The evaluation of rare but high-stakes events remains one of the main difficulties in obtaining reliable policies from intelligent agents, especially in large or continuous state/action spaces where limited scalability enforces the use of a prohibitively large number of testing iterations. On the other hand, a biased or inaccurate policy evaluation in a safety-critical system could potentially cause unexpected catastrophic failures during deployment. In this paper, we propose the Accelerated Policy Evaluation (APE) method, which simultaneously uncovers rare events and estimates the rare event probability in Markov decision processes. The APE method treats the environment nature as an adversarial agent and learns towards, through adaptive importance sampling, the zero-variance sampling distribution for the policy evaluation. Moreover, APE is scalable to large discrete or continuous spaces by incorporating function approximators. We investigate the convergence properties of proposed algorithms under suitable regularity conditions. Our empirical studies show that APE estimates rare event probability with a smaller variance while only using orders of magnitude fewer samples compared to baseline methods in both multi-agent and single-agent environments.

We study rare-event simulation for a class of problems where the target hitting sets of interest are defined via modern machine learning tools such as neural networks and random forests. This problem is motivated from fast emerging studies on the safety evaluation of intelligent systems, robustness quantification of learning models, and other potential applications to large-scale simulation in which machine learning tools can be used to approximate complex rare-event set boundaries. We investigate an importance sampling scheme that integrates the dominating point machinery in large deviations and sequential mixed integer programming to locate the underlying dominating points. Our approach works for a range of neural network architectures including fully connected layers, rectified linear units, normalization, pooling and convolutional layers, and random forests built from standard decision trees. We provide efficiency guarantees and numerical demonstration of our approach using a classification model in the UCI Machine Learning Repository.

Evaluating the reliability of intelligent physical systems against rare catastrophic events poses a huge testing burden for real-world applications. Simulation provides a useful, if not unique, platform to evaluate the extremal risks of these AIenabled systems before their deployments. Importance Sampling (IS), while proven to be powerful for rare-event simulation, faces challenges in handling these systems due to their black-box nature that fundamentally undermines its efficiency guarantee. To overcome this challenge, we propose a framework called Deep Probabilistic Accelerated Evaluation (D-PrAE) to design IS, which leverages rare-event-set learning and and a new notion of efficiency certificate. D-PrAE combines the dominating point method with deep neural network classifiers to achieve superior estimation efficiency. We present theoretical guarantees and demonstrate the empirical effectiveness of D-PrAE via examples on the safety-testing of self-driving algorithms that are beyond the reach of classical variance reduction techniques.

In many learning problems, the training and testing data follow different distributions and a particularly common situation is the \textit{covariate shift}. To correct for sampling biases, most approaches, including the popular kernel mean matching (KMM), focus on estimating the importance weights between the two distributions. Reweighting-based methods, however, are exposed to high variance when the distributional discrepancy is large and the weights are poorly estimated. On the other hand, the alternate approach of using nonparametric regression (NR) incurs high bias when the training size is limited. In this paper, we propose and analyze a new estimator that systematically integrates the residuals of NR with KMM reweighting, based on a control-variate perspective. The proposed estimator can be shown to either strictly outperform or match the best-known existing rates for both KMM and NR, and thus is a robust combination of both estimators. The experiments shows the estimator works well in practice.

Despite an ever growing literature on reinforcement learning algorithms and applications, much less is known about their statistical inference. In this paper, we investigate the large sample behaviors of the Q-value estimates with closed-form characterizations of the asymptotic variances. This allows us to efficiently construct confidence regions for Q-value and optimal value functions, and to develop policies to minimize their estimation errors. This also leads to a policy exploration strategy that relies on estimating the relative discrepancies among the Q estimates. Numerical experiments show superior performances of our exploration strategy than other benchmark approaches.

Safety evaluation of autonomous vehicles is extensively studied recently, one line of studies considers Monte Carlo based evaluation. The Monte Carlo based evaluation usually estimates the probability of safety-critical events as a safety measurement based on Monte Carlo samples. These Monte Carlo samples are generated from a stochastic model that is constructed based on real-world data. In this paper, we propose an approach to assess the potential estimation error in the evaluation procedure caused by data variability. The proposed method merges the classical bootstrap method for estimating input uncertainty with a likelihood ratio based scheme to reuse experiment results. The proposed approach is highly economical and efficient in terms of implementation costs in assessing input uncertainty for autonomous vehicle evaluation.

Effective and accurate model selection is an important problem in modern data analysis. One of the major challenges is the computational burden required to handle large data sets that cannot be stored or processed on one machine. Another challenge one may encounter is the presence of outliers and contaminations that damage the inference quality. The parallel "divide and conquer" model selection strategy divides the observations of the full data set into roughly equal subsets and perform inference and model selection independently on each subset. After local subset inference, this method aggregates the posterior model probabilities or other model/variable selection criteria to obtain a final model by using the notion of geometric median. This approach leads to improved concentration in finding the "correct" model and model parameters and also is provably robust to outliers and data contamination.

Evaluation and validation of complicated control systems are crucial to guarantee usability and safety. Usually, failure happens in some very rarely encountered situations, but once triggered, the consequence is disastrous. Accelerated Evaluation is a methodology that efficiently tests those rarely-occurring yet critical failures via smartly-sampled test cases. The distribution used in sampling is pivotal to the performance of the method, but building a suitable distribution requires case-by-case analysis. This paper proposes a versatile approach for constructing sampling distribution using kernel method. The approach uses statistical learning tools to approximate the critical event sets and constructs distributions based on the unique properties of Gaussian distributions. We applied the method to evaluate the automated vehicles. Numerical experiments show proposed approach can robustly identify the rare failures and significantly reduce the evaluation time.