Multi-Fidelity Methods for Optimization: A Survey

Real-world black-box optimization often involves time-consuming or costly experiments and simulations. Multi-fidelity optimization (MFO) stands out as a cost-effective strategy that balances high-fidelity accuracy with computational efficiency through a hierarchical fidelity approach. This survey presents a systematic exploration of MFO, underpinned by a novel text mining framework based on a pre-trained language model. We delve deep into the foundational principles and methodologies of MFO, focusing on three core components -- multi-fidelity surrogate models, fidelity management strategies, and optimization techniques. Additionally, this survey highlights the diverse applications of MFO across several key domains, including machine learning, engineering design optimization, and scientific discovery, showcasing the adaptability and effectiveness of MFO in tackling complex computational challenges. Furthermore, we also envision several emerging challenges and prospects in the MFO landscape, spanning scalability, the composition of lower fidelities, and the integration of human-in-the-loop approaches at the algorithmic level. We also address critical issues related to benchmarking and the advancement of open science within the MFO community. Overall, this survey aims to catalyze further research and foster collaborations in MFO, setting the stage for future innovations and breakthroughs in the field.

Feature Denoising Diffusion Model for Blind Image Quality Assessment

Blind Image Quality Assessment (BIQA) aims to evaluate image quality in line with human perception, without reference benchmarks. Currently, deep learning BIQA methods typically depend on using features from high-level tasks for transfer learning. However, the inherent differences between BIQA and these high-level tasks inevitably introduce noise into the quality-aware features. In this paper, we take an initial step towards exploring the diffusion model for feature denoising in BIQA, namely Perceptual Feature Diffusion for IQA (PFD-IQA), which aims to remove noise from quality-aware features. Specifically, (i) We propose a {Perceptual Prior Discovery and Aggregation module to establish two auxiliary tasks to discover potential low-level features in images that are used to aggregate perceptual text conditions for the diffusion model. (ii) We propose a Perceptual Prior-based Feature Refinement strategy, which matches noisy features to predefined denoising trajectories and then performs exact feature denoising based on text conditions. Extensive experiments on eight standard BIQA datasets demonstrate the superior performance to the state-of-the-art BIQA methods, i.e., achieving the PLCC values of 0.935 ( vs. 0.905 in KADID) and 0.922 ( vs. 0.894 in LIVEC).

ProvNeRF: Modeling per Point Provenance in NeRFs as a Stochastic Process

Neural radiance fields (NeRFs) have gained popularity across various applications. However, they face challenges in the sparse view setting, lacking sufficient constraints from volume rendering. Reconstructing and understanding a 3D scene from sparse and unconstrained cameras is a long-standing problem in classical computer vision with diverse applications. While recent works have explored NeRFs in sparse, unconstrained view scenarios, their focus has been primarily on enhancing reconstruction and novel view synthesis. Our approach takes a broader perspective by posing the question: "from where has each point been seen?" -- which gates how well we can understand and reconstruct it. In other words, we aim to determine the origin or provenance of each 3D point and its associated information under sparse, unconstrained views. We introduce ProvNeRF, a model that enriches a traditional NeRF representation by incorporating per-point provenance, modeling likely source locations for each point. We achieve this by extending implicit maximum likelihood estimation (IMLE) for stochastic processes. Notably, our method is compatible with any pre-trained NeRF model and the associated training camera poses. We demonstrate that modeling per-point provenance offers several advantages, including uncertainty estimation, criteria-based view selection, and improved novel view synthesis, compared to state-of-the-art methods. Please visit our project page at https://provnerf.github.io

Human-in-the-Loop Policy Optimization for Preference-Based Multi-Objective Reinforcement Learning

Multi-objective reinforcement learning (MORL) aims to find a set of high-performing and diverse policies that address trade-offs between multiple conflicting objectives. However, in practice, decision makers (DMs) often deploy only one or a limited number of trade-off policies. Providing too many diversified trade-off policies to the DM not only significantly increases their workload but also introduces noise in multi-criterion decision-making. With this in mind, we propose a human-in-the-loop policy optimization framework for preference-based MORL that interactively identifies policies of interest. Our method proactively learns the DM's implicit preference information without requiring any a priori knowledge, which is often unavailable in real-world black-box decision scenarios. The learned preference information is used to progressively guide policy optimization towards policies of interest. We evaluate our approach against three conventional MORL algorithms that do not consider preference information and four state-of-the-art preference-based MORL algorithms on two MORL environments for robot control and smart grid management. Experimental results fully demonstrate the effectiveness of our proposed method in comparison to the other peer algorithms.

Evolutionary Alternating Direction Method of Multipliers for Constrained Multi-Objective Optimization with Unknown Constraints

Constrained multi-objective optimization problems (CMOPs) pervade real-world applications in science, engineering, and design. Constraint violation has been a building block in designing evolutionary multi-objective optimization algorithms for solving constrained multi-objective optimization problems. However, in certain scenarios, constraint functions might be unknown or inadequately defined, making constraint violation unattainable and potentially misleading for conventional constrained evolutionary multi-objective optimization algorithms. To address this issue, we present the first of its kind evolutionary optimization framework, inspired by the principles of the alternating direction method of multipliers that decouples objective and constraint functions. This framework tackles CMOPs with unknown constraints by reformulating the original problem into an additive form of two subproblems, each of which is allotted a dedicated evolutionary population. Notably, these two populations operate towards complementary evolutionary directions during their optimization processes. In order to minimize discrepancy, their evolutionary directions alternate, aiding the discovery of feasible solutions. Comparative experiments conducted against five state-of-the-art constrained evolutionary multi-objective optimization algorithms, on 120 benchmark test problem instances with varying properties, as well as two real-world engineering optimization problems, demonstrate the effectiveness and superiority of our proposed framework. Its salient features include faster convergence and enhanced resilience to various Pareto front shapes.

Constrained Bayesian Optimization Under Partial Observations: Balanced Improvements and Provable Convergence

The partially observable constrained optimization problems (POCOPs) impede data-driven optimization techniques since an infeasible solution of POCOPs can provide little information about the objective as well as the constraints. We endeavor to design an efficient and provable method for expensive POCOPs under the framework of constrained Bayesian optimization. Our method consists of two key components. Firstly, we present an improved design of the acquisition functions that introduces balanced exploration during optimization. We rigorously study the convergence properties of this design to demonstrate its effectiveness. Secondly, we propose a Gaussian process embedding different likelihoods as the surrogate model for a partially observable constraint. This model leads to a more accurate representation of the feasible regions compared to traditional classification-based models. Our proposed method is empirically studied on both synthetic and real-world problems. The results demonstrate the competitiveness of our method for solving POCOPs.

How Good Are Deep Generative Models for Solving Inverse Problems?

Deep generative models, such as diffusion models, GANs, and IMLE, have shown impressive capability in tackling inverse problems. However, the validity of model-generated solutions w.r.t. the forward problem and the reliability of associated uncertainty estimates remain understudied. This study evaluates recent diffusion-based, GAN-based, and IMLE-based methods on three inverse problems, i.e., $16\times$ super-resolution, colourization, and image decompression. We assess the validity of these models' outputs as solutions to the inverse problems and conduct a thorough analysis of the reliability of the models' estimates of uncertainty over the solution. Overall, we find that the IMLE-based CHIMLE method outperforms other methods in terms of producing valid solutions and reliable uncertainty estimates.

A Challenger to GPT-4V? Early Explorations of Gemini in Visual Expertise

The surge of interest towards Multi-modal Large Language Models (MLLMs), e.g., GPT-4V(ision) from OpenAI, has marked a significant trend in both academia and industry. They endow Large Language Models (LLMs) with powerful capabilities in visual understanding, enabling them to tackle diverse multi-modal tasks. Very recently, Google released Gemini, its newest and most capable MLLM built from the ground up for multi-modality. In light of the superior reasoning capabilities, can Gemini challenge GPT-4V's leading position in multi-modal learning? In this paper, we present a preliminary exploration of Gemini Pro's visual understanding proficiency, which comprehensively covers four domains: fundamental perception, advanced cognition, challenging vision tasks, and various expert capacities. We compare Gemini Pro with the state-of-the-art GPT-4V to evaluate its upper limits, along with the latest open-sourced MLLM, Sphinx, which reveals the gap between manual efforts and black-box systems. The qualitative samples indicate that, while GPT-4V and Gemini showcase different answering styles and preferences, they can exhibit comparable visual reasoning capabilities, and Sphinx still trails behind them concerning domain generalizability. Specifically, GPT-4V tends to elaborate detailed explanations and intermediate steps, and Gemini prefers to output a direct and concise answer. The quantitative evaluation on the popular MME benchmark also demonstrates the potential of Gemini to be a strong challenger to GPT-4V. Our early investigation of Gemini also observes some common issues of MLLMs, indicating that there still remains a considerable distance towards artificial general intelligence. Our project for tracking the progress of MLLM is released at https://github.com/BradyFU/Awesome-Multimodal-Large-Language-Models.

Weakly Supervised Open-Vocabulary Object Detection

Despite weakly supervised object detection (WSOD) being a promising step toward evading strong instance-level annotations, its capability is confined to closed-set categories within a single training dataset. In this paper, we propose a novel weakly supervised open-vocabulary object detection framework, namely WSOVOD, to extend traditional WSOD to detect novel concepts and utilize diverse datasets with only image-level annotations. To achieve this, we explore three vital strategies, including dataset-level feature adaptation, image-level salient object localization, and region-level vision-language alignment. First, we perform data-aware feature extraction to produce an input-conditional coefficient, which is leveraged into dataset attribute prototypes to identify dataset bias and help achieve cross-dataset generalization. Second, a customized location-oriented weakly supervised region proposal network is proposed to utilize high-level semantic layouts from the category-agnostic segment anything model to distinguish object boundaries. Lastly, we introduce a proposal-concept synchronized multiple-instance network, i.e., object mining and refinement with visual-semantic alignment, to discover objects matched to the text embeddings of concepts. Extensive experiments on Pascal VOC and MS COCO demonstrate that the proposed WSOVOD achieves new state-of-the-art compared with previous WSOD methods in both close-set object localization and detection tasks. Meanwhile, WSOVOD enables cross-dataset and open-vocabulary learning to achieve on-par or even better performance than well-established fully-supervised open-vocabulary object detection (FSOVOD).

SPD-DDPM: Denoising Diffusion Probabilistic Models in the Symmetric Positive Definite Space

Symmetric positive definite~(SPD) matrices have shown important value and applications in statistics and machine learning, such as FMRI analysis and traffic prediction. Previous works on SPD matrices mostly focus on discriminative models, where predictions are made directly on $E(X|y)$, where $y$ is a vector and $X$ is an SPD matrix. However, these methods are challenging to handle for large-scale data, as they need to access and process the whole data. In this paper, inspired by denoising diffusion probabilistic model~(DDPM), we propose a novel generative model, termed SPD-DDPM, by introducing Gaussian distribution in the SPD space to estimate $E(X|y)$. Moreover, our model is able to estimate $p(X)$ unconditionally and flexibly without giving $y$. On the one hand, the model conditionally learns $p(X|y)$ and utilizes the mean of samples to obtain $E(X|y)$ as a prediction. On the other hand, the model unconditionally learns the probability distribution of the data $p(X)$ and generates samples that conform to this distribution. Furthermore, we propose a new SPD net which is much deeper than the previous networks and allows for the inclusion of conditional factors. Experiment results on toy data and real taxi data demonstrate that our models effectively fit the data distribution both unconditionally and unconditionally and provide accurate predictions.