Shangqian Gao

Alireza Ganjdanesh, Shangqian Gao, Heng Huang

Convolutional Neural Networks (CNNs) compression is crucial to deploying these models in edge devices with limited resources. Existing channel pruning algorithms for CNNs have achieved plenty of success on complex models. They approach the pruning problem from various perspectives and use different metrics to guide the pruning process. However, these metrics mainly focus on the model's `outputs' or `weights' and neglect its `interpretations' information. To fill in this gap, we propose to address the channel pruning problem from a novel perspective by leveraging the interpretations of a model to steer the pruning process, thereby utilizing information from both inputs and outputs of the model. However, existing interpretation methods cannot get deployed to achieve our goal as either they are inefficient for pruning or may predict non-coherent explanations. We tackle this challenge by introducing a selector model that predicts real-time smooth saliency masks for pruned models. We parameterize the distribution of explanatory masks by Radial Basis Function (RBF)-like functions to incorporate geometric prior of natural images in our selector model's inductive bias. Thus, we can obtain compact representations of explanations to reduce the computational costs of our pruning method. We leverage our selector model to steer the network pruning by maximizing the similarity of explanatory representations for the pruned and original models. Extensive experiments on CIFAR-10 and ImageNet benchmark datasets demonstrate the efficacy of our proposed method. Our implementations are available at \url{https://github.com/Alii-Ganjj/InterpretationsSteeredPruning}

Haoyan Yang, Reza Shirkavand, Yukai Jin et al.

The ability to recognize one's own limitations and decide whether to solve a problem or delegate is fundamental for reliable intelligent systems. Yet we show that modern large language models systematically lack this ability: across diverse model families and scales, they overestimate their competence and attempt queries they cannot solve. We refer to this ability as Capability Self-Assessment (CSA) and formulate it as a policy-learning problem, aiming to improve self-assessment while preserving the model's original capabilities. Our results show that reinforcement learning teaches CSA effectively, significantly outperforming supervised fine-tuning while preserving original capabilities. In contrast, supervised fine-tuning severely degrades the capabilities the model is meant to assess. Moreover, learned self-assessment behavior generalizes well out of distribution, suggesting that CSA is a transferable model trait. Finally, CSA is practically useful: it improves local-cloud decision making at inference time and provides a signal for targeted data selection during training.

Chi-Heng Lin, Shangqian Gao, James Seale Smith et al.

Large Language Models (LLMs) have reshaped the landscape of artificial intelligence by demonstrating exceptional performance across various tasks. However, substantial computational requirements make their deployment challenging on devices with limited resources. Recently, compression methods using low-rank matrix techniques have shown promise, yet these often lead to degraded accuracy or introduce significant overhead in parameters and inference latency. This paper introduces \textbf{Mo}dular \textbf{De}composition (MoDeGPT), a novel structured compression framework that does not need recovery fine-tuning while resolving the above drawbacks. MoDeGPT partitions the Transformer block into modules comprised of matrix pairs and reduces the hidden dimensions via reconstructing the module-level outputs. MoDeGPT is developed based on a theoretical framework that utilizes three well-established matrix decomposition algorithms -- Nyström approximation, CR decomposition, and SVD -- and applies them to our redefined transformer modules. Our comprehensive experiments show MoDeGPT, without backward propagation, matches or surpasses previous structured compression methods that rely on gradient information, and saves 98% of compute costs on compressing a 13B model. On \textsc{Llama}-2/3 and OPT models, MoDeGPT maintains 90-95% zero-shot performance with 25-30% compression rates. Moreover, the compression can be done on a single GPU within a few hours and increases the inference throughput by up to 46%.

Zhepeng Wang, Runxue Bao, Yawen Wu et al.

Pretrained large language models (LLMs) have revolutionized natural language processing (NLP) tasks such as summarization, question answering, and translation. However, LLMs pose significant security risks due to their tendency to memorize training data, leading to potential privacy breaches and copyright infringement. Accurate measurement of this memorization is essential to evaluate and mitigate these potential risks. However, previous attempts to characterize memorization are constrained by either using prefixes only or by prepending a constant soft prompt to the prefixes, which cannot react to changes in input. To address this challenge, we propose a novel method for estimating LLM memorization using dynamic, prefix-dependent soft prompts. Our approach involves training a transformer-based generator to produce soft prompts that adapt to changes in input, thereby enabling more accurate extraction of memorized data. Our method not only addresses the limitations of previous methods but also demonstrates superior performance in diverse experimental settings compared to state-of-the-art techniques. In particular, our method can achieve the maximum relative improvement of 112.75% and 32.26% over the vanilla baseline in terms of discoverable memorization rate for the text generation task and code generation task respectively.

Xidong Wu, Yukuan Zhang, Yuqiong Ji et al.

Large language model (LLM) routing has emerged as a critical strategy to balance model performance and cost-efficiency by dynamically selecting services from various model providers. However, LLM routing adds an intermediate layer between users and LLMs, creating new privacy risks to user data. These privacy risks have not been systematically studied. Although cryptographic techniques such as Secure Multi-Party Computation (MPC) enable privacy-preserving computation, their protocol design and implementation remain under-explored, and naïve implementations typically incur prohibitive computational overhead. To address this, we propose a privacy-preserving LLM routing framework (PPRoute). PPRoute includes multiple strategies to speed up encoder inference and nearest neighbor search under the MPC and maintain the quality of LLM routing. First, PPRoute uses MPC-friendly operations to boost the encoder inference. Second, PPRoute uses a multiple-step model training algorithm to maintain routing quality despite the constraints of the encrypted domain. Third, PPRoute proposes an unsorted Top-k algorithm with $O(1)$ communication complexity for secure sorting in model search, significantly reducing communication latency. Across different datasets, PPRoute achieves the performance of plaintext counterparts, while achieving approximately a 20$\times$ speedup over naïve MPC implementations.

Khiem Le, Youssef Mroueh, Phuc Nguyen et al.

Large language models trained via next-token prediction are fundamentally pattern-matchers: sensitive to superficial phrasing variations even when the underlying problem is identical. Group Relative Policy Optimization (GRPO) was designed to improve reasoning, but in fact it worsens this situation through two failure modes: diversity collapse, where training amplifies a single solution strategy while ignoring alternatives of gradient signal, and gradient diminishing, where a large portion of questions yield zero gradients because all rollouts receive identical rewards. We propose TA-GRPO (Transform-Augmented GRPO), which generates semantically equivalent transformed variants of each question (via paraphrasing, variable renaming, and format changes) and computes advantages by pooling rewards across the entire group. This pooled computation ensures mixed rewards even when the original question is too easy or too hard, while training on diverse phrasings promotes multiple solution strategies. We provide theoretical justification showing that TA-GRPO reduces zero-gradient probability and improves generalization via reduced train-test distribution shift. Experiments on mathematical reasoning benchmarks show consistent Pass@k improvements, with gains up to 9.84 points on competition math (AMC12, AIME24) and 5.05 points on out-of-distribution scientific reasoning (GPQA-Diamond).

Reza Shirkavand, Shangqian Gao, Peiran Yu et al.

We study cost-aware routing for large language models across diverse and dynamic pools of models. Existing approaches often overlook prompt-specific context, rely on expensive model profiling, assume a fixed set of experts, or use inefficient trial-and-error strategies. We introduce Cost-Spectrum Contrastive Routing (CSCR), a lightweight framework that maps both prompts and models into a shared embedding space to enable fast, cost-sensitive selection. CSCR uses compact, fast-to-compute logit footprints for open-source models and perplexity fingerprints for black-box APIs. A contrastive encoder is trained to favor the cheapest accurate expert within adaptive cost bands. At inference time, routing reduces to a single k-NN lookup via a FAISS index, requiring no retraining when the expert pool changes and enabling microsecond latency. Across multiple benchmarks, CSCR consistently outperforms baselines, improving the accuracy-cost tradeoff by up to 25%, while generalizing robustly to unseen LLMs and out-of-distribution prompts.

Xidong Wu, Shangqian Gao, Zeyu Zhang et al.

Current techniques for deep neural network (DNN) pruning often involve intricate multi-step processes that require domain-specific expertise, making their widespread adoption challenging. To address the limitation, the Only-Train-Once (OTO) and OTOv2 are proposed to eliminate the need for additional fine-tuning steps by directly training and compressing a general DNN from scratch. Nevertheless, the static design of optimizers (in OTO) can lead to convergence issues of local optima. In this paper, we proposed the Auto-Train-Once (ATO), an innovative network pruning algorithm designed to automatically reduce the computational and storage costs of DNNs. During the model training phase, our approach not only trains the target model but also leverages a controller network as an architecture generator to guide the learning of target model weights. Furthermore, we developed a novel stochastic gradient algorithm that enhances the coordination between model training and controller network training, thereby improving pruning performance. We provide a comprehensive convergence analysis as well as extensive experiments, and the results show that our approach achieves state-of-the-art performance across various model architectures (including ResNet18, ResNet34, ResNet50, ResNet56, and MobileNetv2) on standard benchmark datasets (CIFAR-10, CIFAR-100, and ImageNet).

Shangqian Gao, Chi-Heng Lin, Ting Hua et al.

Large Language Models (LLMs) have achieved remarkable success in various natural language processing tasks, including language modeling, understanding, and generation. However, the increased memory and computational costs associated with these models pose significant challenges for deployment on resource-limited devices. Structural pruning has emerged as a promising solution to reduce the costs of LLMs without requiring post-processing steps. Prior structural pruning methods either follow the dependence of structures at the cost of limiting flexibility, or introduce non-trivial additional parameters by incorporating different projection matrices. In this work, we propose a novel approach that relaxes the constraint imposed by regular structural pruning methods and eliminates the structural dependence along the embedding dimension. Our dimension-independent structural pruning method offers several benefits. Firstly, our method enables different blocks to utilize different subsets of the feature maps. Secondly, by removing structural dependence, we facilitate each block to possess varying widths along its input and output dimensions, thereby significantly enhancing the flexibility of structural pruning. We evaluate our method on various LLMs, including OPT, LLaMA, LLaMA-2, Phi-1.5, and Phi-2. Experimental results demonstrate that our approach outperforms other state-of-the-art methods, showing for the first time that structural pruning can achieve an accuracy similar to semi-structural pruning.

Alireza Ganjdanesh, Shangqian Gao, Heng Huang

Structural model pruning is a prominent approach used for reducing the computational cost of Convolutional Neural Networks (CNNs) before their deployment on resource-constrained devices. Yet, the majority of proposed ideas require a pretrained model before pruning, which is costly to secure. In this paper, we propose a novel structural pruning approach to jointly learn the weights and structurally prune architectures of CNN models. The core element of our method is a Reinforcement Learning (RL) agent whose actions determine the pruning ratios of the CNN model's layers, and the resulting model's accuracy serves as its reward. We conduct the joint training and pruning by iteratively training the model's weights and the agent's policy, and we regularize the model's weights to align with the selected structure by the agent. The evolving model's weights result in a dynamic reward function for the agent, which prevents using prominent episodic RL methods with stationary environment assumption for our purpose. We address this challenge by designing a mechanism to model the complex changing dynamics of the reward function and provide a representation of it to the RL agent. To do so, we take a learnable embedding for each training epoch and employ a recurrent model to calculate a representation of the changing environment. We train the recurrent model and embeddings using a decoder model to reconstruct observed rewards. Such a design empowers our agent to effectively leverage episodic observations along with the environment representations to learn a proper policy to determine performant sub-networks of the CNN model. Our extensive experiments on CIFAR-10 and ImageNet using ResNets and MobileNets demonstrate the effectiveness of our method.

Alireza Ganjdanesh, Shangqian Gao, Hirad Alipanah et al.

Generative Adversarial Networks (GANs) have shown remarkable success in modeling complex data distributions for image-to-image translation. Still, their high computational demands prohibit their deployment in practical scenarios like edge devices. Existing GAN compression methods mainly rely on knowledge distillation or convolutional classifiers' pruning techniques. Thus, they neglect the critical characteristic of GANs: their local density structure over their learned manifold. Accordingly, we approach GAN compression from a new perspective by explicitly encouraging the pruned model to preserve the density structure of the original parameter-heavy model on its learned manifold. We facilitate this objective for the pruned model by partitioning the learned manifold of the original generator into local neighborhoods around its generated samples. Then, we propose a novel pruning objective to regularize the pruned model to preserve the local density structure over each neighborhood, resembling the kernel density estimation method. Also, we develop a collaborative pruning scheme in which the discriminator and generator are pruned by two pruning agents. We design the agents to capture interactions between the generator and discriminator by exchanging their peer's feedback when determining corresponding models' architectures. Thanks to such a design, our pruning method can efficiently find performant sub-networks and can maintain the balance between the generator and discriminator more effectively compared to baselines during pruning, thereby showing more stable pruning dynamics. Our experiments on image translation GAN models, Pix2Pix and CycleGAN, with various benchmark datasets and architectures demonstrate our method's effectiveness.

Junqi Qu, Yan Zhang, Shangqian Gao et al.

Large Language Models (LLMs) show promise for equation discovery, yet their outputs are highly sensitive to prompt phrasing, a phenomenon we term instruction brittleness. Static prompts cannot adapt to the evolving state of a multi-step generation process, causing models to plateau at suboptimal solutions. To address this, we propose NeuroSymBO, which reframes prompt engineering as a sequential decision problem. Our method maintains a discrete library of reasoning strategies and uses Bayesian Optimization to select the optimal instruction at each step based on numerical feedback. Experiments on PDE discovery benchmarks show that adaptive instruction selection significantly outperforms fixed prompts, achieving higher recovery rates with more parsimonious solutions.

Reza Shirkavand, Peiran Yu, Shangqian Gao et al.

Recent advances in diffusion generative models have yielded remarkable progress. While the quality of generated content continues to improve, these models have grown considerably in size and complexity. This increasing computational burden poses significant challenges, particularly in resource-constrained deployment scenarios such as mobile devices. The combination of model pruning and knowledge distillation has emerged as a promising solution to reduce computational demands while preserving generation quality. However, this technique inadvertently propagates undesirable behaviors, including the generation of copyrighted content and unsafe concepts, even when such instances are absent from the fine-tuning dataset. In this paper, we propose a novel bilevel optimization framework for pruned diffusion models that consolidates the fine-tuning and unlearning processes into a unified phase. Our approach maintains the principal advantages of distillation-namely, efficient convergence and style transfer capabilities-while selectively suppressing the generation of unwanted content. This plug-in framework is compatible with various pruning and concept unlearning methods, facilitating efficient, safe deployment of diffusion models in controlled environments.

Zhankai Ye, Bofan Li, Yukai Jin et al.

Discrete motion tokenization has recently enabled Large Language Models (LLMs) to serve as versatile backbones for motion understanding and motion-language reasoning. However, existing pipelines typically decouple motion quantization from semantic embedding learning, linking them solely via token IDs. This approach fails to effectively align the intrinsic geometry of the motion space with the embedding space, thereby hindering the LLM's capacity for nuanced motion reasoning. We argue that alignment is most effective when both modalities share a unified geometric basis. Therefore, instead of forcing the LLM to reconstruct the complex geometry among motion tokens from scratch, we present a novel framework that explicitly enforces orthogonality on both the motion codebook and the LLM embedding space, ensuring that their relational structures naturally mirror each other. Specifically, we employ a decoder-only quantizer with Gumbel-Softmax for differentiable training and balanced codebook usage. To bridge the modalities, we use a sparse projection that maps motion codes into the LLM embedding space while preserving orthogonality. Finally, a two-stage orthonormal regularization schedule enforces soft constraints during tokenizer training and LLM fine-tuning to maintain geometric alignment without hindering semantic adaptation. Extensive experiments on HumanML3D demonstrate that our framework achieves a 20% performance improvement over current state-of-the-art methods, validating that a unified geometric basis effectively empowers the LLM for nuanced motion reasoning.

Lei Lu, Zhepeng Wang, Runxue Bao et al.

Existing pruning techniques for large language models (LLMs) targeting domain-specific applications typically follow a two-stage process: pruning the pretrained general-purpose LLMs and then fine-tuning the pruned LLMs on specific domains. However, the pruning decisions, derived from the pretrained weights, remain unchanged during fine-tuning, even if the weights have been updated. Therefore, such a combination of the pruning decisions and the finetuned weights may be suboptimal, leading to non-negligible performance degradation. To address these limitations, we propose ATP: All-in-One Tuning and Structural Pruning, a unified one-stage structural pruning and fine-tuning approach that dynamically identifies the current optimal substructure throughout the fine-tuning phase via a trainable pruning decision generator. Moreover, given the limited available data for domain-specific applications, Low-Rank Adaptation (LoRA) becomes a common technique to fine-tune the LLMs. In ATP, we introduce LoRA-aware forward and sparsity regularization to ensure that the substructures corresponding to the learned pruning decisions can be directly removed after the ATP process. ATP outperforms the state-of-the-art two-stage pruning methods on tasks in the legal and healthcare domains. More specifically, ATP recovers up to 88% and 91% performance of the dense model when pruning 40% parameters of LLaMA2-7B and LLaMA3-8B models, respectively.

Haoyan Yang, Ting Hua, Shangqian Gao et al.

Although LLMs have achieved significant success, their reliance on large volumes of human-annotated data has limited their potential for further scaling. In this situation, utilizing self-generated synthetic data has become crucial for fine-tuning LLMs without extensive human annotation. However, current methods often fail to ensure consistent improvements across iterations, with performance stagnating after only minimal updates. To overcome these challenges, we introduce Dynamic Noise Preference Optimization (DNPO). DNPO employs a dynamic sample labeling mechanism to construct preference pairs for training and introduces controlled, trainable noise into the preference optimization process. Our approach effectively prevents stagnation and enables continuous improvement. In experiments with Zephyr-7B, DNPO consistently outperforms existing methods, showing an average performance boost of 2.6% across multiple benchmarks. Additionally, DNPO shows a significant improvement in model-generated data quality, with a 29.4% win-loss rate gap compared to the baseline in GPT-4 evaluations. This highlights its effectiveness in enhancing model performance through iterative refinement.

Shangqian Gao, Ting Hua, Reza Shirkavand et al.

Large Language Models (LLMs) have demonstrated remarkable abilities in tackling a wide range of complex tasks. However, their huge computational and memory costs raise significant challenges in deploying these models on resource-constrained devices or efficiently serving them. Prior approaches have attempted to alleviate these problems by permanently removing less important model structures, yet these methods often result in substantial performance degradation due to the permanent deletion of model parameters. In this work, we tried to mitigate this issue by reducing the number of active parameters without permanently removing them. Specifically, we introduce a differentiable dynamic pruning method that pushes dense models to maintain a fixed number of active parameters by converting their MLP layers into a Mixture of Experts (MoE) architecture. Our method, even without fine-tuning, consistently outperforms previous structural pruning techniques across diverse model families, including Phi-2, LLaMA-2, LLaMA-3, and Qwen-2.5.

James Seale Smith, Chi-Heng Lin, Shikhar Tuli et al.

The rapid proliferation of large language models (LLMs) in natural language processing (NLP) has created a critical need for techniques that enable efficient deployment on memory-constrained devices without compromising performance. We present a method to prune LLMs that selectively prunes model blocks based on an importance score and replaces them with a low-parameter replacement strategy. Specifically, we propose a principled metric to replace each pruned block using a weight-sharing mechanism that leverages unpruned counterparts from the model and block-specific low-rank adapters. Furthermore, we facilitate the learning of these replacement blocks with output feature normalization and an adapter initialization scheme built on low-rank SVD reconstructions. Empirical evaluations demonstrate substantial performance gains over existing methods, achieving state-of-the-art performance on 5/6 benchmarks for a compression rate of 30% and 6/6 benchmarks for a compression rate of 40%. We also demonstrate that our approach can extend smaller models, boosting performance on 6/6 benchmarks using only ~0.3% tokens of extended training with minimal additional parameter costs.

Yiming Zeng, Jinghan Cao, Zexin Li et al.

Instruction-based text editing is increasingly critical for real-world applications such as code editors (e.g., Cursor), but Large Language Models (LLMs) continue to struggle with this task. Unlike free-form generation, editing requires faithfully implementing user instructions while preserving unchanged content, as even minor unintended modifications can break functionality. Existing approaches treat editing as generic text generation, leading to two key failures: they struggle to faithfully align edits with diverse user intents, and they often over-edit unchanged regions. We propose HyperEdit to address both issues. First, we introduce hypernetwork-based dynamic adaptation that generates request-specific parameters, enabling the model to tailor its editing strategy to each instruction. Second, we develop difference-aware regularization that focuses supervision on modified spans, preventing over-editing while ensuring precise, minimal changes. HyperEdit achieves a 9%--30% relative improvement in BLEU on modified regions over state-of-the-art baselines, despite utilizing only 3B parameters.

Xiaomeng Yang, Lei Lu, Qihui Fan et al.

Diffusion models have demonstrated exceptional capabilities in generating high-fidelity images. However, their iterative denoising process results in significant computational overhead during inference, limiting their practical deployment in resource-constrained environments. Existing acceleration methods often adopt uniform strategies that fail to capture the temporal variations during diffusion generation, while the commonly adopted sequential pruning-then-fine-tuning strategy suffers from sub-optimality due to the misalignment between pruning decisions made on pretrained weights and the model's final parameters. To address these limitations, we introduce ALTER: All-in-One Layer Pruning and Temporal Expert Routing, a unified framework that transforms diffusion models into a mixture of efficient temporal experts. ALTER achieves a single-stage optimization that unifies layer pruning, expert routing, and model fine-tuning by employing a trainable hypernetwork, which dynamically generates layer pruning decisions and manages timestep routing to specialized, pruned expert sub-networks throughout the ongoing fine-tuning of the UNet. This unified co-optimization strategy enables significant efficiency gains while preserving high generative quality. Specifically, ALTER achieves same-level visual fidelity to the original 50-step Stable Diffusion v2.1 model while utilizing only 25.9% of its total MACs with just 20 inference steps and delivering a 3.64x speedup through 35% sparsity.

Alireza Ganjdanesh, Reza Shirkavand, Shangqian Gao et al.

Text-to-image (T2I) diffusion models have demonstrated impressive image generation capabilities. Still, their computational intensity prohibits resource-constrained organizations from deploying T2I models after fine-tuning them on their internal target data. While pruning techniques offer a potential solution to reduce the computational burden of T2I models, static pruning methods use the same pruned model for all input prompts, overlooking the varying capacity requirements of different prompts. Dynamic pruning addresses this issue by utilizing a separate sub-network for each prompt, but it prevents batch parallelism on GPUs. To overcome these limitations, we introduce Adaptive Prompt-Tailored Pruning (APTP), a novel prompt-based pruning method designed for T2I diffusion models. Central to our approach is a prompt router model, which learns to determine the required capacity for an input text prompt and routes it to an architecture code, given a total desired compute budget for prompts. Each architecture code represents a specialized model tailored to the prompts assigned to it, and the number of codes is a hyperparameter. We train the prompt router and architecture codes using contrastive learning, ensuring that similar prompts are mapped to nearby codes. Further, we employ optimal transport to prevent the codes from collapsing into a single one. We demonstrate APTP's effectiveness by pruning Stable Diffusion (SD) V2.1 using CC3M and COCO as target datasets. APTP outperforms the single-model pruning baselines in terms of FID, CLIP, and CMMD scores. Our analysis of the clusters learned by APTP reveals they are semantically meaningful. We also show that APTP can automatically discover previously empirically found challenging prompts for SD, e.g. prompts for generating text images, assigning them to higher capacity codes.

Feihu Huang, Shangqian Gao, Heng Huang

In the paper, we design a novel Bregman gradient policy optimization framework for reinforcement learning based on Bregman divergences and momentum techniques. Specifically, we propose a Bregman gradient policy optimization (BGPO) algorithm based on the basic momentum technique and mirror descent iteration. Meanwhile, we further propose an accelerated Bregman gradient policy optimization (VR-BGPO) algorithm based on the variance reduced technique. Moreover, we provide a convergence analysis framework for our Bregman gradient policy optimization under the nonconvex setting. We prove that our BGPO achieves a sample complexity of $O(ε^{-4})$ for finding $ε$-stationary policy only requiring one trajectory at each iteration, and our VR-BGPO reaches the best known sample complexity of $O(ε^{-3})$, which also only requires one trajectory at each iteration. In particular, by using different Bregman divergences, our BGPO framework unifies many existing policy optimization algorithms such as the existing (variance reduced) policy gradient algorithms such as natural policy gradient algorithm. Extensive experimental results on multiple reinforcement learning tasks demonstrate the efficiency of our new algorithms.

Feihu Huang, Shangqian Gao

In the paper, we study a class of useful minimax problems on Riemanian manifolds and propose a class of effective Riemanian gradient-based methods to solve these minimax problems. Specifically, we propose an effective Riemannian gradient descent ascent (RGDA) algorithm for the deterministic minimax optimization. Moreover, we prove that our RGDA has a sample complexity of $O(κ^2ε^{-2})$ for finding an $ε$-stationary solution of the Geodesically-Nonconvex Strongly-Concave (GNSC) minimax problems, where $κ$ denotes the condition number. At the same time, we present an effective Riemannian stochastic gradient descent ascent (RSGDA) algorithm for the stochastic minimax optimization, which has a sample complexity of $O(κ^4ε^{-4})$ for finding an $ε$-stationary solution. To further reduce the sample complexity, we propose an accelerated Riemannian stochastic gradient descent ascent (Acc-RSGDA) algorithm based on the momentum-based variance-reduced technique. We prove that our Acc-RSGDA algorithm achieves a lower sample complexity of $\tilde{O}(κ^{4}ε^{-3})$ in searching for an $ε$-stationary solution of the GNSC minimax problems. Extensive experimental results on the robust distributional optimization and robust Deep Neural Networks (DNNs) training over Stiefel manifold demonstrate efficiency of our algorithms.

Feihu Huang, Shangqian Gao, Jian Pei et al.

In the paper, we propose a class of accelerated zeroth-order and first-order momentum methods for both nonconvex mini-optimization and minimax-optimization. Specifically, we propose a new accelerated zeroth-order momentum (Acc-ZOM) method for black-box mini-optimization where only function values can be obtained. Moreover, we prove that our Acc-ZOM method achieves a lower query complexity of $\tilde{O}(d^{3/4}ε^{-3})$ for finding an $ε$-stationary point, which improves the best known result by a factor of $O(d^{1/4})$ where $d$ denotes the variable dimension. In particular, our Acc-ZOM does not need large batches required in the existing zeroth-order stochastic algorithms. Meanwhile, we propose an accelerated zeroth-order momentum descent ascent (Acc-ZOMDA) method for black-box minimax optimization, where only function values can be obtained. Our Acc-ZOMDA obtains a low query complexity of $\tilde{O}((d_1+d_2)^{3/4}κ_y^{4.5}ε^{-3})$ without requiring large batches for finding an $ε$-stationary point, where $d_1$ and $d_2$ denote variable dimensions and $κ_y$ is condition number. Moreover, we propose an accelerated first-order momentum descent ascent (Acc-MDA) method for minimax optimization, whose explicit gradients are accessible. Our Acc-MDA achieves a low gradient complexity of $\tilde{O}(κ_y^{4.5}ε^{-3})$ without requiring large batches for finding an $ε$-stationary point. In particular, our Acc-MDA can obtain a lower gradient complexity of $\tilde{O}(κ_y^{2.5}ε^{-3})$ with a batch size $O(κ_y^4)$, which improves the best known result by a factor of $O(κ_y^{1/2})$. Extensive experimental results on black-box adversarial attack to deep neural networks and poisoning attack to logistic regression demonstrate efficiency of our algorithms.

Feihu Huang, Shangqian Gao, Jian Pei et al.

In the paper, we propose a class of efficient momentum-based policy gradient methods for the model-free reinforcement learning, which use adaptive learning rates and do not require any large batches. Specifically, we propose a fast important-sampling momentum-based policy gradient (IS-MBPG) method based on a new momentum-based variance reduced technique and the importance sampling technique. We also propose a fast Hessian-aided momentum-based policy gradient (HA-MBPG) method based on the momentum-based variance reduced technique and the Hessian-aided technique. Moreover, we prove that both the IS-MBPG and HA-MBPG methods reach the best known sample complexity of $O(ε^{-3})$ for finding an $ε$-stationary point of the non-concave performance function, which only require one trajectory at each iteration. In particular, we present a non-adaptive version of IS-MBPG method, i.e., IS-MBPG*, which also reaches the best known sample complexity of $O(ε^{-3})$ without any large batches. In the experiments, we apply four benchmark tasks to demonstrate the effectiveness of our algorithms.

Feihu Huang, Shangqian Gao, Jian Pei et al.

Zeroth-order (a.k.a, derivative-free) methods are a class of effective optimization methods for solving complex machine learning problems, where gradients of the objective functions are not available or computationally prohibitive. Recently, although many zeroth-order methods have been developed, these approaches still have two main drawbacks: 1) high function query complexity; 2) not being well suitable for solving the problems with complex penalties and constraints. To address these challenging drawbacks, in this paper, we propose a class of faster zeroth-order stochastic alternating direction method of multipliers (ADMM) methods (ZO-SPIDER-ADMM) to solve the nonconvex finite-sum problems with multiple nonsmooth penalties. Moreover, we prove that the ZO-SPIDER-ADMM methods can achieve a lower function query complexity of $O(nd+dn^{\frac{1}{2}}ε^{-1})$ for finding an $ε$-stationary point, which improves the existing best nonconvex zeroth-order ADMM methods by a factor of $O(d^{\frac{1}{3}}n^{\frac{1}{6}})$, where $n$ and $d$ denote the sample size and data dimension, respectively. At the same time, we propose a class of faster zeroth-order online ADMM methods (ZOO-ADMM+) to solve the nonconvex online problems with multiple nonsmooth penalties. We also prove that the proposed ZOO-ADMM+ methods achieve a lower function query complexity of $O(dε^{-\frac{3}{2}})$, which improves the existing best result by a factor of $O(ε^{-\frac{1}{2}})$. Extensive experimental results on the structure adversarial attack on black-box deep neural networks demonstrate the efficiency of our new algorithms.

Feihu Huang, Shangqian Gao, Songcan Chen et al.

Alternating direction method of multipliers (ADMM) is a popular optimization tool for the composite and constrained problems in machine learning. However, in many machine learning problems such as black-box attacks and bandit feedback, ADMM could fail because the explicit gradients of these problems are difficult or infeasible to obtain. Zeroth-order (gradient-free) methods can effectively solve these problems due to that the objective function values are only required in the optimization. Recently, though there exist a few zeroth-order ADMM methods, they build on the convexity of objective function. Clearly, these existing zeroth-order methods are limited in many applications. In the paper, thus, we propose a class of fast zeroth-order stochastic ADMM methods (i.e., ZO-SVRG-ADMM and ZO-SAGA-ADMM) for solving nonconvex problems with multiple nonsmooth penalties, based on the coordinate smoothing gradient estimator. Moreover, we prove that both the ZO-SVRG-ADMM and ZO-SAGA-ADMM have convergence rate of $O(1/T)$, where $T$ denotes the number of iterations. In particular, our methods not only reach the best convergence rate $O(1/T)$ for the nonconvex optimization, but also are able to effectively solve many complex machine learning problems with multiple regularized penalties and constraints. Finally, we conduct the experiments of black-box binary classification and structured adversarial attack on black-box deep neural network to validate the efficiency of our algorithms.