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1,217篇论文匹配“Discrete Optimization”
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Zicheng Zhou, Min Huang, Qinghai Miao

Learning high-quality sentence embeddings from Natural Language Inference (NLI) data is often challenged by a critical signal conflict between discrete labels and the continuous spectrum of semantic similarity, as well as information loss from discarded neutral sentence pairs during training. To address this, we introduce Rank-Awareness and Angular Optimization Embeddings (RAOE), a framework that leverages the full NLI dataset (Entailment, Neutral, Contradiction) augmented with pre-computed continuous similarity scores (S). RAOE employs a novel composite objective which features: (1) a Rank Margin objective that enforces rank consistency against S using an explicit margin, and (2) a Gated Angular objective that conditionally refines embedding geometry based on NLI label (L) and S score agreement. Extensive evaluations on STS tasks and the MTEB benchmark demonstrate RAOE’s effectiveness. Our general-purpose RAOE-S1 model (BERT-base) significantly outperforms strong baselines, achieving an average Spearman’s correlation of 85.11 (vs. SimCSE’s 81.57 and AnglE’s 82.43), and shows consistent improvements on MTEB. Further STS-specialized fine-tuning (RAOE-S2) establishes new state-of-the-art performance on STS (88.17 with BERT-base). These results confirm RAOE’s ability to efficiently learn robust and nuanced sentence representations through the synergy of rank-awareness and conditional angular constraints. Code is available at https://github.com/Shengjingwa/RAOE.

Ibne Farabi Shihab, Sanjeda Akter, Anuj Sharma

Integrating large language models (LLMs) as action proposers in reinforcement learning (RL) significantly boosts performance in text-based environments but incurs prohibitive computational costs. We introduce a cache-efficient framework for Bayesian RL that leverages LLM-derived action suggestions, drastically reducing these costs while maintaining near-optimal performance. Our approach features an adaptive caching mechanism, optimized via meta-learning based on policy performance, to enable efficient inference across text-based games (e.g., TextWorld, ALFWorld) and robotic control tasks (e.g., MuJoCo, MetaWorld). This framework achieves a 3.8\times–4.7\times reduction in LLM queries and 4.0\times–12.0\times lower median latencies (85–93ms on consumer hardware), while retaining 96–98% of the uncached policy’s performance. We provide theoretical guarantees on the reliability of cached decisions with Kullback-Leibler (KL) divergence bounds, which are validated empirically by high success rates (90.4–95.6%) in complex text environments. For offline RL, our proposed CQL-Prior variant improves performance by 14–29% and reduces training time by 38–40%. Evaluations across eight diverse tasks demonstrate the framework’s generalizability and practicality for resource-constrained settings, making LLM-guided RL a viable and accessible approach for both text-based and robotic applications.

Optimization · Discrete Optimization

Wenzhao Liu, Haoran Li, Congying Han, Zicheng Zhang, Anqi Li, Tiande Guo

Achieving generalization in neural approaches across different scales and distributions remains a significant challenge for routing problems. A key obstacle is that neural networks often fail to learn robust principles for identifying universal patterns and deriving optimal solutions from diverse instances. In this paper, we first uncover Purity Law, a fundamental structural principle for optimal solutions of routing problems, defining that edge prevalence grows exponentially with the sparsity of surrounding vertices. Statistically and theoretically validated across diverse instances, Purity Law reveals a consistent bias toward local sparsity in global optima. Building on this insight, we propose Purity Policy Optimization (PUPO), a novel training paradigm that explicitly aligns characteristics of neural solutions with Purity Law during the solution construction process to enhance generalization. Extensive experiments demonstrate that PUPO can be seamlessly integrated with popular neural solvers, significantly enhancing their generalization performance without incurring additional computational overhead during inference.

Optimization · Discrete Optimization

Yang Li, Lvda Chen, Haonan Wang, Runzhong Wang, Junchi Yan

While diffusion models have shown promise for combinatorial optimization (CO), their inference-time scaling cost-efficiency remains relatively underexplored. Existing methods improve solution quality by increasing denoising steps, but the performance often becomes saturated quickly. This paper proposes GenSCO to systematically scale diffusion solvers by an orthogonal dimension of inference-time computation beyond denoising step expansion, i.e., search-driven generation. GenSCO takes generation as a search operator rather than a complete solving process, where each operator cycle combines solution disruption (via local search operators) and diffusion sampling, enabling iterative exploration of the learned solution space. Rather than over-refining current solutions, this paradigm encourages the model to leave local optima and explore a broader area of the solution space, ensuring a more consistent scaling effect. The search loop is supported by a search-friendly solution-enhancement training procedure that incorporates a rectified flow model learning to establish diffusion trajectories between suboptimal solutions and the optimal ones. The flow model is empowered by a lightweight transformer architecture to learn neural ODEs that linearize solution trajectories, accelerating convergence of the scaling effect with efficiency. The resulting enhanced scaling efficiency and practical scalability lead to synergistic performance improvements. Extensive experiments show that GenSCO delivers performance improvements by orders of magnitude over previous state-of-the-art neural methods. Notably, GenSCO even achieves significant speedups compared to the state-of-the-art classic mathematical solver LKH3, delivering a 141x speedup to reach 0.000% optimality gap on TSP-100, and approximately a 10x speedup to reach 0.02% on TSP-500.

Computer Vision · Vision Models & Multimodal

Wenxuan Wang, Fan Zhang, Yufeng Cui, Haiwen Diao, Zhuoyan Luo, Huchuan Lu, Jing Liu, Xinlong Wang

Existing vision tokenization isolates the optimization of vision tokenizers from downstream training, implicitly assuming the visual tokens can generalize well across various tasks, e.g., image generation and visual question answering. The vision tokenizer optimized for low-level reconstruction is agnostic to downstream tasks requiring varied representations and semantics. This decoupled paradigm introduces a critical misalignment: The loss of the vision tokenization can be the representation bottleneck for target tasks. For example, errors in tokenizing text in a given image lead to poor results when recognizing or generating them. To address this, we propose ETT, an end-to-end vision tokenizer tuning approach that enables joint optimization between vision tokenization and target autoregressive tasks. Unlike prior autoregressive models that use only discrete indices from a frozen vision tokenizer, ETT leverages the visual embeddings of the tokenizer codebook, and optimizes the vision tokenizers end-to-end with both reconstruction and caption objectives. ETT can be seamlessly integrated into existing training pipelines with minimal architecture modifications. Our ETT is simple to implement and integrate, without the need to adjust the original codebooks or architectures of the employed large language models. Extensive experiments demonstrate that our proposed end-to-end vision tokenizer tuning unlocks significant performance gains, i.e., 2-6% for multimodal understanding and visual generation tasks compared to frozen tokenizer baselines, while preserving the original reconstruction capability. We hope this very simple and strong method can empower multimodal foundation models besides image generation and understanding.

Theory · Reinforcement Learning and Planning

Nicolas Nguyen, Solenne Gaucher, Claire Vernade

We study the problem of non-stationary Lipschitz bandits, where the number of actions is infinite and the reward function, satisfying a Lipschitz assumption, can change arbitrarily over time. We design an algorithm that adaptively tracks the recently introduced notion of significant shifts, defined by large deviations of the cumulative reward function. To detect such reward changes, our algorithm leverages a hierarchical discretization of the action space. Without requiring any prior knowledge of the non-stationarity, our algorithm achieves a minimax-optimal dynamic regret bound of $\mathcal{\widetilde{O}}(\tilde{L}^{1/3}T^{2/3})$, where $\tilde{L}$ is the number of significant shifts and $T$ the horizon. This result provides the first optimal guarantee in this setting.

Computer Vision · 3D Rendering & Reconstruction

Bohao Liao, Wei Zhai, Zengyu Wan, Zhixin Cheng, Wenfei Yang, Yang Cao, Tianzhu Zhang, Zheng-Jun Zha

Scene reconstruction from casually captured videos has wide real-world applications. Despite recent progress, existing methods relying on traditional cameras tend to fail in high-speed scenarios due to insufficient observations and inaccurate pose estimation. Event cameras, inspired by biological vision, record pixel-wise intensity changes asynchronously with high temporal resolution and low latency, providing valuable scene and motion information in blind inter-frame intervals. In this paper, we introduce the event cameras to aid scene construction from a casually captured video for the first time, and propose Event-Aided Free-Trajectory 3DGS, called EF-3DGS, which seamlessly integrates the advantages of event cameras into 3DGS through three key components. First, we leverage the Event Generation Model (EGM) to fuse events and frames, enabling continuous supervision between discrete frames. Second, we extract motion information through Contrast Maximization (CMax) of warped events, which calibrates camera poses and provides gradient-domain constraints for 3DGS. Third, to address the absence of color information in events, we combine photometric bundle adjustment (PBA) with a Fixed-GS training strategy that separates structure and color optimization, effectively ensuring color consistency across different views. We evaluate our method on the public Tanks and Temples benchmark and a newly collected real-world dataset, RealEv-DAVIS. Our method achieves up to 3dB higher PSNR and 40% lower Absolute Trajectory Error (ATE) compared to state-of-the-art methods under challenging high-speed scenarios.

Fan Yang, Yousong Zhu, Xin Li, Yufei Zhan, Hongyin Zhao, Shurong Zheng, Yaowei Wang, Ming Tang, Jinqiao Wang

Recent Large Vision Language Models (LVLMs) demonstrate promising capabilities in unifying visual understanding and generative modeling, enabling both accurate content understanding and flexible editing. However, current approaches treat \textbf{\textit{"what to see"}} and \textbf{\textit{"how to edit"}} separately: they either perform isolated object segmentation or utilize segmentation masks merely as conditional prompts for local edit generation tasks, often relying on multiple disjointed models. To bridge these gaps, we introduce FOCUS, a unified LVLM that integrates segmentation-aware perception and controllable object-centric generation within an end-to-end framework. FOCUS employs a dual-branch visual encoder to simultaneously capture global semantic context and fine-grained spatial details. In addition, we leverage a MoVQGAN-based visual tokenizer to produce discrete visual tokens that enhance generation quality. To enable accurate and controllable image editing, we propose a progressive multi-stage training pipeline, where segmentation masks are jointly optimized and used as spatial condition prompts to guide the diffusion decoder. This strategy aligns visual encoding, segmentation, and generation modules, effectively bridging segmentation-aware perception with fine-grained visual synthesis. Extensive experiments across three core tasks, including multimodal understanding, referring segmentation accuracy, and controllable image generation, demonstrate that FOCUS achieves strong performance by jointly optimizing visual perception and generative capabilities.

Deep Learning · Generative Models and Autoencoders

Feiyang Fu, Tongxian Guo, Zhaoqiang Liu

Discrete diffusion models (DDMs) have shown powerful generation ability for discrete data modalities like text and molecules. However, their practical application is hindered by inefficient sampling, requiring a large number of sampling steps. Accelerating DDMs by using larger step sizes typically introduces significant problems in generation quality, as it amplifies the impact of both the compounding decoding error due to factorized predictions and discretization error from numerical approximations, leading to a significant decrease in sampling quality. To address these challenges, we propose learnable sampler distillation (LSD), a novel approach to train fast and high-fidelity samplers for DDMs. LSD employs a distillation approach where a student sampler with a few steps learns to align its intermediate score trajectory with that of a high-quality teacher sampler with numerous steps. This alignment is achieved by optimizing learnable sampler coefficients that adaptively adjust sampling dynamics. Additionally, we further propose LSD+, which also learns time schedules that allocate steps non-uniformly. Experiments across text generation, image generation, and synthetic tasks demonstrate that our proposed approaches outperform existing samplers for DDMs, achieving substantially higher sampling quality with significantly fewer sampling steps.

Optimization · Large Scale, Parallel and Distributed

Sikai Bai, Haoxi Li, Jie ZHANG, Zicong Hong, Song Guo

Despite the significant breakthrough of Mixture-of-Experts (MoE), the increasing scale of these MoE models presents huge memory and storage challenges. Existing MoE pruning methods, which involve reducing parameter size with a uniform sparsity across all layers, often lead to suboptimal outcomes and performance degradation due to varying expert redundancy in different MoE layers. To address this, we propose a non-uniform pruning strategy, dubbed Differentiable Expert Pruning (DiEP), which adaptively adjusts pruning rates at the layer level while jointly learning inter-layer importance, effectively capturing the varying redundancy across different MoE layers. By transforming the global discrete search space into a continuous one, our method handles exponentially growing non-uniform expert combinations, enabling adaptive gradient-based pruning. Extensive experiments on five advanced MoE models demonstrate the efficacy of our method across various NLP tasks. Notably, \textbf{DiEP} retains around 92\% of original performance on Mixtral 8$\times$7B with only half the experts, outperforming other pruning methods by up to 7.1% on the challenging MMLU dataset.

General Machine Learning · Transfer, Multitask and Meta-learning

Xueqing Sun, Renzhen Wang, Quanziang Wang, Yichen WU, Xixi Jia, Deyu Meng

Pseudo-labeling is a commonly used paradigm in semi-supervised learning, yet its application to semi-supervised regression (SSR) remains relatively under-explored. Unlike classification, where pseudo-labels are discrete and confidence-based filtering is effective, SSR involves continuous outputs with heteroscedastic noise, making it challenging to assess pseudo-label reliability. As a result, naive pseudo-labeling can lead to error accumulation and overfitting to incorrect labels. To address this, we propose an uncertainty-aware pseudo-labeling framework that dynamically adjusts pseudo-label influence from a bi-level optimization perspective. By jointly minimizing empirical risk over all data and optimizing uncertainty estimates to enhance generalization on labeled data, our method effectively mitigates the impact of unreliable pseudo-labels. We provide theoretical insights and extensive experiments to validate our approach across various benchmark SSR datasets, and the results demonstrate superior robustness and performance compared to existing methods.

Applications · Physics

Hong Wang, Jie Wang, Minghao Ma, Haoran Shao, Haoyang Liu

Matrix preconditioning is a critical technique to accelerate the solution of linear systems, where performance heavily depends on the selection of preconditioning parameters. Traditional parameter selection approaches often define fixed constants for specific scenarios. However, they rely on domain expertise and fail to consider the instance-wise features for individual problems, limiting their performance. In contrast, machine learning (ML) approaches, though promising, are hindered by high inference costs and limited interpretability. To combine the strengths of both approaches, we propose a symbolic discovery framework—namely, **Sym**bolic **Ma**trix **P**reconditioning (**SymMaP**)—to learn efficient symbolic expressions for preconditioning parameters. Specifically, we employ a neural network to search the high-dimensional discrete space for expressions that can accurately predict the optimal parameters. The learned expression allows for high inference efficiency and excellent interpretability (expressed in concise symbolic formulas), making it simple and reliable for deployment. Experimental results show that SymMaP consistently outperforms traditional strategies across various benchmarks.

Deep Learning · Algorithms

Shuli Zhang, Hao Zhou, Jiaqi Zheng, Guibin Jiang, Cheng Bing, Wei Lin, Guihai Chen

Online Internet platforms require sophisticated marketing strategies to optimize user retention and platform revenue — a classical resource allocation problem. Traditional solutions adopt a two-stage pipeline: machine learning (ML) for predicting individual treatment effects to marketing actions, followed by operations research (OR) optimization for decision-making. This paradigm presents two fundamental technical challenges. First, the prediction-decision misalignment: Conventional ML methods focus solely on prediction accuracy without considering downstream optimization objectives, leading to improved predictive metrics that fail to translate to better decisions. Second, the bias-variance dilemma: Observational data suffers from multiple biases (e.g., selection bias, position bias), while experimental data (e.g., randomized controlled trials), though unbiased, is typically scarce and costly --- resulting in high-variance estimates. We propose **Bi**-level **D**ecision-**F**ocused **C**ausal **L**earning (**Bi-DFCL**) that systematically addresses these challenges. First, we develop an unbiased estimator of OR decision quality using experimental data, which guides ML model training through surrogate loss functions that bridge discrete optimization gradients. Second, we establish a bi-level optimization framework that jointly leverages observational and experimental data, solved via implicit differentiation. This novel formulation enables our unbiased OR estimator to correct learning directions from biased observational data, achieving optimal bias-variance tradeoff. Extensive evaluations on public benchmarks, industrial marketing datasets, and large-scale online A/B tests demonstrate the effectiveness of Bi-DFCL, showing statistically significant improvements over state-of-the-art. Currently, Bi-DFCL has been deployed across several marketing scenarios at Meituan, one of the largest online food delivery platforms in the world.

Zhen Zhang, Prof Javen Qinfeng Shi, Wee Sun Lee

The Asymmetric Traveling Salesman Problem (ATSP) ranks among the most fundamental and notoriously difficult problems in combinatorial optimization. We propose a novel continuous relaxation framework for the Asymmetric Traveling Salesman Problem (ATSP) by leveraging differentiable constraints that encourage acyclic structures and valid permutations. Our approach integrates a differentiable trace-based Directed Acyclic Graph (DAG) constraint with a doubly stochastic matrix relaxation of the assignment problem, enabling gradient-based optimization over soft permutations. We develop a projected exponentiated gradient method with adaptive step size to minimize tour cost while satisfying the relaxed constraints. To recover high-quality discrete tours, we introduce a greedy post-processing procedure that iteratively corrects subtours using cost-aware cycle merging. Our method achieves state-of-the-art performance on standard asymmetric TSP benchmarks and demonstrates competitive scalability and accuracy, particularly on large or asymmetric instances where heuristic solvers such as LKH-3 struggle.

Applications · Robotics

Zewei Zhou, Tianhui Cai, Seth Zhao, Yun Zhang, Zhiyu Huang, Bolei Zhou, Jiaqi Ma

Recent advancements in Vision-Language-Action (VLA) models have shown promise for end-to-end autonomous driving by leveraging world knowledge and reasoning capabilities. However, current VLA models often struggle with physically infeasible action outputs, complex model structures, or unnecessarily long reasoning. In this paper, we propose AutoVLA, a novel VLA model that unifies reasoning and action generation within a single autoregressive generation model for end-to-end autonomous driving. AutoVLA performs semantic reasoning and trajectory planning directly from raw visual inputs and language instructions. We tokenize continuous trajectories into discrete, feasible actions, enabling direct integration into the language model. For training, we employ supervised fine-tuning to equip the model with dual thinking modes: fast thinking (trajectory-only) and slow thinking (enhanced with chain-of-thought reasoning). To further enhance planning performance and efficiency, we introduce a reinforcement fine-tuning method based on Group Relative Policy Optimization (GRPO), reducing unnecessary reasoning in straightforward scenarios. Extensive experiments across real-world and simulated datasets and benchmarks, including nuPlan, nuScenes, Waymo, and CARLA, demonstrate the competitive performance of AutoVLA in both open-loop and closed-loop settings. Qualitative results showcase the adaptive reasoning and accurate planning capabilities of AutoVLA in diverse scenarios.

Applications · Genetics, Cell Biology, etc

Hanqun Cao, Haosen Shi, Chenyu Wang, Sinno Pan, Pheng-Ann Heng

The design of biological sequences is essential for engineering functional biomolecules that contribute to advancements in human health and biotechnology. Recent advances in diffusion models, with their generative power and efficient conditional sampling, have made them a promising approach for sequence generation. To enhance model performance on limited data and enable multi-objective design and optimization, reinforcement learning (RL)-based fine-tuning has shown great potential. However, existing post-sampling and fine-tuning methods either lack stability in discrete optimization when avoiding gradients or incur high computational costs when employing gradient-based approaches, creating significant challenges for achieving both control and stability in the tuning process. To address these limitations, we propose GLID$^2$E, a gradient-free RL-based tuning approach for discrete diffusion models. Our method introduces a clipped likelihood constraint to regulate the exploration space and implements reward shaping to better align the generative process with design objectives, ensuring a more stable and efficient tuning process. By integrating these techniques, GLID$^2$E mitigates training instabilities commonly encountered in RL and diffusion-based frameworks, enabling robust optimization even in challenging biological design tasks. In the DNA sequence and protein sequence design systems, GLID$^2$E achieves competitive performance in function-based design while maintaining computational efficiency and a flexible tuning mechanism.

Optimization · Discrete Optimization

Marie-Charlotte Brandenburg, Katharina Jochemko

We consider binary classification restricted to a class of continuous piecewise linear functions whose decision boundaries are (possibly nonconvex) starshaped polyhedral sets, supported on a fixed polyhedral simplicial fan. We investigate the expressivity of these function classes and describe the combinatorial and geometric structure of the loss landscape, most prominently the sublevel sets, for two loss-functions: the 0/1-loss (discrete loss) and a log-likelihood loss function. In particular, we give explicit bounds on the VC dimension of this model, and concretely describe the sublevel sets of the discrete loss as chambers in a hyperplane arrangement. For the log-likelihood loss, we give sufficient conditions for the optimum to be unique, and describe the geometry of the optimum when varying the rate parameter of the underlying exponential probability distribution.

Reinforcement Learning · Multi-agent

Chao Li, Bingkun BAO, Yang Gao

In this paper, we consider fully decentralized cooperative multi-agent reinforcement learning, where each agent has access only to the states, its local actions, and the shared rewards. The absence of information about other agents' actions typically leads to the non-stationarity problem during per-agent value function updates, and the relative overgeneralization issue during value function estimation. However, existing works fail to address both issues simultaneously, as they lack the capability to model the agents' joint policy in a fully decentralized setting. To overcome this limitation, we propose a simple yet effective method named Return-Aware Context (RAC). RAC formalizes the dynamically changing task, as locally perceived by each agent, as a contextual Markov Decision Process (MDP), and addresses both non-stationarity and relative overgeneralization through return-aware context modeling. Specifically, the contextual MDP attributes the non-stationary local dynamics of each agent to switches between contexts, each corresponding to a distinct joint policy. Then, based on the assumption that the joint policy changes only between episodes, RAC distinguishes different joint policies by the training episodic return and constructs contexts using discretized episodic return values. Accordingly, RAC learns a context-based value function for each agent to address the non-stationarity issue during value function updates. For value function estimation, an individual optimistic marginal value is constructed to encourage the selection of optimal joint actions, thereby mitigating the relative overgeneralization problem. Experimentally, we evaluate RAC on various cooperative tasks (including matrix game, predator and prey, and SMAC), and its significant performance validates its effectiveness.

Computer Vision · Everything Else

Daniele Baieri, Filippo Maggioli, Emanuele Rodolà, Simone Melzi, Zorah Laehner

Neural fields have emerged as a powerful representation for 3D geometry, enabling compact and continuous modeling of complex shapes. Despite their expressive power, manipulating neural fields in a controlled and accurate manner -- particularly under spatial constraints -- remains an open challenge, as existing approaches struggle to balance surface quality, robustness, and efficiency. We address this by introducing a novel method for handle-guided neural field deformation, which leverages discrete local surface representations to optimize the As-Rigid-As-Possible deformation energy. To this end, we propose the local patch mesh representation, which discretizes level sets of a neural signed distance field by projecting and deforming flat mesh patches guided solely by the SDF and its gradient. We conduct a comprehensive evaluation showing that our method consistently outperforms baselines in deformation quality, robustness, and computational efficiency. We also present experiments that motivate our choice of discretization over marching cubes. By bridging classical geometry processing and neural representations through local patch meshing, our work enables scalable, high-quality deformation of neural fields and paves the way for extending other geometric tasks to neural domains.

Optimization · Discrete Optimization

Peng Chen, Hailiang Zhao, Jiaji Zhang, Xueyan Tang, Yixuan Wang, Shuiguang Deng

The online caching problem aims to minimize cache misses when serving a sequence of requests under a limited cache size. While naive learning-augmented caching algorithms achieve ideal $1$-consistency, they lack robustness guarantees. Existing robustification methods either sacrifice $1$-consistency or introduce excessive computational overhead. In this paper, we introduce Guard, a lightweight robustification framework that enhances the robustness of a broad class of learning-augmented caching algorithms to $2H_{k-1} + 2$, while preserving their $1$-consistency. Guard achieves the current best-known trade-off between consistency and robustness, with only $\mathcal{O}(1)$ additional per-request overhead, thereby maintaining the original time complexity of the base algorithm. Extensive experiments across multiple real-world datasets and prediction models validate the effectiveness of Guard in practice.