Zhiyuan Yang

Xi Lin, Zhiyuan Yang, Qingfu Zhang

Multiobjective combinatorial optimization (MOCO) problems can be found in many real-world applications. However, exactly solving these problems would be very challenging, particularly when they are NP-hard. Many handcrafted heuristic methods have been proposed to tackle different MOCO problems over the past decades. In this work, we generalize the idea of neural combinatorial optimization, and develop a learning-based approach to approximate the whole Pareto set for a given MOCO problem without further search procedure. We propose a single preference-conditioned model to directly generate approximate Pareto solutions for any trade-off preference, and design an efficient multiobjective reinforcement learning algorithm to train this model. Our proposed method can be treated as a learning-based extension for the widely-used decomposition-based multiobjective evolutionary algorithm (MOEA/D). It uses a single model to accommodate all the possible preferences, whereas other methods use a finite number of solutions to approximate the Pareto set. Experimental results show that our proposed method significantly outperforms some other methods on the multiobjective traveling salesman problem, multiobjective vehicle routing problem, and multiobjective knapsack problem in terms of solution quality, speed, and model efficiency.

Xi Lin, Zhiyuan Yang, Xiaoyuan Zhang et al.

Expensive multi-objective optimization problems can be found in many real-world applications, where their objective function evaluations involve expensive computations or physical experiments. It is desirable to obtain an approximate Pareto front with a limited evaluation budget. Multi-objective Bayesian optimization (MOBO) has been widely used for finding a finite set of Pareto optimal solutions. However, it is well-known that the whole Pareto set is on a continuous manifold and can contain infinite solutions. The structural properties of the Pareto set are not well exploited in existing MOBO methods, and the finite-set approximation may not contain the most preferred solution(s) for decision-makers. This paper develops a novel learning-based method to approximate the whole Pareto set for MOBO, which generalizes the decomposition-based multi-objective optimization algorithm (MOEA/D) from finite populations to models. We design a simple and powerful acquisition search method based on the learned Pareto set, which naturally supports batch evaluation. In addition, with our proposed model, decision-makers can readily explore any trade-off area in the approximate Pareto set for flexible decision-making. This work represents the first attempt to model the Pareto set for expensive multi-objective optimization. Experimental results on different synthetic and real-world problems demonstrate the effectiveness of our proposed method.

Xi Lin, Zhiyuan Yang, Xiaoyuan Zhang et al.

Homotopy optimization is a traditional method to deal with a complicated optimization problem by solving a sequence of easy-to-hard surrogate subproblems. However, this method can be very sensitive to the continuation schedule design and might lead to a suboptimal solution to the original problem. In addition, the intermediate solutions, often ignored by classic homotopy optimization, could be useful for many real-world applications. In this work, we propose a novel model-based approach to learn the whole continuation path for homotopy optimization, which contains infinite intermediate solutions for any surrogate subproblems. Rather than the classic unidirectional easy-to-hard optimization, our method can simultaneously optimize the original problem and all surrogate subproblems in a collaborative manner. The proposed model also supports real-time generation of any intermediate solution, which could be desirable for many applications. Experimental studies on different problems show that our proposed method can significantly improve the performance of homotopy optimization and provide extra helpful information to support better decision-making.

Anqi Cheng, Zhiyuan Yang, Haiyue Zhu et al.

Self-supervised depth estimation has evolved into an image reconstruction task that minimizes a photometric loss. While recent methods have made strides in indoor depth estimation, they often produce inconsistent depth estimation in textureless areas and unsatisfactory depth discrepancies at object boundaries. To address these issues, in this work, we propose GAM-Depth, developed upon two novel components: gradient-aware mask and semantic constraints. The gradient-aware mask enables adaptive and robust supervision for both key areas and textureless regions by allocating weights based on gradient magnitudes.The incorporation of semantic constraints for indoor self-supervised depth estimation improves depth discrepancies at object boundaries, leveraging a co-optimization network and proxy semantic labels derived from a pretrained segmentation model. Experimental studies on three indoor datasets, including NYUv2, ScanNet, and InteriorNet, show that GAM-Depth outperforms existing methods and achieves state-of-the-art performance, signifying a meaningful step forward in indoor depth estimation. Our code will be available at https://github.com/AnqiCheng1234/GAM-Depth.

Xi Lin, Xiaoyuan Zhang, Zhiyuan Yang et al.

Multi-objective optimization problems can be found in many real-world applications, where the objectives often conflict each other and cannot be optimized by a single solution. In the past few decades, numerous methods have been proposed to find Pareto solutions that represent optimal trade-offs among the objectives for a given problem. However, these existing methods could have high computational complexity or may not have good theoretical properties for solving a general differentiable multi-objective optimization problem. In this work, by leveraging the smooth optimization technique, we propose a lightweight and efficient smooth Tchebycheff scalarization approach for gradient-based multi-objective optimization. It has good theoretical properties for finding all Pareto solutions with valid trade-off preferences, while enjoying significantly lower computational complexity compared to other methods. Experimental results on various real-world application problems fully demonstrate the effectiveness of our proposed method.

Ping Guo, Cheng Gong, Xi Lin et al.

The escalating threat of adversarial attacks on deep learning models, particularly in security-critical fields, has underscored the need for robust deep learning systems. Conventional robustness evaluations have relied on adversarial accuracy, which measures a model's performance under a specific perturbation intensity. However, this singular metric does not fully encapsulate the overall resilience of a model against varying degrees of perturbation. To address this gap, we propose a new metric termed adversarial hypervolume, assessing the robustness of deep learning models comprehensively over a range of perturbation intensities from a multi-objective optimization standpoint. This metric allows for an in-depth comparison of defense mechanisms and recognizes the trivial improvements in robustness afforded by less potent defensive strategies. Additionally, we adopt a novel training algorithm that enhances adversarial robustness uniformly across various perturbation intensities, in contrast to methods narrowly focused on optimizing adversarial accuracy. Our extensive empirical studies validate the effectiveness of the adversarial hypervolume metric, demonstrating its ability to reveal subtle differences in robustness that adversarial accuracy overlooks. This research contributes a new measure of robustness and establishes a standard for assessing and benchmarking the resilience of current and future defensive models against adversarial threats.

Jianfei Guo, Zhiyuan Yang, Xi Lin et al.

We present neural radiance fields (NeRF) with templates, dubbed Template-NeRF, for modeling appearance and geometry and generating dense shape correspondences simultaneously among objects of the same category from only multi-view posed images, without the need of either 3D supervision or ground-truth correspondence knowledge. The learned dense correspondences can be readily used for various image-based tasks such as keypoint detection, part segmentation, and texture transfer that previously require specific model designs. Our method can also accommodate annotation transfer in a one or few-shot manner, given only one or a few instances of the category. Using periodic activation and feature-wise linear modulation (FiLM) conditioning, we introduce deep implicit templates on 3D data into the 3D-aware image synthesis pipeline NeRF. By representing object instances within the same category as shape and appearance variation of a shared NeRF template, our proposed method can achieve dense shape correspondences reasoning on images for a wide range of object classes. We demonstrate the results and applications on both synthetic and real-world data with competitive results compared with other methods based on 3D information.