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Courant Institute of Mathematical Sciences

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Selected work

Representative Papers

Enhanced $H$-Consistency Bounds

Jul 18, 2024

Existing H-consistency bounds rely heavily on strong convexity assumptions, limiting their applicability and yielding loose guarantees. Method: We propose a generalized conditional regret inequality framework that—without requiring the surrogate loss lower bound to be convex—derives tighter H-consistency bounds under broader, non-convex settings with predictor- and instance-dependent conditions. By precisely modeling finite-sample relationships between surrogate and target losses (e.g., 0–1 loss) and integrating functional inequalities with statistical learning theory, we obtain unified, improved bounds. Contribution/Results: Our framework encompasses standard multiclass classification, binary/multiclass classification under Tsybakov noise, and bipartite ranking. It substantially enhances both the tightness and generality of theoretical guarantees, overcoming key limitations of prior work while extending H-consistency analysis to previously intractable non-convex and heterogeneous regimes.

12 citations2 influentialRead paper

Beyond Binary: Continuous State Optimization with Graph-Structured Objectives

Aug 10, 2026

This work addresses the challenge of jointly optimizing multiple objectives—such as fairness, accuracy, and latency—in large-scale learning systems with continuous state spaces, where frequent adjustments often lead to system instability. To tackle this issue, the paper introduces dependency graphs into continuous-state multi-objective online optimization for the first time and proposes the Lazy Graph-LinUCB algorithm. This approach integrates three key mechanisms: asynchronous update scheduling, adaptive graph structure learning, and joint parameter estimation. It achieves near-optimal cumulative regret while substantially reducing state-switching overhead. Empirical evaluations in heterogeneous environments demonstrate that, compared to baseline methods, the proposed algorithm reduces movement cost by more than threefold while maintaining comparable cumulative loss.

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L-TGVN: Leveraging Longitudinal Priors for Personalized Rapid MRI

Jun 02, 2026

This work addresses the challenges of prolonged MRI scan times—leading to patient discomfort, high costs, and low throughput—particularly when leveraging historical scans as priors, which introduces complications such as lesion evolution, inter-scan misalignment, and protocol inconsistencies. To overcome these issues, the authors propose L-TGVN (Longitudinal Trust-Guided Variational Network), a method that dynamically modulates the contribution of historical priors to current image reconstruction through a trust mechanism, without requiring explicit image registration. Integrated within an end-to-end variational network framework, L-TGVN effectively fuses longitudinal information while reconstructing images from highly undersampled k-space data. Experimental results demonstrate that L-TGVN significantly outperforms existing approaches under high acceleration factors, achieving superior quantitative metrics and better preservation of fine anatomical details, thereby highlighting its clinical potential for personalized accelerated MRI.

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Theoretical Foundations and Effective Algorithms for Policy-Aware Simulator Learning

May 27, 2026

This work addresses the challenge in model-based reinforcement learning where policies trained in simulation fail in the real world due to model prediction errors. To mitigate this, the authors propose shifting the model-learning objective from predictive accuracy to policy robustness by formulating a zero-sum minimax game between the dynamics model and an adversarial policy. Leveraging online learning theory guarantees, a critic-based simplified algorithm, and the Error-MDP duality, they design a provably convergent active data selection mechanism. Evaluated on continuous control tasks, the method reduces prediction errors in critical regions by 1.5–2.2×, enabling policies trained purely in simulation to achieve near-optimal performance when deployed in the real environment.

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Latest Papers

Beyond Binary: Continuous State Optimization with Graph-Structured Objectives

Aug 10, 2026

This work addresses the challenge of jointly optimizing multiple objectives—such as fairness, accuracy, and latency—in large-scale learning systems with continuous state spaces, where frequent adjustments often lead to system instability. To tackle this issue, the paper introduces dependency graphs into continuous-state multi-objective online optimization for the first time and proposes the Lazy Graph-LinUCB algorithm. This approach integrates three key mechanisms: asynchronous update scheduling, adaptive graph structure learning, and joint parameter estimation. It achieves near-optimal cumulative regret while substantially reducing state-switching overhead. Empirical evaluations in heterogeneous environments demonstrate that, compared to baseline methods, the proposed algorithm reduces movement cost by more than threefold while maintaining comparable cumulative loss.

0 citationsRead paper

L-TGVN: Leveraging Longitudinal Priors for Personalized Rapid MRI

Jun 02, 2026

This work addresses the challenges of prolonged MRI scan times—leading to patient discomfort, high costs, and low throughput—particularly when leveraging historical scans as priors, which introduces complications such as lesion evolution, inter-scan misalignment, and protocol inconsistencies. To overcome these issues, the authors propose L-TGVN (Longitudinal Trust-Guided Variational Network), a method that dynamically modulates the contribution of historical priors to current image reconstruction through a trust mechanism, without requiring explicit image registration. Integrated within an end-to-end variational network framework, L-TGVN effectively fuses longitudinal information while reconstructing images from highly undersampled k-space data. Experimental results demonstrate that L-TGVN significantly outperforms existing approaches under high acceleration factors, achieving superior quantitative metrics and better preservation of fine anatomical details, thereby highlighting its clinical potential for personalized accelerated MRI.

0 citationsRead paper

Theoretical Foundations and Effective Algorithms for Policy-Aware Simulator Learning

May 27, 2026

This work addresses the challenge in model-based reinforcement learning where policies trained in simulation fail in the real world due to model prediction errors. To mitigate this, the authors propose shifting the model-learning objective from predictive accuracy to policy robustness by formulating a zero-sum minimax game between the dynamics model and an adversarial policy. Leveraging online learning theory guarantees, a critic-based simplified algorithm, and the Error-MDP duality, they design a provably convergent active data selection mechanism. Evaluated on continuous control tasks, the method reduces prediction errors in critical regions by 1.5–2.2×, enabling policies trained purely in simulation to achieve near-optimal performance when deployed in the real environment.

0 citationsRead paper

Optimized Deferral for Imbalanced Settings

Apr 30, 2026

This work addresses the bias toward majority experts in two-stage “learning-to-defer” systems caused by imbalanced expert categories. It formalizes this issue for the first time as a cost-sensitive learning problem over the input-expert domain and introduces MILD, a theoretically grounded margin-based loss function together with a tailored optimization algorithm, to achieve more balanced expert routing within the two-stage deferral framework. Theoretical analysis provides strong generalization guarantees for the proposed loss. Extensive experiments on both image classification and large language model routing benchmarks demonstrate that MILD significantly outperforms existing methods, confirming its effectiveness and robustness.

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