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Miscellaneous Aspects of Machine Learning · Transfer, Multitask and Meta-learning

Ruilin Tong, Yuhang Liu, Javen Qinfeng Shi, Dong Gong

Rehearsal-based continual learning (CL) aims to mitigate catastrophic forgetting by maintaining a subset of samples from previous tasks and replaying them. The rehearsal memory can be naturally constructed as a coreset, designed to form a compact subset that enables training with performance comparable to using the full dataset. The coreset selection task can be formulated as bilevel optimization that solves for the subset to minimize the outer objective of the learning task. Existing methods primarily rely on inefficient probabilistic sampling or local gradient-based scoring to approximate sample importance through an iterative process that can be susceptible to ambiguity or noise. Specifically, non-representative samples like ambiguous or noisy samples are difficult to learn and incur high loss values even when training on the full dataset. However, existing methods relying on local gradient tend to highlight these samples in an attempt to minimize the outer loss, leading to a suboptimal coreset. To enhance coreset selection, especially in CL where high-quality samples are essential, we propose a coreset selection method that measures sample importance using reducible loss (ReL) that quantifies the impact of adding a sample to model performance. By leveraging ReL and a process derived from bilevel optimization, we identify and retain samples that yield the highest performance gain. They are shown to be informative and representative. Furthermore, ReL requires only forward computation, making it significantly more efficient than previous methods. To better apply coreset selection in CL, we extend our method to address key challenges such as task interference, streaming data, and knowledge distillation. Experiments on data summarization and continual learning demonstrate the effectiveness and efficiency of our approach.

Peiran Yu, Junyi Li, Heng Huang

Bilevel optimization problems have been actively studied in recent machine learning research due to their broad applications. In this work, we investigate single-loop methods with iterative differentiation (ITD) for nonconvex bilevel optimization problems. For deterministic bilevel problems, we propose an efficient single-loop ITD-type method (ES-ITDM). Our method employs historical updates to approximate the hypergradient. More importantly, based on ES-ITDM, we propose a new method that avoids computing Hessians. This Hessian-free method requires fewer backpropagations and thus has a lower computational cost. We analyze the convergence properties of the proposed methods in two aspects. We provide the convergence rates of the sequences generated by ES-ITD based on the Kurdyka-\L ojasiewicz (KL) property. We also show that the Hessian-free stochastic ES-ITDM has the best-known complexity while has cheaper computation. The empirical studies show that our Hessian-free stochastic variant is more efficient than existing Hessian-free methods and other state-of-the-art bilevel optimization approaches.

Applications · Chemistry and Drug Discovery

Michael Sun, Alston Lo, Minghao Guo, Jie Chen, Connor Coley, Wojciech Matusik

Designing synthetically accessible molecules and recommending analogs to unsynthesizable molecules are important problems for accelerating molecular discovery. We reconceptualize both problems using ideas from program synthesis. Drawing inspiration from syntax-guided synthesis approaches, we decouple the syntactic skeleton from the semantics of a synthetic tree to create a bilevel framework for reasoning about the combinatorial space of synthesis pathways. Given a molecule we aim to generate analogs for, we iteratively refine its skeletal characteristics via Markov Chain Monte Carlo simulations over the space of syntactic skeletons. Given a black-box oracle to optimize, we formulate a joint design space over syntactic templates and molecular descriptors and introduce evolutionary algorithms that optimize both syntactic and semantic dimensions synergistically. Our key insight is that once the syntactic skeleton is set, we can amortize over the search complexity of deriving the program's semantics by training policies to fully utilize the fixed horizon Markov Decision Process imposed by the syntactic template. We demonstrate performance advantages of our bilevel framework for synthesizable analog generation and synthesizable molecule design. Notably, our approach offers the user explicit control over the resources required to perform synthesis and biases the design space towards simpler solutions, making it particularly promising for autonomous synthesis platforms. Supporting code is at https://github.com/shiningsunnyday/SynthesisNet.

Chen Wang, Dasong Gao, Yun-Jou Lin, Youjie Xia, Chen Wang

Learning feature correspondence is a foundational task in computer vision, holding immense importance for downstream applications such as visual odometry and 3D reconstruction. Despite recent progress in data-driven models, feature correspondence learning is still limited by the lack of accurate per-pixel correspondence labels. To overcome this difficulty, we introduce a new self-supervised scheme, imperative learning (IL), for training feature correspondence. It enables correspondence learning on arbitrary uninterrupted videos without any camera pose or depth labels, heralding a new era for self-supervised correspondence learning. Specifically, we formulated the problem of correspondence learning as a bilevel optimization, which takes the reprojection error from bundle adjustment as a supervisory signal for the model. To avoid large memory and computation overhead, we leverage the stationary point to effectively back-propagate the implicit gradients through bundle adjustment. Through extensive experiments, we demonstrate superior performance on tasks including feature matching and pose estimation, in which we obtained an average of 30% accuracy gain over the state-of-the-art matching models. The source code will be made public to benefit the community.

Yongjian Zhong, Hieu Vu, Tianbao Yang, Bijaya Adhikari

Implicit graph neural networks have gained popularity in recent years as they capture long-range dependencies while improving predictive performance in static graphs. Despite the tussle between performance degradation due to the oversmoothing of learned embeddings and long-range dependency being more pronounced in dynamic graphs, as features are aggregated both across neighborhood and time, no prior work has proposed an implicit graph neural model in a dynamic setting. In this paper, we present Implicit Dynamic Graph Neural Network (IDGNN) a novel implicit neural network for dynamic graphs which is the first of its kind. A key characteristic of IDGNN is that it demonstrably is well-posed, i.e., it is theoretically guaranteed to have a fixed-point representation. We then demonstrate that the standard iterative algorithm often used to train implicit models is computationally expensive in our dynamic setting as it involves computing gradients, which themselves have to be estimated in an iterative manner. To overcome this, we pose an equivalent bilevel optimization problem and propose an efficient single-loop training algorithm that avoids iterative computation by maintaining moving averages of key components of the gradients. We conduct extensive experiments on real-world datasets on both classification and regression tasks to demonstrate the superiority of our approach over state-of-the-art baselines. We also demonstrate that our bi-level optimization framework maintains the performance of the expensive iterative algorithm while obtaining up to 1600x speed-up.

Yuxiang Wang 0013, Xiao Yan 0002, Shiyu Jin, Hao Huang 0001, Quanqing Xu, Qingchen Zhang 0001, Bo Du 0001, Jiawei Jiang 0001

Graph dataset condensation (GDC) reduces a dataset with many graphs into a smaller dataset with fewer graphs while maintaining model training accuracy. GDC saves the storage cost and hence accelerates training. Although several GDC methods have been proposed, they are all supervised and require massive labels for the graphs, while graph labels can be scarce in many practical scenarios. To fill this gap, we propose a self-supervised graph dataset condensation method called SGDC, which does not require label information. Our initial design starts with the classical bilevel optimization paradigm for dataset condensation and incorporates contrastive learning techniques. But such a solution yields poor accuracy due to the biased gradient estimation caused by data augmentation. To solve this problem, we introduce representation matching, which conducts training by aligning the representations produced by the condensed graphs with the target representations generated by a pre-trained SSL model. This design eliminates the need for data augmentation and avoids biased gradient. We further propose a graph attention kernel, which not only improves accuracy but also reduces running time when combined with self-supervised kernel ridge regression (KRR). To simplify SGDC and make it more robust, we adopt a adjacency matrix reusing approach, which reuses the topology of the original graphs for the condensed graphs instead of repeatedly learning topology during training. Our evaluations on seven graph datasets find that SGDC improves model accuracy by up to 9.7% compared with 5 state-of-the-art baselines, even if they use label information. Moreover, SGDC is significantly more efficient than the baselines.

Xuelin Zhang, Hong Chen, Bin Gu, Tieliang Gong, Feng Zheng

Stochastic bilevel optimization (SBO) has been integrated into many machine learning paradigms recently including hyperparameter optimization, meta learning, reinforcement learning, etc. Along with the wide range of applications, there have been abundant studies on concerning the computing behaviors of SBO. However, the generalization guarantees of SBO methods are far less understood from the lens of statistical learning theory. In this paper, we provide a systematical generalization analysis of the first-order gradient-based bilevel optimization methods. Firstly, we establish the quantitative connections between the on-average argument stability and the generalization gap of SBO methods. Then, we derive the upper bounds of on-average argument stability for single timescale stochastic gradient descent (SGD) and two timescale SGD, where three settings (nonconvex-nonconvex (NC-NC), convex-convex (C-C) and strongly-convex-strongly-convex (SC-SC)) are considered respectively. Experimental analysis validates our theoretical findings. Compared with the previous algorithmic stability analysis, our results do not require the re-initialization of the inner-level parameters before each iteration and are suit for more general objective functions.

Abdoulatif Cissé, Xenophon Evangelopoulos, Sam Carruthers, Vladimir V. Gusev, Andrew I. Cooper

Robotics and automation offer massive acceleration for solving intractable, multivariate scientific problems such as materials discovery, but the available search spaces can be dauntingly large. Bayesian optimization has emerged as a popular sample-efficient optimization engine, thriving in tasks where no analytic form of the target function/property is known. Here, we exploit expert human knowledge in the form of hypotheses to direct Bayesian searches more quickly to promising regions of chemical space. Previous methods have used underlying distributions derived from existing experimental measurements, which is unfeasible for new, unexplored scientific tasks. Also, such distributions cannot capture intricate hypotheses. Our proposed method uses expert human hypotheses to generate improved seed samples. Unpromising seeds are automatically discounted, while promising seeds are used to augment the surrogate model data, thus achieving better-informed sampling. This process continues in a global versus local search fashion, organized in a bilevel optimization framework. We validate the performance of our method on a range of synthetic functions and demonstrate its practical utility on a real chemical design task where the use of expert hypotheses accelerates the search performance significantly.

Yaohua Liu, Jiaxin Gao, Xuan Liu, Xianghao Jiao, Xin Fan, Risheng Liu

Transfer attacks generate significant interest for real-world black-box applications by crafting transferable adversarial examples through surrogate models. Whereas, existing works essentially directly optimize the single-level objective w.r.t. the surrogate model, which always leads to poor interpretability of attack mechanism and limited generalization performance over unknown victim models. In this work, we propose the BilEvel Transfer AttacK (BETAK) framework by establishing an initialization derived bilevel optimization paradigm, which explicitly reformulates the nested constraint relationship between the Upper-Level (UL) pseudo-victim attacker and the Lower-Level (LL) surrogate attacker. Algorithmically, we introduce the Hyper Gradient Response (HGR) estimation as an effective feedback for the transferability over pseudo-victim attackers, and propose the Dynamic Sequence Truncation (DST) technique to dynamically adjust the back-propagation path for HGR and reduce computational overhead simultaneously. Meanwhile, we conduct detailed algorithmic analysis and provide convergence guarantee to support non-convexity of the LL surrogate attacker. Extensive evaluations demonstrate substantial improvement of BETAK (e.g., 53.41% increase of attack success rates against IncRes-v2_ens victim) against different victims and defense methods in targeted and untargeted attack scenarios.

Michael Curry, Vinzenz Thoma, Darshan Chakrabarti, Stephen McAleer, Christian Kroer, Tuomas Sandholm, Niao He, Sven Seuken

Dynamic mechanism design is a challenging extension to ordinary mechanism design in which the mechanism designer must make a sequence of decisions over time in the face of possibly untruthful reports of participating agents. Optimizing dynamic mechanisms for welfare is relatively well understood. However, there has been less work on optimizing for other goals (e.g., revenue), and without restrictive assumptions on valuations, it is remarkably challenging to characterize good mechanisms. Instead, we turn to automated mechanism design to find mechanisms with good performance in specific problem instances. We extend the class of affine maximizer mechanisms to MDPs where agents may untruthfully report their rewards. This extension results in a challenging bilevel optimization problem in which the upper problem involves choosing optimal mechanism parameters, and the lower problem involves solving the resulting MDP. Our approach can find truthful dynamic mechanisms that achieve strong performance on goals other than welfare, and can be applied to essentially any problem setting---without restrictions on valuations---for which RL can learn optimal policies.

Xingdi Chen, Yu Xiong, Kai Yang

Utilization of inter-base station cooperation for information processing has shown great potential in enhancing the overall quality of communication services (QoS) in wireless communication networks. Nevertheless, such cooperations require the knowledge of channel state information (CSI) at base stations (BSs), which is assumed to be perfectly known. However, CSI errors are inevitable in practice which necessitates beamforming technique that can achieve robust performance in the presence of channel estimation errors. Existing approaches relax the robust beamforming design problems into semidefinite programming (SDP), which can only achieve a solution that is far from being optimal. To this end, this paper views robust beamforming design problems from a bilevel optimization perspective. In particular, we focus on maximizing the worst-case weighted sum-rate (WSR) in the downlink multi-cell multi-user multiple-input single-output (MISO) system considering bounded CSI errors. We first reformulate this problem into a bilevel optimization problem and then develop an efficient algorithm based on the cutting plane method. A distributed optimization algorithm has also been developed to facilitate the parallel processing in practical settings. Numerical results are provided to confirm the effectiveness of the proposed algorithm in terms of performance and complexity, particularly in the presence of CSI uncertainties.

Yang Zou, Xingyuan Li, Zhiying Jiang, Jinyuan Liu

Neural Radiance Fields (NeRF) have made significant strides in the modeling and rendering of 3D scenes. However, due to the complexity of luminance information, existing NeRF methods often struggle to produce satisfactory renderings when dealing with high and low exposure images. To address this issue, we propose an innovative approach capable of effectively modeling and rendering images under multiple exposure conditions. Our method adaptively learns the characteristics of images under different exposure conditions through an unsupervised evaluator-simulator structure for HDR (High Dynamic Range) fusion. This approach enhances NeRF's comprehension and handling of light variations, leading to the generation of images with appropriate brightness. Simultaneously, we present a bilevel optimization method tailored for novel view synthesis, aiming to harmonize the luminance information of input images while preserving their structural and content consistency. This approach facilitates the concurrent optimization of multi-exposure correction and novel view synthesis, in an unsupervised manner. Through comprehensive experiments conducted on the LOM and LOL datasets, our approach surpasses existing methods, markedly enhancing the task of novel view synthesis for multi-exposure environments and attaining state-of-the-art results. The source code can be found at https://github.com/Archer-204/AME-NeRF.

Yixin Liu, Chenrui Fan, Yutong Dai, Xun Chen, Pan Zhou, Lichao Sun

Text-to-image diffusion models allow seamless generation of personalized images from scant reference photos. Yet these tools in the wrong hands can fabricate misleading or harmful content endangering individuals. To address this problem existing poisoning-based approaches perturb user images in an imperceptible way to render them "unlearnable" from malicious uses. We identify two limitations of these defending approaches: i) sub-optimal due to the hand-crafted heuristics for solving the intractable bilevel optimization and ii) lack of robustness against simple data transformations like Gaussian filtering. To solve these challenges we propose MetaCloak which solves the bi-level poisoning problem with a meta-learning framework with an additional transformation sampling process to craft transferable and robust perturbation. Specifically we employ a pool of surrogate diffusion models to craft transferable and model-agnostic perturbation. Furthermore by incorporating an additional transformation process we design a simple denoising-error maximization loss that is sufficient for causing transformation-robust semantic distortion and degradation in a personalized generation. Extensive experiments on the VGGFace2 and CelebA-HQ datasets show that MetaCloak outperforms existing approaches. Notably MetaCloak can successfully fool online training services like Replicate in a black-box manner demonstrating the effectiveness of MetaCloak in real-world scenarios.

Xiaoning Sun, Huaijiang Sun, Bin Li, Dong Wei, Weiqing Li, Jianfeng Lu

In the academic field the research on human motion prediction tasks mainly focuses on exploiting the observed information to forecast human movements accurately in the near future horizon. However a significant gap appears when it comes to the application field as current models are all trained offline with fixed parameters that are inherently suboptimal to handle the complex yet ever-changing nature of human behaviors. To bridge this gap in this paper we introduce the task of online meta adaptation for human motion prediction based on the insight that finding "smart weights" capable of swift adjustments to suit different motion contexts along the time is a key to improving predictive accuracy. We propose MoML which ingeniously borrows the bilevel optimization spirit of model-agnostic meta-learning to transform previous predictive mistakes into strong inductive biases to guide online adaptation. This is achieved by our MoAdapter blocks that can learn error information by facilitating efficient adaptation via a few gradient steps which fine-tunes our meta-learned "smart" initialization produced by the generic predictor. Considering real-time requirements in practice we further propose Fast-MoML a more efficient variant of MoML that features a closed-form solution instead of conventional gradient update. Experimental results show that our approach can effectively bring many existing offline motion prediction models online and improves their predictive accuracy.

Reinforcement Learning · Deep RL

Dohyeong Kim, Taehyun Cho, Seungyub Han, Hojun Chung, Kyungjae Lee, Songhwai Oh

The field of risk-constrained reinforcement learning (RCRL) has been developed to effectively reduce the likelihood of worst-case scenarios by explicitly handling risk-measure-based constraints.However, the nonlinearity of risk measures makes it challenging to achieve convergence and optimality.To overcome the difficulties posed by the nonlinearity, we propose a spectral risk measure-constrained RL algorithm, spectral-risk-constrained policy optimization (SRCPO), a bilevel optimization approach that utilizes the duality of spectral risk measures.In the bilevel optimization structure, the outer problem involves optimizing dual variables derived from the risk measures, while the inner problem involves finding an optimal policy given these dual variables.The proposed method, to the best of our knowledge, is the first to guarantee convergence to an optimum in the tabular setting.Furthermore, the proposed method has been evaluated on continuous control tasks and showed the best performance among other RCRL algorithms satisfying the constraints.Our code is available at https://github.com/rllab-snu/Spectral-Risk-Constrained-RL.

Optimization · Bilevel optimization

Huaqing Zhang, Lesi Chen, Jing Xu, Jingzhao Zhang

This paper studies simple bilevel problems, where a convex upper-level function is minimized over the optimal solutions of a convex lower-level problem. We first show the fundamental difficulty of simple bilevel problems, that the approximate optimal value of such problems is not obtainable by first-order zero-respecting algorithms. Then we follow recent works to pursue the weak approximate solutions. For this goal, we propose a novel method by reformulating them into functionally constrained problems. Our method achieves near-optimal rates for both smooth and nonsmooth problems. To the best of our knowledge, this is the first near-optimal algorithm that works under standard assumptions of smoothness or Lipschitz continuity for the objective functions.

Xiaochuan Gong, Jie Hao, Mingrui Liu

This paper investigates a class of stochastic bilevel optimization problems where the upper-level function is nonconvex with potentially unbounded smoothness and the lower-level problem is strongly convex. These problems have significant applications in sequential data learning, such as text classification using recurrent neural networks. The unbounded smoothness is characterized by the smoothness constant of the upper-level function scaling linearly with the gradient norm, lacking a uniform upper bound. Existing state-of-the-art algorithms require $\widetilde{O}(\epsilon^{-4})$ oracle calls of stochastic gradient or Hessian/Jacobian-vector product to find an $\epsilon$-stationary point. However, it remains unclear if we can further improve the convergence rate when the assumptions for the function in the population level also hold for each random realization almost surely (e.g., Lipschitzness of each realization of the stochastic gradient). To address this issue, we propose a new Accelerated Bilevel Optimization algorithm named AccBO. The algorithm updates the upper-level variable by normalized stochastic gradient descent with recursive momentum and the lower-level variable by the stochastic Nesterov accelerated gradient descent algorithm with averaging. We prove that our algorithm achieves an oracle complexity of $\widetilde{O}(\epsilon^{-3})$ to find an $\epsilon$-stationary point, when the lower-level stochastic gradient has a small variance $O(\epsilon)$. Our proof relies on a novel lemma characterizing the dynamics of stochastic Nesterov accelerated gradient descent algorithm under distribution drift with high probability for the lower-level variable, which is of independent interest and also plays a crucial role in analyzing the hypergradient estimation error over time. Experimental results on various tasks confirm that our proposed algorithm achieves the predicted theoretical acceleration and significantly outperforms baselines in bilevel optimization.

Trustworthy Machine Learning

Ye Sun, Hao Zhang, Tiehua Zhang, Xingjun Ma, Yu-Gang Jiang

Image segmentation is a crucial vision task that groups pixels within an image into semantically meaningful segments, which is pivotal in obtaining a fine-grained understanding of real-world scenes. However, an increasing privacy concern exists regarding training large-scale image segmentation models on unauthorized private data. In this work, we exploit the concept of unlearnable examples to make images unusable to model training by generating and adding unlearnable noise into the original images. Particularly, we propose a novel Unlearnable Segmentation (UnSeg) framework to train a universal unlearnable noise generator that is capable of transforming any downstream images into their unlearnable version. The unlearnable noise generator is finetuned from the Segment Anything Model (SAM) via bilevel optimization on an interactive segmentation dataset towards minimizing the training error of a surrogate model that shares the same architecture with SAM (but trains from scratch). We empirically verify the effectiveness of UnSeg across 6 mainstream image segmentation tasks, 10 widely used datasets, and 7 different network architectures, and show that the unlearnable images can reduce the segmentation performance by a large margin. Our work provides useful insights into how to leverage foundation models in a data-efficient and computationally affordable manner to protect images against image segmentation models.

Learning Theory

Rongzhen Wang, Chenyu Zheng, Guoqiang Wu, Xu Min, Xiaolu Zhang, Jun Zhou, Chongxuan LI

Gradient-based bilevel programming leverages unrolling differentiation (UD) or implicit function theorem (IFT) to solve hyperparameter optimization (HO) problems, and is proven effective and scalable in practice. To understand their generalization behavior, existing works establish upper bounds on the uniform stability of these algorithms, while their tightness is still unclear. To this end, this paper attempts to establish stability lower bounds for UD-based and IFT-based algorithms. A central technical challenge arises from the dependency of each outer-level update on the concurrent stage of inner optimization in bilevel programming. To address this problem, we introduce lower-bounded expansion properties to characterize the instability in update rules which can serve as general tools for lower-bound analysis. These properties guarantee the hyperparameter divergence at the outer level and the Lipschitz constant of inner output at the inner level in the context of HO.Guided by these insights, we construct a quadratic example that yields tight lower bounds for the UD-based algorithm and meaningful bounds for a representative IFT-based algorithm.Our tight result indicates that uniform stability has reached its limit in stability analysis for the UD-based algorithm.

Optimization · Bilevel optimization

Andi Han, Bamdev Mishra, Pratik Kumar Jawanpuria, Akiko Takeda

Bilevel optimization has gained prominence in various applications. In this study, we introduce a framework for solving bilevel optimization problems, where the variables in both the lower and upper levels are constrained on Riemannian manifolds. We present several hypergradient estimation strategies on manifolds and analyze their estimation errors. Furthermore, we provide comprehensive convergence and complexity analyses for the proposed hypergradient descent algorithm on manifolds. We also extend our framework to encompass stochastic bilevel optimization and incorporate the use of general retraction. The efficacy of the proposed framework is demonstrated through several applications.