ICLR 2025 论文列表

International Conference on Learning Representations

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3,703篇论文

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  • Oral
    2135.8%
  • Spotlight
    38010.3%
  • Poster
    3,11084.0%

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Cyclic Contrastive Knowledge Transfer for Open-Vocabulary Object Detection

Chuhan Zhang, Chaoyang Zhu, Pingcheng Dong, Long Chen, Dong Zhang

展开摘要

In pursuit of detecting unstinted objects that extend beyond predefined categories, prior arts of open-vocabulary object detection (OVD) typically resort to pretrained vision-language models (VLMs) for base-to-novel category generalization. However, to mitigate the misalignment between upstream image-text pretraining and downstream region-level perception, additional supervisions are indispensable, e.g., image-text pairs or pseudo annotations generated via self-training strategies. In this work, we propose CCKT-Det trained without any extra supervision. The proposed framework constructs a cyclic and dynamic knowledge transfer from language queries and visual region features extracted from VLMs, which forces the detector to closely align with the visual-semantic space of VLMs. Specifically, 1) we prefilter and inject semantic priors to guide the learning of queries, and 2) introduce a regional contrastive loss to improve the awareness of queries on novel objects. CCKT-Det can consistently improve performance as the scale of VLMs increases, all while requiring the detector at a moderate level of computation overhead. Comprehensive experimental results demonstrate that our method achieves performance gain of +2.9% and +10.2% AP_{50} over previous state-of-the-arts on the challenging COCO benchmark, both without and with a stronger teacher model.

Poster
Reinforcement Learning from Imperfect Corrective Actions and Proxy Rewards

Zhaohui JIANG, Xuening Feng, Paul Weng, Yifei Zhu, Yan Song, Tianze Zhou, Yujing Hu, Tangjie Lv, Changjie Fan

展开摘要

In practice, reinforcement learning (RL) agents are often trained with a possibly imperfect proxy reward function, which may lead to a human-agent alignment issue (i.e., the learned policy either converges to non-optimal performance with low cumulative rewards, or achieves high cumulative rewards but in an undesired manner). To tackle this issue, we consider a framework where a human labeler can provide additional feedback in the form of corrective actions, which expresses the labeler's action preferences although this feedback may possibly be imperfect as well. In this setting, to obtain a better-aligned policy guided by both learning signals, we propose a novel value-based deep RL algorithm called **I**terative learning from **Co**rrective actions and **Pro**xy rewards (ICoPro), which cycles through three phases: (1) Solicit sparse corrective actions from a human labeler on the agent's demonstrated trajectories; (2) Incorporate these corrective actions into the Q-function using a margin loss to enforce adherence to labeler's preferences; (3) Train the agent with standard RL losses regularized with a margin loss to learn from proxy rewards and propagate the Q-values learned from human feedback. Moreover, another novel design in our approach is to integrate pseudo-labels from the target Q-network to reduce human labor and further stabilize training. We experimentally validate our proposition on a variety of tasks (Atari games and autonomous driving on highway). On the one hand, using proxy rewards with different levels of imperfection, our method can better align with human and is more sample-efficient than baseline methods. On the other hand, facing corrective actions with different types of imperfection, our method can overcome the non-optimality of this feedback thanks to the guidance from proxy rewards.

Poster
Efficiently Democratizing Medical LLMs for 50 Languages via a Mixture of Language Family Experts

Guorui Zheng, Xidong Wang, Juhao Liang, Nuo Chen, Yuping Zheng, Benyou Wang

展开摘要

Adapting medical Large Language Models to local languages can reduce barriers to accessing healthcare services, but data scarcity remains a significant challenge, particularly for low-resource languages. To address this, we first construct a high-quality medical dataset and conduct analysis to ensure its quality. In order to leverage the generalization capability of multilingual LLMs to efficiently scale to more resource-constrained languages, we explore the internal information flow of LLMs from a multilingual perspective using Mixture of Experts (MoE) modularity. Technically, we propose a novel MoE routing method that employs language-specific experts and cross-lingual routing. Inspired by circuit theory, our routing analysis revealed a \textit{``Spread Out in the End``} information flow mechanism: while earlier layers concentrate cross-lingual information flow, the later layers exhibit language-specific divergence. This insight directly led to the development of the Post-MoE architecture, which applies sparse routing only in the later layers while maintaining dense others. Experimental results demonstrate that this approach enhances the generalization of multilingual models to other languages while preserving interpretability. Finally, to efficiently scale the model to 50 languages, we introduce the concept of \textit{language family} experts, drawing on linguistic priors, which enables scaling the number of languages without adding additional parameters.

Poster
Conformalized Survival Analysis for General Right-Censored Data

Hen Davidov, Shai Feldman, Gil Shamai, Ron Kimmel, Yaniv Romano

展开摘要

We develop a framework to quantify predictive uncertainty in survival analysis, providing a reliable lower predictive bound (LPB) for the true, unknown patient survival time. Recently, conformal prediction has been used to construct such valid LPBs for *type-I right-censored data*, with the guarantee that the bound holds with high probability. Crucially, under the type-I setting, the censoring time is observed for all data points. As such, informative LPBs can be constructed by framing the calibration as an estimation task with covariate shift, relying on the conditionally independent censoring assumption. This paper expands the conformal toolbox for survival analysis, with the goal of handling the ubiquitous *general right-censored setting*, in which either the censoring or survival time is observed, but not both. The key challenge here is that the calibration cannot be directly formulated as a covariate shift problem anymore. Yet, we show how to construct LPBs with distribution-free finite-sample guarantees, under the same assumptions as conformal approaches for type-I censored data. Experiments demonstrate the informativeness and validity of our methods in simulated settings and showcase their practical utility using several real-world datasets.

Poster
Private Mechanism Design via Quantile Estimation

Yuanyuan Yang, Tao Xiao, Bhuvesh Kumar, Jamie Heather Morgenstern

展开摘要

We investigate the problem of designing differentially private (DP), revenue-maximizing single item auction. Specifically, we consider broadly applicable settings in mechanism design where agents' valuation distributions are **independent**, **non-identical**, and can be either **bounded** or **unbounded**. Our goal is to design such auctions with **pure**, i.e., $(\epsilon,0)$ privacy in polynomial time. In this paper, we propose two computationally efficient auction learning framework that achieves **pure** privacy under bounded and unbounded distribution settings. These frameworks reduces the problem of privately releasing a revenue-maximizing auction to the private estimation of pre-specified quantiles. Our solutions increase the running time by polylog factors compared to the non-private version. As an application, we show how to extend our results to the multi-round online auction setting with non-myopic bidders. To our best knowledge, this paper is the first to efficiently deliver a Myerson auction with **pure** privacy and near-optimal revenue, and the first to provide such auctions for **unbounded** distributions.

Poster
$\sigma$-zero: Gradient-based Optimization of $\ell_0$-norm Adversarial Examples

Antonio Emanuele Cinà, Francesco Villani, Maura Pintor, Lea Schönherr, Battista Biggio, Marcello Pelillo

展开摘要

Evaluating the adversarial robustness of deep networks to gradient-based attacks is challenging. While most attacks consider $\ell_2$- and $\ell_\infty$-norm constraints to craft input perturbations, only a few investigate sparse $\ell_1$- and $\ell_0$-norm attacks. In particular, $\ell_0$-norm attacks remain the least studied due to the inherent complexity of optimizing over a non-convex and non-differentiable constraint. However, evaluating adversarial robustness under these attacks could reveal weaknesses otherwise left untested with more conventional $\ell_2$- and $\ell_\infty$-norm attacks. In this work, we propose a novel $\ell_0$-norm attack, called $\sigma$-zero, which leverages a differentiable approximation of the $\ell_0$ norm to facilitate gradient-based optimization, and an adaptive projection operator to dynamically adjust the trade-off between loss minimization and perturbation sparsity. Extensive evaluations using MNIST, CIFAR10, and ImageNet datasets, involving robust and non-robust models, show that $\sigma$-zero finds minimum $\ell_0$-norm adversarial examples without requiring any time-consuming hyperparameter tuning, and that it outperforms all competing sparse attacks in terms of success rate, perturbation size, and efficiency.

Poster
Jamba: Hybrid Transformer-Mamba Language Models

Barak Lenz, Opher Lieber, Alan Arazi, Amir Bergman, Avshalom Manevich, Barak Peleg, Ben Aviram, Chen Almagor, Clara Fridman, Dan Padnos, Daniel Gissin, Daniel Jannai, Dor Muhlgay, Dor Zimberg, Edden M. Gerber, Elad Dolev, Eran Krakovsky, Erez Safahi, Erez Schwartz, Gal Cohen, Gal Shachaf, Haim Rozenblum, Hofit Bata, Ido Blass, Inbal Magar, Itay Dalmedigos, Jhonathan Osin, Julie Fadlon, Maria Rozman, Matan Danos, Michael Gokhman, Mor Zusman, Naama Gidron, Nir Ratner, Noam Gat, Noam Rozen, Oded Fried, Ohad Leshno, Omer Antverg, Omri Abend, Or Dagan, Orit Cohavi, Raz Alon, Ro'i Belson, Roi Cohen, Rom Gilad, Roman Glozman, Shahar Lev, Shai Shalev-Shwartz, Shaked Haim Meirom, Tal Delbari, Tal Ness, Tomer Asida, Tom Ben Gal, Tom Braude, Uriya Pumerantz, Josh Cohen, Yonatan Belinkov, Yuval Globerson, Yuval Peleg Levy, Yoav Shoham

展开摘要

We present Jamba, a novel hybrid Transformer-Mamba mixture-of-experts (MoE) architecture. Jamba interleaves blocks of Transformer and Mamba layers, enjoying the benefits of both model families. MoE is added in some of these layers to increase model capacity while keeping active parameter usage manageable. This flexible architecture allows resource- and objective-specific configurations. We implement two configurations: Jamba-1.5-Large, with 94B active parameters, and Jamba-1.5-mini, with 12B active parameters. Built at large scale, Jamba models provide high throughput and small memory footprint compared to vanilla Transformers, especially at long-context tasks, with an effective context length of 256K tokens, the largest amongst open-weight models. At the same time, they are also competitive on standard language modeling and chatbot benchmarks. We study various architectural decisions, such as how to combine Transformer and Mamba layers, and how to mix experts, and show that some of them are crucial in large scale modeling. To support cost-effective inference, we introduce ExpertsInt8, a novel quantization technique that allows fitting Jamba-1.5-Large on a machine with 8 80GB GPUs when processing 256K-token contexts without loss of quality. We also describe several interesting properties of this architecture that the training and evaluation of Jamba have revealed. The model weights are publicly available.

Poster
From Decoupling to Adaptive Transformation: a Wider Optimization Space for PTQ

Zhaojing Wen, Qiulin Zhang, Yuan Zhang, Rudan Chen, Xichao Yang, Di Xie, Jiang Zhu

展开摘要

Post-Training low-bit Quantization (PTQ) is useful to accelerate DNNs due to its high efficiency, the current SOTAs of which mostly adopt feature reconstruction with self-distillation finetuning. However, when bitwidth goes to be extremely low, we find the current reconstruction optimization space is not optimal. Considering all possible parameters and the ignored fact that integer weight can be obtained early before actual inference, we thoroughly explore different optimization space by quant-step decoupling, where a wider PTQ optimization space, which consistently makes a better optimum, is found out. Based on these, we propose an Adaptive Quantization Transformation (AdaQTransform) for PTQ reconstruction, which makes the quantized output feature better fit the FP32 counterpart with adaptive per-channel transformation, thus achieves lower feature reconstruction error. In addition, it incurs negligible extra finetuning cost and no extra inference cost. Based on AdaQTransform, for the first time, we build a general quantization setting paradigm subsuming current PTQs, QATs and other potential forms. Experiments demonstrate AdaQTransform expands the optimization space for PTQ and helps current PTQs find a better optimum over CNNs, ViTs, LLMs and image super-resolution networks, e.g., it improves NWQ by 5.7% on ImageNet for W2A2-MobileNet-v2.

Poster
Autoregressive Video Generation without Vector Quantization

Haoge Deng, Ting Pan, Haiwen Diao, Zhengxiong Luo, Yufeng Cui, Huchuan Lu, Shiguang Shan, Yonggang Qi, Xinlong Wang

展开摘要

This paper presents a novel approach that enables autoregressive video generation with high efficiency. We propose to reformulate the video generation problem as a non-quantized autoregressive modeling of temporal frame-by-frame prediction and spatial set-by-set prediction. Unlike raster-scan prediction in prior autoregressive models or joint distribution modeling of fixed-length tokens in diffusion models, our approach maintains the causal property of GPT-style models for flexible in-context capabilities, while leveraging bidirectional modeling within individual frames for efficiency. With the proposed approach, we train a novel video autoregressive model without vector quantization, termed NOVA. Our results demonstrate that NOVA surpasses prior autoregressive video models in data efficiency, inference speed, visual fidelity, and video fluency, even with a much smaller model capacity, i.e., 0.6B parameters. NOVA also outperforms state-of-the-art image diffusion models in text-to-image generation tasks, with a significantly lower training cost. Additionally, NOVA generalizes well across extended video durations and enables diverse zero-shot applications in one unified model. Code and models are publicly available at https://github.com/baaivision/NOVA.

Poster
Efficient Off-Policy Learning for High-Dimensional Action Spaces

Fabian Otto, Philipp Becker, Vien Anh Ngo, Gerhard Neumann

展开摘要

Existing off-policy reinforcement learning algorithms often rely on an explicit state-action-value function representation, which can be problematic in high-dimensional action spaces due to the curse of dimensionality. This reliance results in data inefficiency as maintaining a state-action-value function in such spaces is challenging. We present an efficient approach that utilizes only a state-value function as the critic for off-policy deep reinforcement learning. This approach, which we refer to as Vlearn, effectively circumvents the limitations of existing methods by eliminating the necessity for an explicit state-action-value function. To this end, we leverage a weighted importance sampling loss for learning deep value functions from off-policy data. While this is common for linear methods, it has not been combined with deep value function networks. This transfer to deep methods is not straightforward and requires novel design choices such as robust policy updates, twin value function networks to avoid an optimization bias, and importance weight clipping. We also present a novel analysis of the variance of our estimate compared to commonly used importance sampling estimators such as V-trace. Our approach improves sample complexity as well as final performance and ensures consistent and robust performance across various benchmark tasks. Eliminating the state-action-value function in Vlearn facilitates a streamlined learning process, yielding high-return agents.

Poster
Accelerated training through iterative gradient propagation along the residual path

Erwan Fagnou, Paul Caillon, Blaise Delattre, Alexandre Allauzen

展开摘要

Despite being the cornerstone of deep learning, backpropagation is criticized for its inherent sequentiality, which can limit the scalability of very deep models. Such models faced convergence issues due to vanishing gradient, later resolved using residual connections. Variants of these are now widely used in modern architectures. However, the computational cost of backpropagation remains a major burden, accounting for most of the training time. Taking advantage of residual-like architectural designs, we introduce Highway backpropagation, a parallelizable iterative algorithm that approximates backpropagation, by alternatively i) accumulating the gradient estimates along the residual path, and ii) backpropagating them through every layer in parallel. This algorithm is naturally derived from a decomposition of the gradient as the sum of gradients flowing through all paths, and is adaptable to a diverse set of common architectures, ranging from ResNets and Transformers to recurrent neural networks. Through an extensive empirical study on a large selection of tasks and models, we evaluate Highway-BP and show that major speedups can be achieved with minimal performance degradation.

Oral
MMAD: A Comprehensive Benchmark for Multimodal Large Language Models in Industrial Anomaly Detection

Xi Jiang, Jian Li, Hanqiu Deng, Yong Liu, Bin-Bin Gao, Yifeng Zhou, Jialin Li, Chengjie Wang, Feng Zheng

展开摘要

In the field of industrial inspection, Multimodal Large Language Models (MLLMs) have a high potential to renew the paradigms in practical applications due to their robust language capabilities and generalization abilities. However, despite their impressive problem-solving skills in many domains, MLLMs' ability in industrial anomaly detection has not been systematically studied. To bridge this gap, we present MMAD, a full-spectrum MLLM benchmark in industrial Anomaly Detection. We defined seven key subtasks of MLLMs in industrial inspection and designed a novel pipeline to generate the MMAD dataset with 39,672 questions for 8,366 industrial images. With MMAD, we have conducted a comprehensive, quantitative evaluation of various state-of-the-art MLLMs. The commercial models performed the best, with the average accuracy of GPT-4o models reaching 74.9\%. However, this result falls far short of industrial requirements. Our analysis reveals that current MLLMs still have significant room for improvement in answering questions related to industrial anomalies and defects. We further explore two training-free performance enhancement strategies to help models improve in industrial scenarios, highlighting their promising potential for future research. The code and data are available at https://github.com/jam-cc/MMAD.

Poster
How Does Critical Batch Size Scale in Pre-training?

Hanlin Zhang, Depen Morwani, Nikhil Vyas, Jingfeng Wu, Difan Zou, Udaya Ghai, Dean Foster, Sham M. Kakade

展开摘要

Training large-scale models under given resources requires careful design of parallelism strategies. In particular, the efficiency notion of critical batch size (CBS), concerning the compromise between time and compute, marks the threshold beyond which greater data parallelism leads to diminishing returns. To operationalize it, we propose a measure of CBS and pre-train a series of auto-regressive language models, ranging from 85 million to 1.2 billion parameters, on the C4 dataset. Through extensive hyper-parameter sweeps and careful control of factors such as batch size, momentum, and learning rate along with its scheduling, we systematically investigate the impact of scale on CBS. Then we fit scaling laws with respect to model and data sizes to decouple their effects. Overall, our results demonstrate that CBS scales primarily with data size rather than model size, a finding we justify theoretically through the analysis of infinite-width limits of neural networks and infinite-dimensional least squares regression. Of independent interest, we highlight the importance of common hyper-parameter choices and strategies for studying large-scale pre-training beyond fixed training durations.

Poster
From Few to Many: Self-Improving Many-Shot Reasoners Through Iterative Optimization and Generation

Xingchen Wan, Han Zhou, Ruoxi Sun, Sercan O Arik

展开摘要

Recent advances in long-context large language models (LLMs) have led to the emerging paradigm of many-shot in-context learning (ICL), where it is observed that scaling many more demonstrating examples beyond the conventional few-shot setup in the context can lead to performance benefits. However, despite its promise, it is unclear what aspects dominate the benefits and whether simply scaling to more examples is the most effective way of improving many-shot ICL. In this work, we first provide an analysis on the factors driving many-shot ICL, and we find that 1) many-shot performance can still be attributed to often a few disproportionately influential examples and 2) identifying such influential examples ("optimize") and using them as demonstrations to regenerate new examples ("generate") can lead to further improvements. Inspired by the findings, we propose BRIDGE, an algorithm that alternates between the optimize step with Bayesian optimization to discover the influential sets of examples and the generate step to reuse this set to expand the reasoning paths of the examples back to the many-shot regime automatically. On Gemini, Claude, and Mistral LLMs of different sizes, we show BRIDGE led to significant improvements across a diverse set of tasks including symbolic reasoning, numerical reasoning and code generation.

Poster
Active Task Disambiguation with LLMs

Kasia Kobalczyk, Nicolás Astorga, Tennison Liu, Mihaela van der Schaar

展开摘要

Despite the impressive performance of large language models (LLMs) across various benchmarks, their ability to address ambiguously specified problems—frequent in real-world interactions—remains underexplored. To address this gap, we introduce a formal definition of task ambiguity and frame the problem of task disambiguation through the lens of Bayesian Experimental Design. By posing clarifying questions, LLM agents can acquire additional task specifications, progressively narrowing the space of viable solutions and reducing the risk of generating unsatisfactory outputs. Yet, generating effective clarifying questions requires LLM agents to engage in a form of meta-cognitive reasoning, an ability LLMs may presently lack. Our proposed approach of active task disambiguation enables LLM agents to generate targeted questions maximizing the information gain. Effectively, this approach shifts the load from implicit to explicit reasoning about the space of viable solutions. Empirical results demonstrate that this form of question selection leads to more effective task disambiguation in comparison to approaches relying on reasoning solely within the space of questions.

Spotlight
Words in Motion: Extracting Interpretable Control Vectors for Motion Transformers

Omer Sahin Tas, Royden Wagner

展开摘要

Transformer-based models generate hidden states that are difficult to interpret. In this work, we analyze hidden states and modify them at inference, with a focus on motion forecasting. We use linear probing to analyze whether interpretable features are embedded in hidden states. Our experiments reveal high probing accuracy, indicating latent space regularities with functionally important directions. Building on this, we use the directions between hidden states with opposing features to fit control vectors. At inference, we add our control vectors to hidden states and evaluate their impact on predictions. Remarkably, such modifications preserve the feasibility of predictions. We further refine our control vectors using sparse autoencoders (SAEs). This leads to more linear changes in predictions when scaling control vectors. Our approach enables mechanistic interpretation as well as zero-shot generalization to unseen dataset characteristics with negligible computational overhead.

Poster
Systems with Switching Causal Relations: A Meta-Causal Perspective

Moritz Willig, Tim Tobiasch, Florian Peter Busch, Jonas Seng, Devendra Singh Dhami, Kristian Kersting

展开摘要

Most work on causality in machine learning assumes that causal relationships are driven by a constant underlying process. However, the flexibility of agents' actions or tipping points in the environmental process can change the qualitative dynamics of the system. As a result, new causal relationships may emerge, while existing ones change or disappear, resulting in an altered causal graph. To analyze these qualitative changes on the causal graph, we propose the concept of meta-causal states, which groups classical causal models into clusters based on equivalent qualitative behavior and consolidates specific mechanism parameterizations. We demonstrate how meta-causal states can be inferred from observed agent behavior, and discuss potential methods for disentangling these states from unlabeled data. Finally, we direct our analysis towards the application of a dynamical system, showing that meta-causal states can also emerge from inherent system dynamics, and thus constitute more than a context-dependent framework in which mechanisms emerge only as a result of external factors.

Spotlight
Discretization-invariance? On the Discretization Mismatch Errors in Neural Operators

Wenhan Gao, Ruichen Xu, Yuefan Deng, Yi Liu

展开摘要

In recent years, neural operators have emerged as a prominent approach for learning mappings between function spaces, such as the solution operators of parametric PDEs. A notable example is the Fourier Neural Operator (FNO), which models the integral kernel as a convolution operator and uses the Convolution Theorem to learn the kernel directly in the frequency domain. The parameters are decoupled from the resolution of the data, allowing the FNO to take inputs of different resolutions. However, training at a lower resolution and inferring at a finer resolution does not guarantee consistent performance, nor can fine details, present only in fine-scale data, be learned solely from coarse data. In this work, we address this misconception by defining and examining the discretization mismatch error: the discrepancy between the outputs of the neural operator when using different discretizations of the input data. We demonstrate that neural operators may suffer from discretization mismatch errors that hinder their effectiveness when inferred on data with resolutions different from that of the training data or when trained on data with varying resolutions. As neural operators underpin many critical cross-resolution scientific tasks, such as climate modeling and fluid dynamics, understanding discretization mismatch errors is essential. Based on our findings, we propose a Cross-Resolution Operator-learning Pipeline that is free of aliasing and discretization mismatch errors, enabling efficient cross-resolution and multi-spatial-scale learning, and resulting in superior performance.

Poster
PostEdit: Posterior Sampling for Efficient Zero-Shot Image Editing

Feng Tian, Yixuan Li, Yichao Yan, Shanyan Guan, Yanhao Ge, Xiaokang Yang

展开摘要

In the field of image editing, three core challenges persist: controllability, background preservation, and efficiency. Inversion-based methods rely on time-consuming optimization to preserve the features of the initial images, which results in low efficiency due to the requirement for extensive network inference. Conversely, inversion-free methods lack theoretical support for background similarity, as they circumvent the issue of maintaining initial features to achieve efficiency. As a consequence, none of these methods can achieve both high efficiency and background consistency. To tackle the challenges and the aforementioned disadvantages, we introduce PostEdit, a method that incorporates a posterior scheme to govern the diffusion sampling process. Specifically, a corresponding measurement term related to both the initial features and Langevin dynamics is introduced to optimize the estimated image generated by the given target prompt. Extensive experimental results indicate that the proposed PostEdit achieves state-of-the-art editing performance while accurately preserving unedited regions. Furthermore, the method is both inversion- and training-free, necessitating approximately 1.5 seconds and 18 GB of GPU memory to generate high-quality results.

Poster
Exploiting Hidden Symmetry to Improve Objective Perturbation for DP Linear Learners with a Nonsmooth L1-Norm

Du Chen, Geoffrey A. Chua

展开摘要

Objective Perturbation (OP) is a classic approach to differentially private (DP) convex optimization with smooth loss functions but is less understood for nonsmooth cases. In this work, we study how to apply OP to DP linear learners under loss functions with an implicit $\ell_1$-norm structure, such as $\max(0,x)$ as a motivating example. We propose to first smooth out the implicit $\ell_1$-norm by convolution, and then invoke standard OP. Convolution has many advantages that distinguish itself from Moreau Envelope, such as approximating from above and a higher degree of hyperparameters. These advantages, in conjunction with the symmetry of $\ell_1$-norm, result in tighter pointwise approximation, which further facilitates tighter analysis of generalization risks by using pointwise bounds. Under mild assumptions on groundtruth distributions, the proposed OP-based algorithm is found to be rate-optimal, and can achieve the excess generalization risk $\mathcal{O}(\frac{1}{\sqrt{n}}+\frac{\sqrt{d\ln(1/\delta)}}{n\varepsilon})$. Experiments demonstrate the competitive performance of the proposed method to Noisy-SGD.

Poster