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In data-driven optimization, sample average approximation is known to suffer from the so-called optimizer's curse that causes optimistic bias in evaluating the solution performance. This can be tackled by adding a "margin" to the estimated objective value, or via distributionally robust optimization (DRO), a fast-growing approach based on worst-case analysis, which gives a protective bound on the attained objective value. However, in all these existing approaches, a statistically guaranteed bound on the true solution performance either requires restrictive conditions and knowledge on the objective function complexity, or otherwise exhibits an over-conservative rate that depends on the distribution dimension. We argue that a special type of DRO offers strong theoretical advantages in regard to these challenges: It attains a statistical bound on the true solution performance that is the tightest possible in terms of exponential decay rate, for a wide class of objective functions that notably does not hinge on function complexity. Correspondingly, its calibration also does not require any complexity information. This DRO uses an ambiguity set based on a KL-divergence smoothed by the Wasserstein or Levy-Prokhorov distance via a suitable distance optimization. Computationally, we also show that such a DRO, and its generalized version using smoothed $f$-divergence, is not much harder than standard DRO problems using the $f$-divergence or Wasserstein distance, thus supporting the strengths of such DRO as both statistically optimal and computationally viable.

Pre-silicon side-channel leakage assessment is a useful tool to identify hardware vulnerabilities at design time, but it requires many high-resolution power traces and increases the power simulation cost of the design. By downsampling and averaging these high-resolution traces, we show that the power simulation cost can be considerably reduced without significant loss of side-channel leakage assessment quality. We introduce a theoretical basis for our claims. Our results demonstrate up to 6.5-fold power-simulation speed improvement on a gate-level side-channel leakage assessment of a RISC-V SoC. Furthermore, we clarify the conditions under which the averaged sampling technique can be successfully used.

While side-channel leakage is traditionally evaluated from a fabricated chip, it is more time-efficient and cost-effective to do so during the design phase of the chip. We present a methodology to rank the gates of a design according to their contribution to the side-channel leakage of the chip. The methodology relies on logic synthesis, logic simulation, gate-level power estimation, and gate leakage assessment to compute a ranking. The ranking metric can be defined as a specific test by correlating gate-level activity with a leakage model, or else as a non-specific test by evaluating gate-level activity in response to distinct test vector groups. Our results show that only a minority of the gates in a design contribute most of the side-channel leakage. We demonstrate this property for several designs, including a hardware AES coprocessor and a cryptographic hardware/software interface in a five-stage pipelined RISC processor.

Evaluating the performance of autonomous vehicles (AV) and their complex subsystems to high precision under naturalistic circumstances remains a challenge, especially when failure or dangerous cases are rare. Rarity does not only require an enormous sample size for a naive method to achieve high confidence estimation, but it also causes dangerous underestimation of the true failure rate and it is extremely hard to detect. Meanwhile, the state-of-the-art approach that comes with a correctness guarantee can only compute an upper bound for the failure rate under certain conditions, which could limit its practical uses. In this work, we present Deep Importance Sampling (Deep IS) framework that utilizes a deep neural network to obtain an efficient IS that is on par with the state-of-the-art, capable of reducing the required sample size 43 times smaller than the naive sampling method to achieve 10% relative error and while producing an estimate that is much less conservative. Our high-dimensional experiment estimating the misclassification rate of one of the state-of-the-art traffic sign classifiers further reveals that this efficiency still holds true even when the target is very small, achieving over 600 times efficiency boost. This highlights the potential of Deep IS in providing a precise estimate even against high-dimensional uncertainties.

The bootstrap is a popular data-driven method to quantify statistical uncertainty, but for modern high-dimensional problems, it could suffer from huge computational costs due to the need to repeatedly generate resamples and refit models. We study the use of bootstraps in high-dimensional environments with a small number of resamples. In particular, we show that with a recent "cheap" bootstrap perspective, using a number of resamples as small as one could attain valid coverage even when the dimension grows closely with the sample size, thus strongly supporting the implementability of the bootstrap for large-scale problems. We validate our theoretical results and compare the performance of our approach with other benchmarks via a range of experiments., Comment: Accepted to Proceedings of the 40th International Conference on Machine Learning (ICML)

This paper studies a basic notion of distributional shape known as orthounimodality (OU) and its use in shape-constrained distributionally robust optimization (DRO). As a key motivation, we argue how such type of DRO is well-suited to tackle multivariate extreme event estimation by giving statistically valid confidence bounds on target extremal probabilities. In particular, we explain how DRO can be used as a nonparametric alternative to conventional extreme value theory that extrapolates tails based on theoretical limiting distributions, which could face challenges in bias-variance control and other technical complications. We also explain how OU resolves the challenges in interpretability and robustness faced by existing distributional shape notions used in the DRO literature. Methodologically, we characterize the extreme points of the OU distribution class in terms of what we call OU sets and build a corresponding Choquet representation, which subsequently allows us to reduce OU-DRO into moment problems over infinite-dimensional random variables. We then develop, in the bivariate setting, a geometric approach to reduce such moment problems into finite dimension via a specially constructed variational problem designed to eliminate suboptimal solutions. Numerical results illustrate how our approach gives rise to valid and competitive confidence bounds for extremal probabilities.