Retargeting human kinematic reference motion onto a robot's morphology remains a formidable challenge. Existing methods often produce physical inconsistencies, such as foot sliding, self-collisions, or dynamically infeasible motions, which hinder downstream imitation learning. We propose a bilevel optimization framework that jointly adapts reference motions to a robot's morphology while training a tracking policy using reinforcement learning. To make the optimization tractable, we derive an approximate gradient for the upper-level loss. Our framework requires only a sparse set of semantic rigid-body correspondences and eliminates the need for manual tuning by identifying optimal values for a parameterization expressive enough to preserve characteristic motion across different embodiments. Moreover, by integrating retargeting directly with physics simulation, we produce physically plausible motions that facilitate robust imitation learning. We validate our method in simulation and on hardware, demonstrating challenging motions for morphologies that differ significantly from a human, including retargeting onto a quadruped.
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Single-frame Infrared Small Target Detection (ISTD) aims to localize weak targets under heavy background clutter, yet dense pixel-wise annotations are expensive. Point supervision with online label evolution reduces annotation cost; however, lightweight CNN detectors often lack sufficient semantics, leading to noisy pseudo-masks and unstable optimization. To address this, we propose a hierarchical VFM-driven knowledge distillation framework that uses a frozen Vision Foundation Model (VFM) during training. We formulate point-supervised learning as a bilevel optimization process: the inner loop adapts a VFM-embedded teacher on reweighted training samples, while the outer loop transfers validation-guided knowledge to a lightweight student to mitigate pseudo-label noise and training-set bias. We further introduce Semantic-Conditioned Affine Modulation (SCAM) to inject VFM semantics into CNN features at multiple layers. In addition, a dynamic collaborative learning strategy with cluster-level sample reweighting enhances robustness to imperfect pseudo-masks. Experiments on diverse challenging cases across multiple ISTD backbones demonstrate consistent improvements in detection accuracy and training stability. Our code is available at https://github.com/yuanhang-yao/semantic-prior.
SICNav: Safe and Interactive Crowd Navigation Using Model Predictive Control and Bilevel Optimization (Abstract Reprint)
PDF ↗Robots need to predict and react to human motions to navigate through a crowd without collisions. Many existing methods decouple prediction from planning, which does not account for the interaction between robot and human motions and can lead to the robot getting stuck. We propose SICNav, a Model Predictive Control (MPC) method that jointly solves for robot motion and predicted crowd motion in closed-loop. We model each human in the crowd to be following an Optimal Reciprocal Collision Avoidance (ORCA) scheme and embed that model as a constraint in the robot's local planner, resulting in a bilevel nonlinear MPC optimization problem. We use a KKT-reformulation to cast the bilevel problem as a single level and use a nonlinear solver to optimize. Our MPC method can influence pedestrian motion while explicitly satisfying safety constraints in a single-robot multi-human environment. We analyze the performance of SICNav in two simulation environments and indoor experiments with a real robot to demonstrate safe robot motion that can influence the surrounding humans. We also validate the trajectory forecasting performance of ORCA on a human trajectory dataset.
The Knowledge of Optimization And Learning Algorithms (KOALA) group studies how to integrate optimization, machine learning, and generative modeling to enable data-driven decision-making under uncertainty. We study decision-focused learning, embedding optimization as a differentiable layer to train models end-to-end for decision quality. We design scalable reinforcement learning algorithms for population and personalized healthcare, and develop efficient bilevel optimization methods for nested and multi-agent decision-making. These directions form a unified framework linking optimization and learning for impactful AI in healthcare. Through collaborations with hospitals and NGOs, our group designs and deploys algorithms for pediatric, diabetes, maternal, and mental health applications. Looking ahead, we aim to unite these foundations with generative AI to build theoretically grounded and socially responsible algorithms that advance trustworthy, real-world AI for health and beyond.
As machine learning (ML) applications grow increasingly complex in recent years, modern ML frameworks often need to address multiple potentially conflicting objectives with coupled decision variables across different layers. This creates a compelling need for multi-objective bilevel learning (MOBL). So far, however, the field of MOBL remains in its infancy and many important problems remain under-explored. This motivates us to fill this gap and systematically investigate the theoretical and algorithmic foundation of MOBL. Specifically, we consider MOBL problems with multiple conflicting objectives guided by preferences at the upper-level subproblem, where part of the inputs depend on the optimal solution of the lower-level subproblem. Our goal is to develop efficient MOBL optimization algorithms to (1) identify a preference-guided Pareto-stationary solution with low oracle complexity; and (2) enable systematic Pareto front exploration. To this end, we propose a unifying algorithmic framework called weighted-Chebyshev multi-hyper-gradient-descent (WC-MHGD) for both deterministic and stochastic settings with finite-time Pareto-stationarity convergence rate guarantees, which not only implies low oracle complexity but also induces systematic Pareto front exploration. We further conduct extensive experiments to confirm our theoretical results.
Reinforcement learning (RL) has shown significant promise in sequential portfolio optimization. A typical solution involves optimizing cumulative returns using historical offline data. However, it may produce less generalizable policies that merely ''memorize'' optimal buying and selling actions from the offline data while neglecting the non-stationary nature of the financial market. We frame portfolio optimization of stock data as a specific type of offline RL problem. Our method, MetaTrader, presents two key contributions. First, it introduces a novel bilevel RL algorithm that operates on both the original stock data and its transformations. The core idea is that a robust policy should generalize effectively to out-of-distribution data. Second, we propose a new temporal difference (TD) method that leverages a transformation-based conservative TD target to address value overestimation under limited offline data. Empirical results on two publicly available datasets demonstrate that MetaTrader outperforms existing methods, including both traditional stock prediction models and RL-based trading approaches.
Backdoor attacks pose a persistent security risk to deep neural networks (DNNs) due to their stealth and durability. While recent research has explored leveraging model unlearning mechanisms to enhance backdoor concealment, existing attack strategies still leave persistent traces that may be detected through static analysis. In this work, we introduce the first paradigm of revocable backdoor attacks, where the backdoor can be proactively and thoroughly removed after the attack objective is achieved. We formulate the trigger optimization in revocable backdoor attacks as a bilevel optimization problem: by simulating both backdoor injection and unlearning processes, the trigger generator is optimized to achieve a high attack success rate (ASR) while ensuring that the backdoor can be easily erased through unlearning. To mitigate the optimization conflict between injection and removal objectives, we employ a deterministic partition of poisoning and unlearning samples to reduce sampling-induced variance, and further apply the Projected Conflicting Gradient (PCGrad) technique to resolve the remaining gradient conflicts. Experiments on CIFAR-10 and ImageNet demonstrate that our method maintains ASR comparable to state-of-the-art backdoor attacks, while enabling effective removal of backdoor behavior after unlearning. This work opens a new direction for backdoor attack research and presents new challenges for the security of machine learning systems.
Dormant Backdoor: Weaponizing Model Finetuning for Feasible Backdoor Attacks Against Pretrained Models
PDF ↗As the pretraining-finetuning paradigm becomes dominant in modern AI, the security of model supply chains faces new risks from backdoor attacks. Existing work primarily studies backdoors injected during pretraining and treats subsequent finetuning with clean data as a defense, while recent finetuning-activated attacks assume white-box access to the downstream data distribution, which is rarely realistic in practice. We introduce Dormant Backdoor, a finetuning-activated attack that requires no prior knowledge of downstream tasks. Instead of binding the backdoor to static input patterns, Dormant Backdoor exploits the universal dynamics of gradient-based optimization as a process-as-trigger mechanism. We formulate the attack as a bilevel optimization problem that simulates the victim's finetuning trajectory on proxy data, and jointly optimizes the poisoned model and trigger under lethality, utility, and stealth objectives. Before finetuning, the poisoned model remains behaviorally close to a clean model and can evade existing backdoor detectors; after finetuning, the same adaptation process reliably amplifies the backdoor on diverse downstream datasets and finetuning strategies. Our results reveal a previously underexplored class of process-as-trigger vulnerabilities and highlight the need for defenses that explicitly secure the model adaptation process.
Inferring Heterogeneous Private Valuations from Offline Market Data via Entropic Risk-Sensitive Utility Maximization
PDF ↗Inferring humans' private valuations for goods from their observed market behavior is essential for evaluating market efficiency and improving trading mechanism design. A core challenge lies in uncovering the human decision function that maps private valuations and observed market states to actions. In complex market settings where humans make sequential decisions in stochastic environments, neural networks offer the flexibility to model this decision function. However, training them without access to private valuations or environment dynamics remains challenging. We tackle this challenge and study how to infer heterogeneous human valuations from offline decision data in continuous double auctions. We propose learning the decision function via risk‑sensitive utility maximization. First, we train a generative model on offline bid and ask data to simulate individual trading behavior. Using this generative model, we instantiate simulated markets composed of randomly generated buyers and sellers. Second, we introduce an agent into these simulated markets and use reinforcement learning to learn a risk-sensitive utility-maximizing decision function for the agent. Third, we formulate a bilevel optimization to jointly recover private valuations and risk preference parameters. Our extensive experiments on a large‑scale continuous double auction dataset demonstrate that our framework significantly reduces errors in inferring real human valuations.
BiO-HMC: Dynamic Human-Machine Collaboration for Consensus Decision-Making via Bilevel Optimization
PDF ↗Consensus decision-making uses crowd responses (usually from non-experts) to questions to reach a consensus answer based on human-machine collaboration. The crucial point is dynamic, which should not only enable rapid self-iteration toward the correct answer through crowd workers' responses but also adaptively suggest the next most valuable question(s) to accelerate the integration of the answer. However, existing methods reach consensus using either offline data or fixed question search structures, thereby largely sidestepping this dynamic nature. In response, we propose a bilevel optimization-based human-machine collaboration (BiO-HMC), which explores an inner & outer-level optimization to enable effective answer integration and efficient question selection. The resulting optimization problem is intractable because there is no closed-form expression in the inner-level optimization. We employ a gradient-based method and guarantee the method's theoretical convergence. Experimental results on synthetic and real-world datasets demonstrate the effectiveness and efficiency of the BiO-HMC model, i.e., achieving the highest confidence in the correct answer with the lowest labor cost.
The emergence of large generative models has substantially advanced learning-based scene recovery in the synthetic domain. However, these models generalize poorly to real scenarios stemming from the significant distribution gap, alongside poor adaptation to complex and unforeseen degradations. Consequently, it is imperative to develop a real scene adaptation strategy that yields faithful restorations with reliable generalizability. To this end, we propose Bilevel Prompt LoRA, a novel learning paradigm designed to effectively adapt pre-trained generative models for real scene recovery. First, we introduce a self-supervised distribution-fidelity learning scheme to calibrate the autoencoding pathway under task-irrelevant real distributions to improve texture fidelity. Subsequently, a bilevel joint modeling via hyperparameter optimization is further established, empowering robust synthetic-to-real adaptation for both seen and unseen scenes by exploiting the complementary advantages between LoRA and Prompts to foster mutual promotion. Extensive evaluations on diverse real adverse scenarios demonstrate our superiority, with comprehensive algorithm analyses proving our effectiveness.
Event cameras, with their high dynamic range, show great promise for Low-light Image Enhancement (LLIE). Existing works primarily focus on designing effective modal fusion strategies. However, a key challenge is the dual degradation from intrinsic background activity (BA) noise in events and low signal-to-noise ratio (SNR) in images, which causes severe noise coupling during modal fusion, creating a critical performance bottleneck. We therefore posit that precise event denoising is the prerequisite to unlocking the full potential of event-based fusion. To this end, we propose BiEvLight, a hierarchical and task-aware framework that collaboratively optimizes enhancement and denoising by exploiting their intrinsic interdependence. Specifically, BiEvLight exploits the strong gradient correlation between images and events to build a gradient-guided event denoising prior that alleviates insufficient denoising in heavily noisy regions. Moreover, instead of treating event denoising as a static pre-processing stage--which inevitably incurs a trade-off between over- and under-denoising and cannot adapt to the requirements of a specific enhancement objective--we recast it as a bilevel optimization problem constrained by the enhancement task. Through cross-task interaction, the upper-level denoising problem learns event representations tailored to the lower-level enhancement objective, thereby substantially improving overall enhancement quality. Extensive experiments on the Real-world noise Dataset SED demonstrate that our method significantly outperforms state-of-the-art (SOTA) approaches, with average improvements of 1.30dB in PSNR , 2.03dB in PSNR* and 0.047 in SSIM, respectively. The code will be publicly available at https://github.com/iijjlk/BiEvlight.
UniFusion: A Unified Image Fusion Framework with Robust Representation and Source-Aware Preservation
PDF ↗Image fusion aims to integrate complementary information from multiple source images to produce a more informative and visually consistent representation, benefiting both human perception and downstream vision tasks. Despite recent progress, most existing fusion methods are designed for specific tasks (i.e., multi-modal, multi-exposure, or multi-focus fusion) and struggle to effectively preserve source information during the fusion process. This limitation primarily arises from task-specific architectures and the degradation of source information caused by deep-layer propagation. To overcome these issues, we propose UniFusion, a unified image fusion framework designed to achieve cross-task generalization. First, leveraging DINOv3 for modality-consistent feature extraction, UniFusion establishes a shared semantic space for diverse inputs. Second, to preserve the understanding of each source image, we introduce a reconstruction-alignment loss to maintain consistency between fused outputs and inputs. Finally, we employ a bilevel optimization strategy to decouple and jointly optimize reconstruction and fusion objectives, effectively balancing their coupling relationship and ensuring smooth convergence. Extensive experiments across multiple fusion tasks demonstrate UniFusion's superior visual quality, generalization ability, and adaptability to real-world scenarios.
Underwater instance segmentation is essential for fine-grained scene understanding. However, underwater imagery exhibits a strong domain gap from in-air vision due to severe degradation (e.g., turbidity). Consequently, despite its general segmentation ability, SAM degrades sharply underwater. In this work, we propose BiPA, which effectively adapts SAM to the underwater domain. To be concrete, we construct an underwater SAM with dual prompts and introduce a foreground-attentive injection block to enhance local foreground representation. We formulate dense prompt learning as a bilevel optimization, explicitly capturing the mutual dependency between prompt and model. To make this tractable, we design a two-stage learning strategy. The first stage adapts the dense prompt itself, updating it with Bayesian optimization to learn efficiently. The second stage fine-tunes the model parameters under the frozen optimized prompt, which finally enables effective cross-domain adaptation. Extensive experiments and analyses verify the superiority and efficiency of BiPA. The code is publicly available at https://github.com/ZeAstra/BiPA.
Despite the adoption of Large Language Models (LLMs) in legal AI, automated contract revision remains impeded because generic models often treat strict legal constraints as mere suggestions. To address this safety gap, we introduce the Risk-Constrained Bilevel Stackelberg Framework (RCBSF), modeling high-stakes revision as a rigorous strategic interaction rather than an open-ended conversation. RCBSF establishes a hierarchical Leader-Follower structure: a Global Prescriptive Agent (GPA) leader imposes definitive risk budgets, while a follower system—comprising a Constrained Revision Agent (CRA) and a Local Verification Agent (LVA)—iteratively optimizes the output within these strict boundaries. We theoretically prove this bilevel formulation converges to an equilibrium yielding strictly superior utility over unguided methods. Empirically, RCBSF achieves state-of-the-art performance, surpassing iterative baselines with an average Risk Resolution Rate (RRR) of 84.21% and enhanced token efficiency. Our code is available at https://github.com/xjiacs/RCBSF .
Preference optimization is fundamental for aligning large language models. While existing methods use sample weighting, they typically rely on static functions of instantaneous model states and ignore temporal learning dynamics. We contend that a sample’s value evolves throughout training, characterized by patterns such as stable convergence or noisy oscillation. We propose MetaPO, a framework that meta-learns adaptive weights using three temporal features: reward margin evolution, learning volatility, and reference deviation. Through bilevel optimization on validation data, MetaPO automatically discovers weighting strategies tailored to specific datasets. Experiments on models ranging from 7B to 70B parameters demonstrate statistically significant improvements over strong baselines, achieving gains of up to 2.4 points on AlpacaEval 2.0 and Arena-Hard. Interpretability analysis confirms that temporal features drive over 70% of the weighting decisions and that the learned weights correlate strongly with sample quality.
Theory · Optimization
Federated bilevel optimization is widely used for nested learning problems across distributed clients, such as federated hyperparameter tuning and meta-learning under privacy and communication constraints. Most existing formulations assume fixed client data distributions, which can be violated by performativity, where deployed decisions reshape client behavior and data collection, inducing client-specific, decision-dependent distribution shift. We study federated bilevel performative prediction, where both upper-level (UL) and lower-level (LL) objectives are evaluated under client-dependent, decision-dependent distributions. We formalize the federated bilevel performatively stable (FBPS) point under a decoupled-risk perspective and provide sufficient conditions for its existence and uniqueness. We then develop two federated methods to compute the FBPS solution: FBi-RRM, which converges linearly under a contraction condition, and FBi-SGD, a communication-efficient stochastic method based on federated hypergradient estimation with convergence guarantees under diminishing step sizes when sensitivities are sufficiently small. Experiments on strategic regression and meta strategic classification validate the predicted stability thresholds and demonstrate improved meta-generalization over non-performative baselines.
Theory · Optimization
In this work, we propose *Natural Hypergradient Descent* (NHGD), a new method for solving bilevel optimization problems. To address the computational bottleneck in hypergradient estimation—namely, the need to compute or approximate Hessian inverses—we exploit the statistical structure of the inner optimization problem and use the empirical Fisher information matrix as an asymptotically consistent surrogate for the Hessian. This design enables a parallel *optimize-and-approximate* framework in which the Hessian-inverse approximation is updated *synchronously* with the stochastic inner optimization, reusing gradient information at negligible additional cost. Our main theoretical contribution establishes high-probability error bounds and sample complexity guarantees for NHGD that match those of state-of-the-art optimize-then-approximate methods, while significantly reducing computational time overhead. Empirical evaluations on representative bilevel learning tasks further demonstrate the practical advantages of NHGD, highlighting its scalability and effectiveness in large-scale machine learning settings.
Theory · Optimization
A wide range of optimization problems can often be written in terms of generalized convex functions (GCFs). When this structure is present, it can convert certain nested bilevel objectives into single-level problems amenable to standard first-order optimization methods. We provide a new differentiable layer with a convex parameter space and show (Theorems 5.1 and 5.2) that it and its gradient are universal approximators for GCFs and their gradients. We demonstrate how this parameterization can be leveraged in practice by (i) learning optimal transport maps with general cost functions and (ii) learning optimal auctions of multiple goods. In both these cases, we show how our layer can be used to convert the existing bilevel or min-max formulations into single-level problems that can be solved efficiently with first-order methods.
Optimization · Non-Convex
This paper studies second-order methods for nonconvex-strongly-convex bilevel optimization. We propose a novel fully second-order bilevel approximation method (FSBA) that achieves an iteration complexity of $\tilde{\mathcal{O}}(\epsilon^{-1.5})$ for finding the $(\epsilon, \mathcal{O}(\sqrt{\epsilon}))$ second-order stationary point of the hyper-objective function. Our results demonstrate that second-order methods can achieve an accelerated convergence rate than first-order methods in bilevel optimization. To address the heavy computational cost associated with the second-order oracle, we introduce a lazy variant of FSBA, called LFSBA, which reuses second-order information across several iterations. We prove that LFSBA exhibits better computational complexity than FSBA by a factor of $\sqrt{d}$, where $d$ is the dimension of the problem. We also apply a similar idea to nonconvex strongly-concave minimax optimization and propose the lazy minimax cubic-regularized Newton (LMCN) method with better computational complexity compared to existing second-order methods.