Zhenyuan Liu

Zhenyuan Liu, Bart P. G. Van Parys, Henry Lam

In data-driven optimization, sample average approximation (SAA) is known to suffer from the so-called optimizer's curse that causes an over-optimistic evaluation of the solution performance. We argue that a special type of distributionallly robust optimization (DRO) formulation offers theoretical advantages in correcting for this optimizer's curse compared to simple ``margin'' adjustments to SAA and other DRO approaches: It attains a statistical bound on the out-of-sample performance, for a wide class of objective functions and distributions, that is nearly tightest in terms of exponential decay rate. This DRO uses an ambiguity set based on a Kullback Leibler (KL) divergence smoothed by the Wasserstein or Lévy-Prokhorov (LP) distance via a suitable distance optimization. Computationally, we also show that such a DRO, and its generalized versions using smoothed $f$-divergence, are not harder than DRO problems based on $f$-divergence or Wasserstein distances, rendering our DRO formulations both statistically optimal and computationally viable.

Zhenyuan Liu, Tong Jia, Xingyu Xing et al.

Autonomous vehicles are exposed to various weather during operation, which is likely to trigger the performance limitations of the perception system, leading to the safety of the intended functionality (SOTIF) problems. To efficiently generate data for testing the performance of visual perception algorithms under various weather conditions, a hierarchical-level rain image generative model, rain conditional CycleGAN (RCCycleGAN), is constructed. RCCycleGAN is based on the generative adversarial network (GAN) and can generate images of light, medium, and heavy rain. Different rain intensities are introduced as labels in conditional GAN (CGAN). Meanwhile, the model structure is optimized and the training strategy is adjusted to alleviate the problem of mode collapse. In addition, natural rain images of different intensities are collected and processed for model training and validation. Compared with the two baseline models, CycleGAN and DerainCycleGAN, the peak signal-to-noise ratio (PSNR) of RCCycleGAN on the test dataset is improved by 2.58 dB and 0.74 dB, and the structural similarity (SSIM) is improved by 18% and 8%, respectively. The ablation experiments are also carried out to validate the effectiveness of the model tuning.