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1,217篇论文匹配“Discrete Optimization”
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Te Song, Lianyong Qi, Weiming Liu 0005, Fan Wang 0020, Xiaolong Xu 0001, Hongsheng Hu, Yang Cao 0019, Xuyun Zhang, Amin Beheshti

Recent advancements in generative models have positioned them as one of the principal tools for sequential recommendation due to their exceptional sample diversity and generalization capabilities. Among these, diffusion model-based sequential recommenders have achieved remarkable success. However, most existing approaches still face critical challenges, resulting in suboptimal generation quality: (1) They fail to leverage multimodal knowledge for constructing item representations with well-structured distributional characteristics and semantically enriched information; (2) They predominantly rely on discrete diffusion processes, leading to high error accumulation, reduced time efficiency, and constrained controllability in generative sampling. To mitigate these challenges, we propose LSGM4Rec, a novel framework that integrates Large Language Models (LLMs) with advanced multimodal encoding models to establish multimodal fusion embeddings for items. This design ensures distinct distributional characteristics while enabling the incorporation of semantically rich modal features into guidance condition. Furthermore, we pioneer the stochastic differential equations (SDEs) for recommendation, facilitating smooth transitions between data distributions and enabling optimal trade-off between sampling efficiency and generation quality. Extensive experiments on three datasets demonstrate that LSGM4Rec outperforms existing state-of-the-art sequential recommendation methods.

Chuhang Zheng, Chunwei Tian, Jie Wen 0001, Daoqiang Zhang, Qi Zhu 0001

Multi-modal emotion recognition has garnered increasing attention as it plays a significant role in human-computer interaction (HCI) in recent years. Since different discrete emotions may exist at the same time, compared with single-class emotion recognition, emotion distribution learning (EDL) that identifies a mixture of basic emotions has gradually emerged as a trend. However, existing EDL methods face challenges in mining the heterogeneity among multiple modalities. Besides, rich semantic correlations across arbitrary basic emotions are not fully exploited. In this paper, we propose a multi-modal emotion distribution learning framework, named HeLo, aimed at fully exploring the heterogeneity and complementary information in multi-modal emotional data and label correlation within mixed basic emotions. Specifically, we first adopt cross-attention to effectively fuse the physiological data. Then, an optimal transport (OT)-based heterogeneity mining module is devised to mine the interaction and heterogeneity between the physiological and behavioral representations. To facilitate label correlation learning, we introduce a learnable label embedding optimized by correlation matrix alignment. Finally, the learnable label embeddings and label correlation matrices are integrated with the multi-modal representations through a novel label correlation-driven cross-attention mechanism for accurate emotion distribution learning. Experimental results on two publicly available datasets demonstrate the superiority of our proposed method in emotion distribution learning.

Yan Chen 0036, Bingbing Jiang 0001, Peng Zhou 0006, Lei Duan, Yuhua Qian, Liang Du 0003

Clustering, a fundamental task in machine learning and data mining, is essential for uncovering patterns by grouping data points with similar characteristics. Traditional methods struggle with nonlinear data structures, but kernel-based approaches alleviate this issue by mapping data to high dimensional spaces. Multiple Kernel Clustering (MKC) further improves clustering by automating kernel selection and integration. However, MKC faces challenges related to kernel graph quality, information loss during relax-and-discretization, neglect of balanced clustering constraints, and the trade-off between high clustering quality and balance. To address these challenges, we introduce Balanced Multiple Kernel Clustering (BMKC). BMKC utilizes local kernel reconstruction and advanced high-order diffusion techniques for comprehensive kernel graph learning. It directly learns a discrete partition matrix using a robust L1-induced local reconstruction criterion, eliminating the two step process. BMKC incorporates an automatic mechanism for trade-off control between clustering and balance, supported by a versatile optimization algorithm accommodating various balance regularization choices. Experimental validation demonstrates the superior performance of MKC on benchmarks data sets, showcasing its effectiveness. The code for our method is publicly available at https://github.com/ChenYan01TYUT/BMKC-ACM-MM-2025.

Lingren Wang, Wenxuan Tu, Jieren Cheng, Jianan Wang, Xiangyan Tang, Chenchen Wang

Multimodal federated learning (MFL) focuses on integrating distributed multimodal data from different clients to improve feature representation while preserving user privacy and has gained popularity in medical image analysis. Existing research idealizes communication efficiency and generalization ability as independent optimization objectives, leading to the failure in the trade-off between model generalization and client resource constraints. To address this challenge, we propose a lightweight Federated Learning with Mid-Frequency consensus-Driven (FedMFD) method, aiming to efficiently generalize multimodal medical image segmentation tasks while reducing communication costs. In the aspect of communication efficiency, client-side images are converted via Discrete Cosine Transform (DCT) from spatial domain into frequency domain coefficients. With only the mid-frequency components selected for transmission. Regarding generalization capability, we adopt the Earth Mover's Distance (EMD) to quantify the maximum similarity of mid-frequency features between clients, generating a global frequency consensus with the optimal transport plan. Guided by global frequency consensus, client-side structural and detailed representations are reconstructed to improve segmentation generalization in the presence of modality shifts and background noise. Extensive experiments across Computed Tomography (CT) and Magnetic Resonance Imaging (MRI) modality datasets have verified the superiority of FedMFD against its competitors.

Junpu Zhang, Shengju Yu, Suyuan Liu, Siwei Wang 0001, Miaomiao Li 0001, Xinwang Liu 0002, En Zhu, Kunlun He

In multi-view clustering (MVC), anchor technique is generally hailed as an effective means for filtering noise and improving computation efficiency. However, existing methods usually construct anchors via heuristic strategy, random sampling, or orthogonal learning, which overlook the distribution differences between anchors and original data, leading to anchors lacking structural characteristics. To generate the anchors that are with similar distributions to original data, in the paper we carefully devise a LASD algorithm from the perspective of optimal transport (OT). Concretely, we firstly design a Multi-View OT (MVOT) framework through complementary and consensus representation learning. Then, we theoretically demonstrate the convexity of MVOT using the positive semidefiniteness of its Hessian matrix, and accordingly the global optimal solution of each transport plan can be reached. Further, we establish the strong dual condition for MVOT by the relative interior. Based on dual programming, consequently, we successfully obtain the transport plan between anchors and original data for each view within linear computational complexity. Afterwards, the spectral clustering operation is employed on the consensus plan to produce the discrete cluster labels. Abundant experiments underscore that our learned anchors do well reflect the distributions of original data, and the generated clustering results outperform multiple strong MVC competitors, even under large-scale scenarios. The source code is available at https://github.com/junpuzhang/LASD.

Zhaoxi Mu, Rilin Chen, Andong Li, Meng Yu 0003, Xinyu Yang 0001, Dong Yu 0001

This paper introduces OmniGSE, a novel general speech enhancement (GSE) framework designed to mitigate the diverse distortions that speech signals encounter in real-world scenarios. These distortions include background noise, reverberation, bandwidth limitations, signal clipping, and network packet loss. Existing methods typically focus on optimizing for a single type of distortion, often struggling to effectively handle the simultaneous presence of multiple distortions in complex scenarios. OmniGSE bridges this gap by integrating the strengths of discriminative and generative approaches through a two-stage architecture that enables cross-domain collaborative optimization. In the first stage, continuous features are enhanced using a lightweight channel-split NAC-RoFormer. In the second stage, discrete tokens are generated to reconstruct high-quality speech through language models. Specifically, we designed a hierarchical language model structure consisting of a RootLM and multiple BranchLMs. The RootLM models general acoustic features across codebook layers, while the BranchLMs explicitly capture the progressive relationships between different codebook levels. Experimental results demonstrate that OmniGSE surpasses existing models across multiple benchmarks, particularly excelling in scenarios involving compound distortions. These findings underscore the framework's potential for robust and versatile speech enhancement in real-world applications.

Jiaqing Zhang, Mingjia Yin, Hao Wang 0076, Yawen Li 0001, Yuyang Ye 0002, Xingyu Lou, Junping Du 0001, Enhong Chen

In the era of data-centric AI, the focus of recommender systems has shifted from model-centric innovations to data-centric approaches. The success of modern AI models is built on large-scale datasets, but this also results in significant training costs. Dataset distillation has emerged as a key solution, condensing large datasets to accelerate model training while preserving model performance. However, condensing discrete and sequentially correlated user-item interactions, particularly with extensive item sets, presents considerable challenges. This paper introduces TD3, a novel Tucker Decomposition based Dataset Distillation method within a meta-learning framework, designed for sequential recommendation. TD3 distills a fully expressive synthetic sequence summary from original data. To efficiently reduce computational complexity and extract refined latent patterns, Tucker decomposition decouples the summary into four factors: synthetic user latent factor, temporal dynamics latent factor, shared item latent factor, and a relation core that models their interconnections. Additionally, a surrogate objective in bi-level optimization is proposed to align feature spaces extracted from models trained on both original data and synthetic sequence summary beyond the naive performance matching approach. In the inner-loop, an augmentation technique allows the learner to closely fit the synthetic summary, ensuring an accurate update of it in the outer-loop. To accelerate the optimization process and address long dependencies, RaT-BPTT is employed for bi-level optimization. Experiments and analyses on multiple public datasets have confirmed the superiority and cross-architecture generalizability of the proposed designs. Codes are released at https://github.com/USTC-StarTeam/TD3.

Saurabh Sharma, Ambuj K. Singh

The problem of maximizing the adoption of a product through viral marketing in social networks has been studied heavily through postulated network models. We present a novel data-driven formulation of the problem. We use Graph Neural Networks (GNNs) to model the adoption of products by utilizing both topological and attribute information. The resulting Dynamic Viral Marketing (DVM) problem seeks to find the minimum budget and minimal set of dynamic topological and attribute changes in order to attain a specified adoption goal. We show that DVM is NP-Hard and is related to the existing influence maximization problem. Motivated by this connection, we develop the idea of Dynamic Gradient Influencing (DGI) that uses gradient ranking to find optimal perturbations and targets low-budget and high influence non-adopters in discrete steps. We use an efficient strategy for computing node budgets and develop the ''Meta-Influence'' heuristic for assessing a node's downstream influence. We evaluate DGI against multiple baselines and demonstrate gains on average of 24% on budget and 37% on AUC on real-world attributed networks. Our code is publicly available at https://github.com/saurabhsharma1993/dynamic_viral_marketing.

Niloy Talukder, Croix Gyurek, Mohammad Al Hasan

With the adoption of deep learning models to low-power, small-memory edge devices, energy consumption and storage usage of such models have become a key concern. The problem exacerbates even further with ever-growing data and equally-matched bulkier models. This concern is particularly pronounced for graph data due to its quadratic storage, irregular (non-grid) geometry, and very large size. Typical graph data, such as road networks, infrastructure networks, and social networks, easily exceeds millions of nodes, and several gigabytes of storage is needed just to store the node embedding vectors, let alone the model parameters. In recent years, the memory issue has been addressed by moving away from memory-intensive double precision floating-point arithmetic towards single-precision or even half-precision, often by trading-off marginally small performance. Along this effort, we propose Node2Binary, which embeds graph nodes in as few as 128 binary bits, thereby reducing the memory footprint of vertex embedding vectors by several orders of magnitude. Node2Binary. leverages a fast community detection algorithm to convert the given graph into a hierarchical partition tree and then find embeddings of graph vertices in binary space by solving a combinatorial optimization (CO) task over the tree edges. CO is NP-hard, but Node2Binary uses an innovative combination of discrete gradient descent and randomization to solve this task effectively and efficiently. Extensive experiments over four real-world graphs show that Node2Binary achieves competitive performance compared to the state-of-the art graph embedding methods in both node classification and link prediction tasks.

Haibo Ding, Shuai Wang, Kiran Ramnath, Yi Zhang, Lin Lee Cheong

Prompt engineering plays a critical role in enabling the effective use of large language models (LLMs). LLMs exhibit unpredictable sensitivity to various input factors that may result in a performance gap between prompts that are semantically indistinguishable. Therefore, LLM researchers and practitioners often optimize their prompts in an ad hoc manner due to the lack of systematic methods. Prompt optimization remains an open problem due to the rapidly evolving landscape of NLP tasks, target LLMs, and associated best practices. To address this gap, we propose the first KDD workshop on Prompt Optimization. This workshop aims to bring together researchers and practitioners working on prompt design, automatic optimization, and evaluation, fostering the exchange of ideas and methodologies. By exploring topics such as discrete and soft prompt tuning, low-resource applications, we aim to establish best practices, identify challenges, and drive future research in this critical area.

Zhongjin Zhang, Yu Liang, Cong Fu 0001, Yuxuan Zhu 0001, Kun Wang 0024, Yabo Ni, Anxiang Zeng, Jiazhi Xia

Embedding-based collaborative filtering, often coupled with nearest neighbor search, is widely deployed in large-scale recommender systems for personalized content selection. Modern systems leverage multiple implicit feedback signals (e.g., clicks, add to cart, purchases) to model user preferences comprehensively. However, prevailing approaches adopt a feedback-wise modeling paradigm, which (1) fails to capture the structured progression of user engagement entailed among different feedback and (2) embeds feedback-specific information into disjoint spaces, making representations incommensurable, increasing system complexity, and leading to suboptimal retrieval performance. A promising alternative is Ordinal Logistic Regression (OLR), which explicitly models discrete ordered relations. However, existing OLR-based recommendation models mainly focus on explicit feedback (e.g., movie ratings) and struggle with implicit, correlated feedback, where ordering is vague and non-linear. Moreover, standard OLR lacks flexibility in handling feedback-dependent covariates, resulting in suboptimal performance in real-world systems. To address these limitations, we propose Generalized Neural Ordinal Logistic Regression (GNOLR), which encodes multiple feature-feedback dependencies into a unified, structured embedding space and enforces feedback-specific dependency learning through a nested optimization framework. Thus, GNOLR enhances predictive accuracy, captures the progression of user engagement, and simplifies the retrieval process. We establish a theoretical comparison with existing paradigms, demonstrating how GNOLR avoids disjoint spaces while maintaining effectiveness. Extensive experiments on ten real-world datasets show that GNOLR significantly outperforms state-of-the-art methods in efficiency and adaptability.

Yang Wang 0102, Jiaqi Zhu 0001, Miaomiao Li 0007, Jiang Liu, Yilin Li 0003, Yi Yang 0060, Jiafan Li, Hongan Wang

Recently, rule-based time series classification models are widely used in safety-critical scenarios demanding strong interpretability, through providing explicit and rigorous rationales. However, due to the discrepancy between discrete rules and continuous neural networks, the generated rules are not completely consistent with the actual decision-making process, rendering users hesitant to trust the model. Additionally, existing methods learn the role (weight) of each time point independently, which is not in line with human understanding and the consecutive nature of temporal properties. In this paper, we propose a novel neuro-symbolic model named TemporalRule, aiming to automatically learn Signal Temporal Logic (STL) rules for interpretable time series classification. Our model directly optimizes the neural networks representing discrete rules via gradient grafting, producing reliable rules that can exactly determine the classification results. Notably, a temporal logical layer is designed to simulate expressive temporal operators, including one 2-predicate operator (Until) and two 2-level composite operators (EA and AE), through adaptively learning the time bounds of involved intervals. That creates consistent weights for consecutive time points, enhancing the intuitiveness of derived rules. Extensive experiments on diverse real-world datasets in safety-critical domains show that TemporalRule achieves superior and stable classification accuracy compared to state-of-the-art rule-based approaches, and the learned rules can precisely and concisely explicate the classification results, leading to a trustable model.

Pavithra Harsha, Chitra Subramanian, Naoki Abe, Shivaram Subramanian, Amadou Ba, Kevin Arturo Fernández Román, Mauricio Longinos Garrido, Chandrasekhar Narayanaswami 0001

We address the contextual bandit problem for high-dimensional combinatorial action spaces involving a class of structured discrete constrained optimization problems. In this setting, key quantities within the optimization formulation, such as performance indicators contributing to the objective or constraints, must be estimated from data during the trial sequence of optimized actions. These problems frequently arise in the many operations management domains including IT resource allocation and retail assortment price optimization. We propose a novel, practical, and transparent approach based on general-purpose regression oracles, leveraging Inverse Gap Weighting (IGW) for seamless integration within an optimization framework. IGW sampling is efficiently managed by: (a) a column generation reformulation of the underlying Mixed Integer Programming (MIP) model which allows for flexible lower-level predictors, causal coherence, and efficient representation of large action spaces;(b) a diverse solution pool generation to balance the exploration-exploitation trade-off in large action spaces. To address non-smoothness in the reward function due to optimization constraints, we incorporate a risk-averse phased learning strategy. We validate our approach on a real-world auto-scaling problem in IT automation, achieving a significant reduction in cumulative regret through skillful exploration, with additional gains from risk-averse methods that effectively manage constraint violations.

Bin Liu 0022, Yu Liu 0129, Zhiqian Li, Jianghong Xiao, Guosheng Yin, Huazhen Lin

Intensity-modulated radiation therapy (IMRT) is a crucial radiotherapy technique, which is often formulated as an optimization problem. However, when the constraints are too restrictive to provide a feasible solution, human planners resort to relaxing the optimization parameters and re-evaluating the problem until an acceptable solution is obtained. However, this process is laborious and time-consuming, which has prompted attempts to automate radiotherapy through inverse planning studies using reinforcement learning. Unfortunately, these studies face two major limitations. First, a separate sub-network must be designed for each organ, rendering it difficult to apply to patients with an inconsistent number of structures. Second, the low signal-to-noise input and discrete action space result in low training efficiency. To address these issues, we propose an organ-sharing network that contains a functional embedding layer to extract curve features of the dose-volume histogram. It outputs continuous actions that can adjust the optimization parameters, thereby automating the radiotherapy planning process. The results from a cervical cancer dataset demonstrate the feasibility and efficiency of the proposed model in real-world radiotherapy. The code is available on https://github.com/Cissise/FatPIN.

Jiapeng Zhu 0002, Zichen Ding 0002, Jianxiang Yu 0001, Jiaqi Tan 0006, Xiang Li 0067, Weining Qian

The advent of the "pre-train, prompt'' paradigm has recently extended its generalization ability and data efficiency to graph representation learning, following its achievements in Natural Language Processing (NLP). Initial graph prompt tuning approaches tailored specialized prompting functions for Graph Neural Network (GNN) models pre-trained with specific strategies, such as edge prediction, thus limiting their applicability. In contrast, another pioneering line of research has explored universal prompting via adding prompts to the input graph's feature space, thereby removing the reliance on specific pre-training strategies. However, the necessity to add feature prompts to all nodes remains an open question. Motivated by findings from prompt tuning research in the NLP domain, which suggest that highly capable pre-trained models need less conditioning signal to achieve desired behaviors, we advocate for strategically incorporating necessary and lightweight feature prompts to certain graph nodes to enhance downstream task performance. This introduces a combinatorial optimization problem, requiring a policy to decide 1) which nodes to prompt and 2) what specific feature prompts to attach. We then address the problem by framing the prompt incorporation process as a sequential decision-making problem and propose our method, RELIEF, which employs Reinforcement Learning (RL) to optimize it. At each step, the RL agent selects a node (discrete action) and determines the prompt content (continuous action), aiming to maximize cumulative performance gain. Extensive experiments on graph and node-level tasks with various pre-training strategies in few-shot scenarios demonstrate that our RELIEF outperforms fine-tuning and other prompt-based approaches in classification performance and data efficiency. The code is available at https://github.com/JasonZhujp/RELIEF.

Mingzhao Wang, You Zhou 0008, Zhiguang Cao, Yubin Xiao, Xuan Wu 0004, Wei Pang 0001, Yuan Jiang 0007, Hui Yang 0015, Peng Zhao 0018, Yuanshu Li

Recent advances in neural models have shown considerable promise in solving Traveling Salesman Problems (TSPs) without relying on much hand-crafted engineering. However, while non-autoregressive (NAR) approaches benefit from faster inference through parallelism, they typically deliver solutions of inferior quality compared to autoregressive ones. To enhance the solution quality while maintaining fast inference, we propose DEITSP, a diffusion model with efficient iterations tailored for TSP that operates in a NAR manner. Firstly, we introduce a one-step diffusion model that integrates the controlled discrete noise addition process with self-consistency enhancement, enabling optimal solution prediction through simultaneous denoising of multiple solutions. Secondly, we design a dual-modality graph transformer to bolster the extraction and fusion of features from node and edge modalities, while further accelerating the inference with fewer layers. Thirdly, we develop an efficient iterative strategy that alternates between adding and removing noise to improve exploration compared to previous diffusion methods. Additionally, we devise a scheduling framework to progressively refine the solution space by adjusting noise levels, facilitating a smooth search for optimal solutions. Extensive experiments on real-world and large-scale TSP instances demonstrate that DEITSP performs favorably against existing neural approaches in terms of solution quality, inference latency, and generalization ability.

Thanh V. T. Tran, Nhat Khang Ngo, Viet Anh Nguyen, Truong Son Hy

Latent space optimization (LSO) is a powerful method for designing discrete, high-dimensional biological sequences that maximize expensive black-box functions, such as wet lab experiments. This is accomplished by learning a latent space from available data and using a surrogate model fΦ to guide optimization algorithms toward optimal outputs. However, existing methods struggle when labeled data is limited, as training fΦ with few labeled data points can lead to subpar outputs, offering no advantage over the training data itself. We address this challenge by introducing GROOT, a GRaph-based Latent SmOOThing for Biological Sequence Optimization. In particular, GROOT generates pseudo-labels for neighbors sampled around the training latent embeddings. These pseudo-labels are then refined and smoothed by Label Propagation. Additionally, we theoretically and empirically justify our approach, demonstrate GROOT's ability to extrapolate to regions beyond the training set while maintaining reliability within an upper bound of their expected distances from the training regions. We evaluate GROOT on various biological sequence design tasks, including protein optimization (GFP and AAV) and three tasks with exact oracles from Design-Bench. The results demonstrate that GROOT equalizes and surpasses existing methods without requiring access to black-box oracles or vast amounts of labeled data, highlighting its practicality and effectiveness. We release our code at https://github.com/Fsoft-AIC/GROOT.

Tianxing Man, Xingchen Li, Zhaogeng Liu, Haozhen Zhang, Bin Gu 0001, Yi Chang 0001

Black-box attacks have emerged as a significant threat to deep neural networks. This challenge is particularly difficult in discrete sequential data compared to continuous data. Recently, the Blockwise Bayesian Attack (BBA) leveraging discrete Bayesian optimization with an adapted RBF kernel has gained prominence as a cutting-edge solution. However, it relies solely on alignment information (i.e., positional differences) within the RBF kernel, which may not fully capture the information (such as statistical, structural, and semantic information) inherent in discrete sequential data and potentially lacks the desired inductive bias necessary to approximate the target function accurately. To overcome this limitation, this paper proposes a novel bilevel Bayesian optimization approach to adaptively learn a hybrid space that better captures the similarity between discrete sequences. Specifically, we introduce a multi-kernel mechanism that incorporates multiple types of information, creating a more comprehensive similarity measure. Moreover, we develop a bilevel Bayesian optimization algorithm, where the outer-level objective determines the optimal weights of the multiple kernels, while the inner-level objective identifies the optimal adversarial sequence. Extensive experiments conducted on discrete sequential data demonstrate that our approach ensures secure multi-kernel selection and achieves a higher attack success rate with only a few additional queries, compared to BBA and other traditional optimization strategies.

Matteo Castiglioni, Alessandro Nuara, Giulia Romano, Giorgio Spadaro, Francesco Trovò, Nicola Gatti 0001

In online marketing, the advertisers aim to balance achieving high volumes and high profitability. The companies' business units address this tradeoff by maximizing the volumes while guaranteeing a minimum Return On Investment (ROI) level. Such a task can be naturally modeled as a combinatorial optimization problem subject to ROI and budget constraints that can be solved online. In this picture, the learner's uncertainty over the constraints' parameters plays a crucial role since the algorithms' exploration choices might lead to their violation during the entire learning process. Such violations represent a major obstacle to adopting online techniques in real-world applications. Thus, controlling the algorithms' exploration during learning is paramount to making humans trust online learning tools. This paper studies the nature of both optimization and learning problems. In particular, we show that the learning problem is inapproximable within any factor (unless P = NP) and provide a pseudo-polynomial-time algorithm to solve its discretized version. Subsequently, we prove that no online learning algorithm can violate the (ROI or budget) constraints a sublinear number of times during the learning process while guaranteeing a sublinear regret. We provide the GCB algorithm that guarantees sublinear regret at the cost of a linear number of constraint violations and GCBsafe that guarantees w.h.p.a constant upper bound on the number of constraint violations at the cost of a linear regret. Moreover, we designed GCBsafe(ψ, φ), which guarantees both sublinear regret and safety w.h.p. at the cost of accepting tolerances ψ and φ in the satisfaction of the ROI and budget constraints, respectively. Finally, we provide experimental results to compare the regret and constraint violations of GCB, GCBsafe, and GCBsafe(ψ, φ).

Wenjing Li, Zhao Li, Xuanwu Liu, Ruihao Zhu, Zhenzhe Zheng, Fan Wu

E-bikes (EBs) are a key transportation mode in urban area, especially for couriers of delivery platforms, but underdeveloped EB systems can hinder courier's productivity due to limited battery capacity. Battery-swapping stations address this issue by enabling riders to exchange depleted batteries for fully charged ones. However, managing supply and demand (SnD) imbalances at these stations has become increasingly complex. To address this, we introduce a new approach that formulates the Battery-Swapping Problem (BSP) as a discrete-time Markov Decision Process (MDP) to capture the dynamics of SnD imbalances. Building on it, we propose a Wasserstein-enhanced Proximal Policy Optimization (W-PPO) algorithm, which integrates Wasserstein distance with reinforcement learning to improve the robustness against uncertainty in forecasting SnD. W-PPO provides a BSP-specific, accurate loss function that reflects reward variations between two policies under real-world simulation. The algorithm’s effectiveness is assessed using key metrics: Shared Battery Utilization Ratio (SBUR) and Battery Supply Ratio (BSR). Simulations on real-world datasets show that W-PPO achieves a 30.59% improvement in SBUR and a 16.09% increase in BSR ensures practical applicability. By optimizing battery utilization and improving EB delivery systems, this work highlights the potential of AI for creating efficient and sustainable urban transportation solutions.