Learning to optimize (L2O) has emerged as a powerful framework for black-box optimization (BBO). L2O learns the optimization strategies from the target task automatically without human intervention. This paper focuses on obtaining better performance when handling high-dimensional and expensive BBO with little function evaluation cost, which is the core challenge of black-box optimization. However, current L2O-based methods are weak for this due to a large number of evaluations on expensive black-box functions during training and poor representation of optimization strategy. To achieve this, 1) we utilize the cheap surrogate functions of the target task to guide the design of the optimization strategies; 2) drawing on the mechanism of evolutionary algorithm (EA), we propose a novel framework called B2Opt, which has a stronger representation of optimization strategies. Compared to the BBO baselines, B2Opt can achieve 3 to $10^6$ times performance improvement with less function evaluation cost. We test our proposal in high-dimensional synthetic functions and two real-world applications. We also find that deep B2Opt performs better than shallow ones.
Quantized neural network (NN) with a reduced bit precision is an effective solution to reduces the computational and memory resource requirements and plays a vital role in machine learning. However, it is still challenging to avoid the significant accuracy degradation due to its numerical approximation and lower redundancy. In this paper, a novel robustness-aware 2-bit quantization scheme is proposed for NN base on binary NN and generative adversarial network(GAN), witch improves the performance by enriching the information of binary NN, efficiently extract the structural information and considering the robustness of the quantized NN. Specifically, using shift addition operation to replace the multiply-accumulate in the quantization process witch can effectively speed the NN. Meanwhile, a structural loss between the original NN and quantized NN is proposed to such that the structural information of data is preserved after quantization. The structural information learned from NN not only plays an important role in improving the performance but also allows for further fine tuning of the quantization network by applying the Lipschitz constraint to the structural loss. In addition, we also for the first time take the robustness of the quantized NN into consideration and propose a non-sensitive perturbation loss function by introducing an extraneous term of spectral norm. The experiments are conducted on CIFAR-10 and ImageNet datasets with popular NN( such as MoblieNetV2, SqueezeNet, ResNet20, etc). The experimental results show that the proposed algorithm is more competitive under 2-bit-precision than the state-of-the-art quantization methods. Meanwhile, the experimental results also demonstrate that the proposed method is robust under the FGSM adversarial samples attack.