimization by virtue of automatically balancing bias and variance. We give corroborating empirical evidence showing that in practice, the estimator indeed trades between variance and absolute performance on a training sample, improving out-of-sample (test) performance over standard empirical risk minimization for a number of classification problems.