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Multiobjective optimization problems (MOPs) are prevalent in machine learning, with applications in multi-task learning, learning under fairness or robustness constraints, etc. Instead of reducing multiple objective functions into a scalar objective, MOPs aim to optimize for the so-called Pareto optimality or Pareto set learning, which involves optimizing more than one objective function simultaneously, over models with millions of parameters. Existing benchmark libraries for MOPs mainly focus on evolutionary algorithms, most of which are zeroth-order methods that do not effectively utilize higher-order information from objectives and cannot scale to large-scale models with millions of parameters. In light of the above gap, this paper introduces LibMOON, the first multiobjective optimization library that supports state-of-the-art gradient-based methods, provides a fair benchmark, and is open-sourced for the community.

The hardness of the Unconstrained Binary Quadratic Program (UBQP) problem is due its rugged landscape. Various algorithms have been proposed for UBQP, including the Landscape Smoothing Iterated Local Search (LSILS). Different from other UBQP algorithms, LSILS tries to smooth the rugged landscape by building a convex combination of the original UBQP and a toy UBQP. In this paper, our study further investigates the impact of smoothing rugged landscapes using different toy UBQP problems, including a toy UBQP with matrix ^Q1 (construct by "+/-1"), a toy UBQP with matrix ^Q2 (construct by "+/-i") and a toy UBQP with matrix ^Q3 (construct randomly). We first assess the landscape flatness of the three toy UBQPs. Subsequently, we test the efficiency of LSILS with different toy UBQPs. Results reveal that the toy UBQP with ^Q1 (construct by "+/-1") exhibits the flattest landscape among the three, while the toy UBQP with ^Q3 (construct randomly) presents the most non-flat landscape. Notably, LSILS using the toy UBQP with ^Q2 (construct by "+/-i") emerges as the most effective, while ^Q3 (construct randomly) has the poorest result. These findings contribute to a detailed understanding of landscape smoothing techniques in optimizing UBQP.

Automated heuristic design (AHD) has gained considerable attention for its potential to automate the development of effective heuristics. The recent advent of large language models (LLMs) has paved a new avenue for AHD, with initial efforts focusing on framing AHD as an evolutionary program search (EPS) problem. However, inconsistent benchmark settings, inadequate baselines, and a lack of detailed component analysis have left the necessity of integrating LLMs with search strategies and the true progress achieved by existing LLM-based EPS methods to be inadequately justified. This work seeks to fulfill these research queries by conducting a large-scale benchmark comprising four LLM-based EPS methods and four AHD problems across nine LLMs and five independent runs. Our extensive experiments yield meaningful insights, providing empirical grounding for the importance of evolutionary search in LLM-based AHD approaches, while also contributing to the advancement of future EPS algorithmic development. To foster accessibility and reproducibility, we have fully open-sourced our benchmark and corresponding results., Comment: Accepted by the 18th International Conference on Parallel Problem Solving From Nature (PPSN 2024)

Neural Network-based active learning (NAL) is a cost-effective data selection technique that utilizes neural networks to select and train on a small subset of samples. While existing work successfully develops various effective or theory-justified NAL algorithms, the understanding of the two commonly used query criteria of NAL: uncertainty-based and diversity-based, remains in its infancy. In this work, we try to move one step forward by offering a unified explanation for the success of both query criteria-based NAL from a feature learning view. Specifically, we consider a feature-noise data model comprising easy-to-learn or hard-to-learn features disrupted by noise, and conduct analysis over 2-layer NN-based NALs in the pool-based scenario. We provably show that both uncertainty-based and diversity-based NAL are inherently amenable to one and the same principle, i.e., striving to prioritize samples that contain yet-to-be-learned features. We further prove that this shared principle is the key to their success-achieve small test error within a small labeled set. Contrastingly, the strategy-free passive learning exhibits a large test error due to the inadequate learning of yet-to-be-learned features, necessitating resort to a significantly larger label complexity for a sufficient test error reduction. Experimental results validate our findings., Comment: Accepted by the 41th Intemational Conference on Machine Learning (lCML 2024)

Multi-objective optimization can be found in many real-world applications where some conflicting objectives can not be optimized by a single solution. Existing optimization methods often focus on finding a set of Pareto solutions with different optimal trade-offs among the objectives. However, the required number of solutions to well approximate the whole Pareto optimal set could be exponentially large with respect to the number of objectives, which makes these methods unsuitable for handling many optimization objectives. In this work, instead of finding a dense set of Pareto solutions, we propose a novel Tchebycheff set scalarization method to find a few representative solutions (e.g., 5) to cover a large number of objectives (e.g., $>100$) in a collaborative and complementary manner. In this way, each objective can be well addressed by at least one solution in the small solution set. In addition, we further develop a smooth Tchebycheff set scalarization approach for efficient optimization with good theoretical guarantees. Experimental studies on different problems with many optimization objectives demonstrate the effectiveness of our proposed method.

Neural combinatorial optimization (NCO) is a promising learning-based approach to solving various vehicle routing problems without much manual algorithm design. However, the current NCO methods mainly focus on the in-distribution performance, while the real-world problem instances usually come from different distributions. A costly fine-tuning approach or generalized model retraining from scratch could be needed to tackle the out-of-distribution instances. Unlike the existing methods, this work investigates an efficient prompt learning approach in NCO for cross-distribution adaptation. To be concrete, we propose a novel prompt learning method to facilitate fast zero-shot adaptation of a pre-trained model to solve routing problem instances from different distributions. The proposed model learns a set of prompts among various distributions and then selects the best-matched one to prompt a pre-trained attention model for each problem instance. Extensive experiments show that the proposed prompt learning approach facilitates the fast adaptation of pre-trained routing models. It also outperforms existing generalized models on both in-distribution prediction and zero-shot generalization to a diverse set of new tasks. Our code implementation is available online https://github.com/FeiLiu36/PromptVRP.

The neural combinatorial optimization (NCO) approach has shown great potential for solving routing problems without the requirement of expert knowledge. However, existing constructive NCO methods cannot directly solve large-scale instances, which significantly limits their application prospects. To address these crucial shortcomings, this work proposes a novel Instance-Conditioned Adaptation Model (ICAM) for better large-scale generalization of neural combinatorial optimization. In particular, we design a powerful yet lightweight instance-conditioned adaptation module for the NCO model to generate better solutions for instances across different scales. In addition, we develop an efficient three-stage reinforcement learning-based training scheme that enables the model to learn cross-scale features without any labeled optimal solution. Experimental results show that our proposed method is capable of obtaining excellent results with a very fast inference time in solving Traveling Salesman Problems (TSPs) and Capacitated Vehicle Routing Problems (CVRPs) across different scales. To the best of our knowledge, our model achieves state-of-the-art performance among all RL-based constructive methods for TSP and CVRP with up to 1,000 nodes., Comment: 17 pages, 6 figures

Many real-world optimization scenarios involve expensive evaluation with unknown and heterogeneous costs. Cost-aware Bayesian optimization stands out as a prominent solution in addressing these challenges. To approach the global optimum within a limited budget in a cost-efficient manner, the design of cost-aware acquisition functions (AFs) becomes a crucial step. However, traditional manual design paradigm typically requires extensive domain knowledge and involves a labor-intensive trial-and-error process. This paper introduces EvolCAF, a novel framework that integrates large language models (LLMs) with evolutionary computation (EC) to automatically design cost-aware AFs. Leveraging the crossover and mutation in the algorithmic space, EvolCAF offers a novel design paradigm, significantly reduces the reliance on domain expertise and model training. The designed cost-aware AF maximizes the utilization of available information from historical data, surrogate models and budget details. It introduces novel ideas not previously explored in the existing literature on acquisition function design, allowing for clear interpretations to provide insights into its behavior and decision-making process. In comparison to the well-known EIpu and EI-cool methods designed by human experts, our approach showcases remarkable efficiency and generalization across various tasks, including 12 synthetic problems and 3 real-world hyperparameter tuning test sets.

Pre-training GNNs to extract transferable knowledge and apply it to downstream tasks has become the de facto standard of graph representation learning. Recent works focused on designing self-supervised pre-training tasks to extract useful and universal transferable knowledge from large-scale unlabeled data. However, they have to face an inevitable question: traditional pre-training strategies that aim at extracting useful information about pre-training tasks, may not extract all useful information about the downstream task. In this paper, we reexamine the pre-training process within traditional pre-training and fine-tuning frameworks from the perspective of Information Bottleneck (IB) and confirm that the forgetting phenomenon in pre-training phase may cause detrimental effects on downstream tasks. Therefore, we propose a novel \underline{D}elayed \underline{B}ottlenecking \underline{P}re-training (DBP) framework which maintains as much as possible mutual information between latent representations and training data during pre-training phase by suppressing the compression operation and delays the compression operation to fine-tuning phase to make sure the compression can be guided with labeled fine-tuning data and downstream tasks. To achieve this, we design two information control objectives that can be directly optimized and further integrate them into the actual model design. Extensive experiments on both chemistry and biology domains demonstrate the effectiveness of DBP.

In many real-world applications, the Pareto Set (PS) of a continuous multiobjective optimization problem can be a piecewise continuous manifold. A decision maker may want to find a solution set that approximates a small part of the PS and requires the solutions in this set share some similarities. This paper makes a first attempt to address this issue. We first develop a performance metric that considers both optimality and variable sharing. Then we design an algorithm for finding the model that minimizes the metric to meet the user's requirements. Experimental results illustrate that we can obtain a linear model that approximates the mapping from the preference vectors to solutions in a local area well., Comment: Preprint of EMO 2023 conference paper

The end-to-end neural combinatorial optimization (NCO) method shows promising performance in solving complex combinatorial optimization problems without the need for expert design. However, existing methods struggle with large-scale problems, hindering their practical applicability. To overcome this limitation, this work proposes a novel Self-Improved Learning (SIL) method for better scalability of neural combinatorial optimization. Specifically, we develop an efficient self-improved mechanism that enables direct model training on large-scale problem instances without any labeled data. Powered by an innovative local reconstruction approach, this method can iteratively generate better solutions by itself as pseudo-labels to guide efficient model training. In addition, we design a linear complexity attention mechanism for the model to efficiently handle large-scale combinatorial problem instances with low computation overhead. Comprehensive experiments on the Travelling Salesman Problem (TSP) and the Capacitated Vehicle Routing Problem (CVRP) with up to 100K nodes in both uniform and real-world distributions demonstrate the superior scalability of our method.

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.

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., Comment: Accepted by the 41st International Conference on Machine Learning (ICML 2024)

Vehicle routing problems (VRPs), which can be found in numerous real-world applications, have been an important research topic for several decades. Recently, the neural combinatorial optimization (NCO) approach that leverages a learning-based model to solve VRPs without manual algorithm design has gained substantial attention. However, current NCO methods typically require building one model for each routing problem, which significantly hinders their practical application for real-world industry problems with diverse attributes. In this work, we make the first attempt to tackle the crucial challenge of cross-problem generalization. In particular, we formulate VRPs as different combinations of a set of shared underlying attributes and solve them simultaneously via a single model through attribute composition. In this way, our proposed model can successfully solve VRPs with unseen attribute combinations in a zero-shot generalization manner. Extensive experiments are conducted on eleven VRP variants, benchmark datasets, and industry logistic scenarios. The results show that the unified model demonstrates superior performance in the eleven VRPs, reducing the average gap to around 5% from over 20% in the existing approach and achieving a significant performance boost on benchmark datasets as well as a real-world logistics application. The source code is included in https://github.com/FeiLiu36/MTNCO.

It is desirable in many multi-objective machine learning applications, such as multi-task learning with conflicting objectives and multi-objective reinforcement learning, to find a Pareto solution that can match a given preference of a decision maker. These problems are often large-scale with available gradient information but cannot be handled very well by the existing algorithms. To tackle this critical issue, this paper proposes a novel predict-and-correct framework for locating a Pareto solution that fits the preference of a decision maker. In the proposed framework, a constraint function is introduced in the search progress to align the solution with a user-specific preference, which can be optimized simultaneously with multiple objective functions. Experimental results show that our proposed method can efficiently find a particular Pareto solution under the demand of a decision maker for standard multiobjective benchmark, multi-task learning, and multi-objective reinforcement learning problems with more than thousands of decision variables. Code is available at: https://github.com/xzhang2523/pmgda. Our code is current provided in the pgmda.rar attached file and will be open-sourced after publication.}

Multiobjective optimization (MOO) is prevalent in numerous applications, in which a Pareto front (PF) is constructed to display optima under various preferences. Previous methods commonly utilize the set of Pareto objectives (particles on the PF) to represent the entire PF. However, the empirical distribution of the Pareto objectives on the PF is rarely studied, which implicitly impedes the generation of diverse and representative Pareto objectives in previous methods. To bridge the gap, we suggest in this paper constructing \emph{uniformly distributed} Pareto objectives on the PF, so as to alleviate the limited diversity found in previous MOO approaches. We are the first to formally define the concept of ``uniformity" for an MOO problem. We optimize the maximal minimal distances on the Pareto front using a neural network, resulting in both asymptotically and non-asymptotically uniform Pareto objectives. Our proposed method is validated through experiments on real-world and synthetic problems, which demonstrates the efficacy in generating high-quality uniform Pareto objectives and the encouraging performance exceeding existing state-of-the-art methods. The detailed model implementation and the code are scheduled to be open-sourced upon publication.

Current methods for large language model alignment typically use scalar human preference labels. However, this convention tends to oversimplify the multi-dimensional and heterogeneous nature of human preferences, leading to reduced expressivity and even misalignment. This paper presents Panacea, an innovative approach that reframes alignment as a multi-dimensional preference optimization problem. Panacea trains a single model capable of adapting online and Pareto-optimally to diverse sets of preferences without the need for further tuning. A major challenge here is using a low-dimensional preference vector to guide the model's behavior, despite it being governed by an overwhelmingly large number of parameters. To address this, Panacea is designed to use singular value decomposition (SVD)-based low-rank adaptation, which allows the preference vector to be simply injected online as singular values. Theoretically, we prove that Panacea recovers the entire Pareto front with common loss aggregation methods under mild conditions. Moreover, our experiments demonstrate, for the first time, the feasibility of aligning a single LLM to represent an exponentially vast spectrum of human preferences through various optimization methods. Our work marks a step forward in effectively and efficiently aligning models to diverse and intricate human preferences in a controllable and Pareto-optimal manner.

In the rapidly evolving field of machine learning, adversarial attacks present a significant challenge to model robustness and security. Decision-based attacks, which only require feedback on the decision of a model rather than detailed probabilities or scores, are particularly insidious and difficult to defend against. This work introduces L-AutoDA (Large Language Model-based Automated Decision-based Adversarial Attacks), a novel approach leveraging the generative capabilities of Large Language Models (LLMs) to automate the design of these attacks. By iteratively interacting with LLMs in an evolutionary framework, L-AutoDA automatically designs competitive attack algorithms efficiently without much human effort. We demonstrate the efficacy of L-AutoDA on CIFAR-10 dataset, showing significant improvements over baseline methods in both success rate and computational efficiency. Our findings underscore the potential of language models as tools for adversarial attack generation and highlight new avenues for the development of robust AI systems., Comment: Camera ready version for GECCO'24 workshop

Black-box query-based attacks constitute significant threats to Machine Learning as a Service (MLaaS) systems since they can generate adversarial examples without accessing the target model's architecture and parameters. Traditional defense mechanisms, such as adversarial training, gradient masking, and input transformations, either impose substantial computational costs or compromise the test accuracy of non-adversarial inputs. To address these challenges, we propose an efficient defense mechanism, PuriDefense, that employs random patch-wise purifications with an ensemble of lightweight purification models at a low level of inference cost. These models leverage the local implicit function and rebuild the natural image manifold. Our theoretical analysis suggests that this approach slows down the convergence of query-based attacks by incorporating randomness into purifications. Extensive experiments on CIFAR-10 and ImageNet validate the effectiveness of our proposed purifier-based defense mechanism, demonstrating significant improvements in robustness against query-based attacks.

Combinatorial optimization problem (COP) is difficult to solve because of the massive number of local optimal solutions in his solution space. Various methods have been put forward to smooth the solution space of COPs, including homotopic convex (HC) transformation for the traveling salesman problem (TSP). This paper extends the HC transformation approach to unconstrained binary quadratic programming (UBQP) by proposing a method to construct a unimodal toy UBQP of any size. We theoretically prove the unimodality of the constructed toy UBQP. After that, we apply this unimodal toy UBQP to smooth the original UBQP by using the HC transformation framework and empirically verify the smoothing effects. Subsequently, we introduce an iterative algorithmic framework incorporating HC transformation, referred as landscape smoothing iterated local search (LSILS). Our experimental analyses, conducted on various UBQP instances show the effectiveness of LSILS. Furthermore, this paper proposes a parallel cooperative variant of LSILS, denoted as PC-LSILS and apply it to both the UBQP and the TSP. Our experimental findings highlight that PC-LSILS improves the smoothing performance of the HC transformation, and further improves the overall performance of the algorithm.

Heuristics are widely used for dealing with complex search and optimization problems. However, manual design of heuristics can be often very labour extensive and requires rich working experience and knowledge. This paper proposes Evolution of Heuristic (EoH), a novel evolutionary paradigm that leverages both Large Language Models (LLMs) and Evolutionary Computation (EC) methods for Automatic Heuristic Design (AHD). EoH represents the ideas of heuristics in natural language, termed thoughts. They are then translated into executable codes by LLMs. The evolution of both thoughts and codes in an evolutionary search framework makes it very effective and efficient for generating high-performance heuristics. Experiments on three widely studied combinatorial optimization benchmark problems demonstrate that EoH outperforms commonly used handcrafted heuristics and other recent AHD methods including FunSearch. Particularly, the heuristic produced by EoH with a low computational budget (in terms of the number of queries to LLMs) significantly outperforms widely-used human hand-crafted baseline algorithms for the online bin packing problem.

In the past few decades, many multiobjective evolutionary optimization algorithms (MOEAs) have been proposed to find a finite set of approximate Pareto solutions for a given problem in a single run, each with its own structure. However, in many real-world applications, it could be desirable to have structure constraints on the entire optimal solution set, which define the patterns shared among all solutions. The current population-based MOEAs cannot properly handle such requirements. In this work, we make the first attempt to incorporate the structure constraints into the whole solution set by a single Pareto set model, which can be efficiently learned by a simple evolutionary stochastic optimization method. With our proposed method, the decision-makers can flexibly trade off the Pareto optimality with preferred structures among all solutions, which is not supported by previous MOEAs. A set of experiments on benchmark test suites and real-world application problems fully demonstrates the efficiency of our proposed method.

Multiobjective evolutionary algorithms (MOEAs) are major methods for solving multiobjective optimization problems (MOPs). Many MOEAs have been proposed in the past decades, of which the search operators need a carefully handcrafted design with domain knowledge. Recently, some attempts have been made to replace the manually designed operators in MOEAs with learning-based operators (e.g., neural network models). However, much effort is still required for designing and training such models, and the learned operators might not generalize well on new problems. To tackle the above challenges, this work investigates a novel approach that leverages the powerful large language model (LLM) to design MOEA operators. With proper prompt engineering, we successfully let a general LLM serve as a black-box search operator for decomposition-based MOEA (MOEA/D) in a zero-shot manner. In addition, by learning from the LLM behavior, we further design an explicit white-box operator with randomness and propose a new version of decomposition-based MOEA, termed MOEA/D-LO. Experimental studies on different test benchmarks show that our proposed method can achieve competitive performance with widely used MOEAs. It is also promising to see the operator only learned from a few instances can have robust generalization performance on unseen problems with quite different patterns and settings. The results reveal the potential benefits of using pre-trained LLMs in the design of MOEAs.To foster reproducibility and accessibility, the source code is https://github.com/FeiLiu36/LLM4MOEA.

Neural combinatorial optimization (NCO) is a promising learning-based approach for solving challenging combinatorial optimization problems without specialized algorithm design by experts. However, most constructive NCO methods cannot solve problems with large-scale instance sizes, which significantly diminishes their usefulness for real-world applications. In this work, we propose a novel Light Encoder and Heavy Decoder (LEHD) model with a strong generalization ability to address this critical issue. The LEHD model can learn to dynamically capture the relationships between all available nodes of varying sizes, which is beneficial for model generalization to problems of various scales. Moreover, we develop a data-efficient training scheme and a flexible solution construction mechanism for the proposed LEHD model. By training on small-scale problem instances, the LEHD model can generate nearly optimal solutions for the Travelling Salesman Problem (TSP) and the Capacitated Vehicle Routing Problem (CVRP) with up to 1000 nodes, and also generalizes well to solve real-world TSPLib and CVRPLib problems. These results confirm our proposed LEHD model can significantly improve the state-of-the-art performance for constructive NCO. The code is available at https://github.com/CIAM-Group/NCO_code/tree/main/single_objective/LEHD., Comment: Accepted at NeurIPS 2023

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., Comment: Accepted by the 40th International Conference on Machine Learning (ICML 2023)

Deep reinforcement learning (RL) has recently shown significant benefits in solving combinatorial optimization (CO) problems, reducing reliance on domain expertise, and improving computational efficiency. However, the field lacks a unified benchmark for easy development and standardized comparison of algorithms across diverse CO problems. To fill this gap, we introduce RL4CO, a unified and extensive benchmark with in-depth library coverage of 23 state-of-the-art methods and more than 20 CO problems. Built on efficient software libraries and best practices in implementation, RL4CO features modularized implementation and flexible configuration of diverse RL algorithms, neural network architectures, inference techniques, and environments. RL4CO allows researchers to seamlessly navigate existing successes and develop their unique designs, facilitating the entire research process by decoupling science from heavy engineering. We also provide extensive benchmark studies to inspire new insights and future work. RL4CO has attracted numerous researchers in the community and is open-sourced at https://github.com/ai4co/rl4co., Comment: A previous version was presented as a workshop paper at the NeurIPS 2023 GLFrontiers Workshop (Oral)

Vehicle routing is a well-known optimization research topic with significant practical importance. Among different approaches to solving vehicle routing, heuristics can produce a satisfactory solution at a reasonable computational cost. Consequently, much effort has been made in the past decades to develop vehicle routing heuristics. In this article, we systematically survey the existing vehicle routing heuristics, particularly on works carried out in recent years. A classification of vehicle routing heuristics is presented, followed by a review of their methodologies, recent developments, and applications. Moreover, we present a general framework of state-of-the-art methods and provide insights into their success. Finally, three emerging research topics with notable works and future directions are discussed.

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., Comment: To appear in 36th Conference on Neural Information Processing Systems (NeurIPS 2022)

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., Comment: Accepted by ICLR 2022, Final Camera-Ready Version

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., Comment: 10 pages, 8 figures

This paper investigates the problem of reconstructing hyperspectral (HS) images from single RGB images captured by commercial cameras, \textbf{without} using paired HS and RGB images during training. To tackle this challenge, we propose a new lightweight and end-to-end learning-based framework. Specifically, on the basis of the intrinsic imaging degradation model of RGB images from HS images, we progressively spread the differences between input RGB images and re-projected RGB images from recovered HS images via effective unsupervised camera spectral response function estimation. To enable the learning without paired ground-truth HS images as supervision, we adopt the adversarial learning manner and boost it with a simple yet effective $\mathcal{L}_1$ gradient clipping scheme. Besides, we embed the semantic information of input RGB images to locally regularize the unsupervised learning, which is expected to promote pixels with identical semantics to have consistent spectral signatures. In addition to conducting quantitative experiments over two widely-used datasets for HS image reconstruction from synthetic RGB images, we also evaluate our method by applying recovered HS images from real RGB images to HS-based visual tracking. Extensive results show that our method significantly outperforms state-of-the-art unsupervised methods and even exceeds the latest supervised method under some settings. The source code is public available at https://github.com/zbzhzhy/Unsupervised-Spectral-Reconstruction., Comment: Accepted to ICCV 2021

This paper investigates the problem of recovering hyperspectral (HS) images from single RGB images. To tackle such a severely ill-posed problem, we propose a physically-interpretable, compact, efficient, and end-to-end learning-based framework, namely AGD-Net. Precisely, by taking advantage of the imaging process, we first formulate the problem explicitly based on the classic gradient descent algorithm. Then, we design a lightweight neural network with a multi-stage architecture to mimic the formed amended gradient descent process, in which efficient convolution and novel spectral zero-mean normalization are proposed to effectively extract spatial-spectral features for regressing an initialization, a basic gradient, and an incremental gradient. Besides, based on the approximate low-rank property of HS images, we propose a novel rank loss to promote the similarity between the global structures of reconstructed and ground-truth HS images, which is optimized with our singular value weighting strategy during training. Moreover, AGD-Net, a single network after one-time training, is flexible to handle the reconstruction with various spectral response functions. Extensive experiments over three commonly-used benchmark datasets demonstrate that AGD-Net can improve the reconstruction quality by more than 1.0 dB on average while saving 67$\times$ parameters and 32$\times$ FLOPs, compared with state-of-the-art methods. The code will be publicly available at https://github.com/zbzhzhy/GD-Net.

Crowd counting is critical for numerous video surveillance scenarios. One of the main issues in this task is how to handle the dramatic scale variations of pedestrians caused by the perspective effect. To address this issue, this paper proposes a novel convolution neural network-based crowd counting method, termed Perspective-guided Fractional-Dilation Network (PFDNet). By modeling the continuous scale variations, the proposed PFDNet is able to select the proper fractional dilation kernels for adapting to different spatial locations. It significantly improves the flexibility of the state-of-the-arts that only consider the discrete representative scales. In addition, by avoiding the multi-scale or multi-column architecture that used in other methods, it is computationally more efficient. In practice, the proposed PFDNet is constructed by stacking multiple Perspective-guided Fractional-Dilation Convolutions (PFC) on a VGG16-BN backbone. By introducing a novel generalized dilation convolution operation, the PFC can handle fractional dilation ratios in the spatial domain under the guidance of perspective annotations, achieving continuous scales modeling of pedestrians. To deal with the problem of unavailable perspective information in some cases, we further introduce an effective perspective estimation branch to the proposed PFDNet, which can be trained in either supervised or weakly-supervised setting once the branch has been pre-trained. Extensive experiments show that the proposed PFDNet outperforms state-of-the-art methods on ShanghaiTech A, ShanghaiTech B, WorldExpo'10, UCF-QNRF, UCF_CC_50 and TRANCOS dataset, achieving MAE 53.8, 6.5, 6.8, 84.3, 205.8, and 3.06 respectively., Comment: Accepted by T-MM 2021