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Wei-Wei Tu

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19 papers
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19

AAAI Conference 2024 Conference Paper

DGPO: Discovering Multiple Strategies with Diversity-Guided Policy Optimization

  • Wentse Chen
  • Shiyu Huang
  • Yuan Chiang
  • Tim Pearce
  • Wei-Wei Tu
  • Ting Chen
  • Jun Zhu

Most reinforcement learning algorithms seek a single optimal strategy that solves a given task. However, it can often be valuable to learn a diverse set of solutions, for instance, to make an agent's interaction with users more engaging, or improve the robustness of a policy to an unexpected perturbance. We propose Diversity-Guided Policy Optimization (DGPO), an on-policy algorithm that discovers multiple strategies for solving a given task. Unlike prior work, it achieves this with a shared policy network trained over a single run. Specifically, we design an intrinsic reward based on an information-theoretic diversity objective. Our final objective alternately constraints on the diversity of the strategies and on the extrinsic reward. We solve the constrained optimization problem by casting it as a probabilistic inference task and use policy iteration to maximize the derived lower bound. Experimental results show that our method efficiently discovers diverse strategies in a wide variety of reinforcement learning tasks. Compared to baseline methods, DGPO achieves comparable rewards, while discovering more diverse strategies, and often with better sample efficiency.

ICML Conference 2024 Conference Paper

Efficient Stochastic Approximation of Minimax Excess Risk Optimization

  • Lijun Zhang 0005
  • Haomin Bai
  • Wei-Wei Tu
  • Ping Yang
  • Yao Hu 0002

While traditional distributionally robust optimization (DRO) aims to minimize the maximal risk over a set of distributions, Agarwal & Zhang (2022) recently proposed a variant that replaces risk with excess risk. Compared to DRO, the new formulation—minimax excess risk optimization (MERO) has the advantage of suppressing the effect of heterogeneous noise in different distributions. However, the choice of excess risk leads to a very challenging minimax optimization problem, and currently there exists only an inefficient algorithm for empirical MERO. In this paper, we develop efficient stochastic approximation approaches which directly target MERO. Specifically, we leverage techniques from stochastic convex optimization to estimate the minimal risk of every distribution, and solve MERO as a stochastic convex-concave optimization (SCCO) problem with biased gradients. The presence of bias makes existing theoretical guarantees of SCCO inapplicable, and fortunately, we demonstrate that the bias, caused by the estimation error of the minimal risk, is under-control. Thus, MERO can still be optimized with a nearly optimal convergence rate. Moreover, we investigate a practical scenario where the quantity of samples drawn from each distribution may differ, and propose a stochastic approach that delivers distribution-dependent convergence rates.

IROS Conference 2024 Conference Paper

MQE: Unleashing the Power of Interaction with Multi-agent Quadruped Environment

  • Ziyan Xiong
  • Bo Chen
  • Shiyu Huang 0001
  • Wei-Wei Tu
  • Zhaofeng He 0001
  • Yang Gao

The advent of deep reinforcement learning (DRL) has significantly advanced the field of robotics, particularly in the control and coordination of quadruped robots. However, the complexity of real-world tasks often necessitates the deployment of multi-robot systems capable of sophisticated interaction and collaboration. To address this need, we introduce the Multi-agent Quadruped Environment (MQE), a novel platform designed to facilitate the development and evaluation of multi-agent reinforcement learning (MARL) algorithms in realistic and dynamic scenarios. MQE emphasizes complex interactions between robots and objects, hierarchical policy structures, and challenging evaluation scenarios that reflect real-world applications. We present a series of collaborative and competitive tasks within MQE, ranging from simple coordination to complex adversarial interactions, and benchmark state-of-the-art MARL algorithms. Our findings indicate that hierarchical reinforcement learning can simplify task learning, but also highlight the need for advanced algorithms capable of handling the intricate dynamics of multi-agent interactions. MQE serves as a stepping stone towards bridging the gap between simulation and practical deployment, offering a rich environment for future research in multi-agent systems and robot learning. For open-sourced code and more details of MQE, please refer to https://ziyanx02.github.io/multiagent-quadruped-environment/.

JMLR Journal 2024 Journal Article

Optimistic Online Mirror Descent for Bridging Stochastic and Adversarial Online Convex Optimization

  • Sijia Chen
  • Yu-Jie Zhang
  • Wei-Wei Tu
  • Peng Zhao
  • Lijun Zhang

The stochastically extended adversarial (SEA) model, introduced by Sachs et al. (2022), serves as an interpolation between stochastic and adversarial online convex optimization. Under the smoothness condition on expected loss functions, it is shown that the expected static regret of optimistic follow-the-regularized-leader (FTRL) depends on the cumulative stochastic variance $\sigma_{1:T}^2$ and the cumulative adversarial variation $\Sigma_{1:T}^2$ for convex functions. Sachs et al. (2022) also provide a regret bound based on the maximal stochastic variance $\sigma_{\max}^2$ and the maximal adversarial variation $\Sigma_{\max}^2$ for strongly convex functions. Inspired by their work, we investigate the theoretical guarantees of optimistic online mirror descent (OMD) for the SEA model with smooth expected loss functions. For convex and smooth functions, we obtain the same $\mathcal{O}(\sqrt{\sigma_{1:T}^2}+\sqrt{\Sigma_{1:T}^2})$ regret bound, but with a relaxation of the convexity requirement from individual functions to expected functions. For strongly convex and smooth functions, we establish an $\mathcal{O}\left(\frac{1}{\lambda}\left(\sigma_{\max}^2+\Sigma_{\max}^2\right)\log \left(\left(\sigma_{1:T}^2 + \Sigma_{1:T}^2\right)/\left(\sigma_{\max}^2+\Sigma_{\max}^2\right)\right)\right)$ bound, better than their $\mathcal{O}((\sigma_{\max}^2$ $ + \Sigma_{\max}^2) \log T)$ result. For exp-concave and smooth functions, our approach yields a new $\mathcal{O}(d\log(\sigma_{1:T}^2+\Sigma_{1:T}^2))$ bound. Moreover, we introduce the first expected dynamic regret guarantee for the SEA model with convex and smooth expected functions, which is more favorable than static regret bounds in non-stationary environments. Furthermore, we expand our investigation to scenarios with non-smooth expected loss functions and propose novel algorithms built upon optimistic OMD with an implicit update, successfully attaining both static and dynamic regret guarantees. [abs] [ pdf ][ bib ] &copy JMLR 2024. ( edit, beta )

AAAI Conference 2024 Conference Paper

Safe Abductive Learning in the Presence of Inaccurate Rules

  • Xiao-Wen Yang
  • Jie-Jing Shao
  • Wei-Wei Tu
  • Yu-Feng Li
  • Wang-Zhou Dai
  • Zhi-Hua Zhou

Integrating complementary strengths of raw data and logical rules to improve the learning generalization has been recently shown promising and effective, e.g., abductive learning is one generic framework that can learn the perception model from data and reason between rules simultaneously. However, the performance would be seriously decreased when inaccurate logical rules appear, which may be even worse than baselines using only raw data. Efforts on this issue are highly desired while remain to be limited. This paper proposes a simple and effective safe abductive learning method to alleviate the harm caused by inaccurate rules. Unlike the existing methods which directly use all rules without correctness checks, it utilizes them selectively by constructing a graphical model with an adaptive reasoning process to prevent performance hazards. Theoretically, we show that induction and abduction are mutually beneficial, and can be rigorously justified from a classical maximum likelihood estimation perspective. Experiments on diverse tasks show that our method can tolerate at least twice as many inaccurate rules as accurate ones and achieve highly competitive performance while other methods can't. Moreover, the proposal can refine inaccurate rules and works well in extended weakly supervised scenarios.

AAMAS Conference 2023 Conference Paper

Learning Graph-Enhanced Commander-Executor for Multi-Agent Navigation

  • Xinyi Yang
  • Shiyu Huang
  • Yiwen Sun
  • Yuxiang Yang
  • Chao Yu
  • Wei-Wei Tu
  • Huazhong Yang
  • Yu Wang

This paper investigates the multi-agent navigation problem, which requires multiple agents to reach the target goals in a limited time. Multi-agent reinforcement learning (MARL) has shown promising results for solving this issue. However, it is inefficient for MARL to directly explore the (nearly) optimal policy in the large search space, which is exacerbated as the agent number increases (e. g. , 10+ agents) or the environment is more complex (e. g. , 3𝐷 simulator). Goal-conditioned hierarchical reinforcement learning (HRL) provides a promising direction to tackle this challenge by introducing a hierarchical structure to decompose the search space, where the low-level policy predicts primitive actions in the guidance of the goals derived from the high-level policy. In this paper, we propose Multi-Agent Graph-Enhanced Commander-EXecutor (MAGE-X), a graph-based goal-conditioned hierarchical method for multi-agent navigation tasks. MAGE-X comprises a high-level Goal Commander and a low-level Action Executor. The Goal Commander predicts the probability distribution of the goals and leverages them to assign the most appropriate final target to each agent. The Action Executor utilizes graph neural networks (GNN) to construct a subgraph for each agent that only contains its crucial partners to improve cooperation. Additionally, the Goal Encoder in the Action Executor captures the relationship between the agent and the designated goal to encourage the agent to reach the final target. The results show that MAGE-X outperforms the state-of-the-art MARL baselines with a 100% success rate with only 3 million training steps in multi-agent particle environments (MPE) with 50 agents, and at least a 12% higher success rate and 2× higher data efficiency in a more complicated quadrotor 3𝐷 navigation task.

ICML Conference 2023 Conference Paper

Optimistic Online Mirror Descent for Bridging Stochastic and Adversarial Online Convex Optimization

  • Sijia Chen
  • Wei-Wei Tu
  • Peng Zhao 0006
  • Lijun Zhang 0005

Stochastically Extended Adversarial (SEA) model is introduced by Sachs et al. (2022) as an interpolation between stochastic and adversarial online convex optimization. Under the smoothness condition, they demonstrate that the expected regret of optimistic follow-the-regularized-leader (FTRL) depends on the cumulative stochastic variance $\sigma_{1: T}^2$ and the cumulative adversarial variation $\Sigma_{1: T}^2$ for convex functions. They also provide a slightly weaker bound based on the maximal stochastic variance $\sigma_{\max}^2$ and the maximal adversarial variation $\Sigma_{\max}^2$ for strongly convex functions. Inspired by their work, we investigate the theoretical guarantees of optimistic online mirror descent (OMD) for the SEA model. For convex and smooth functions, we obtain the same $\mathcal{O}(\sqrt{\sigma_{1: T}^2}+\sqrt{\Sigma_{1: T}^2})$ regret bound, without the convexity requirement of individual functions. For strongly convex and smooth functions, we establish an $\mathcal{O}(\min\{\log (\sigma_{1: T}^2+\Sigma_{1: T}^2), (\sigma_{\max}^2 + \Sigma_{\max}^2) \log T\})$ bound, better than their $\mathcal{O}((\sigma_{\max}^2 + \Sigma_{\max}^2) \log T)$ result. For exp-concave and smooth functions, we achieve a new $\mathcal{O}(d\log(\sigma_{1: T}^2+\Sigma_{1: T}^2))$ bound. Owing to the OMD framework, we further establish dynamic regret for convex and smooth functions, which is more favorable in non-stationary online scenarios.

AAMAS Conference 2023 Conference Paper

TiZero: Mastering Multi-Agent Football with Curriculum Learning and Self-Play

  • Fanqi Lin
  • Shiyu Huang
  • Tim Pearce
  • Wenze Chen
  • Wei-Wei Tu

Multi-agent football poses an unsolved challenge in AI research. Existing work has focused on tackling simplified scenarios of the game, or else leveraging expert demonstrations. In this paper, we develop a multi-agent system to play the full 11 vs. 11 game mode, without demonstrations. This game mode contains aspects that present major challenges to modern reinforcement learning algorithms; multi-agent coordination, long-term planning, and non-transitivity. To address these challenges, we present TiZero; a self-evolving, multi-agent system that learns from scratch. TiZero introduces several innovations, including adaptive curriculum learning, a novel self-play strategy, and an objective that optimizes the policies of multiple agents jointly. Experimentally, it outperforms previous systems by a large margin on the Google Research Football environment, increasing win rates by over 30%. To demonstrate the generality of TiZero’s innovations, they are assessed on several environments beyond football; Overcooked, Multi-agent Particle- Environment, Tic-Tac-Toe and Connect-Four.

NeurIPS Conference 2022 Conference Paper

Online Frank-Wolfe with Arbitrary Delays

  • Yuanyu Wan
  • Wei-Wei Tu
  • Lijun Zhang

The online Frank-Wolfe (OFW) method has gained much popularity for online convex optimization due to its projection-free property. Previous studies show that OFW can attain an $O(T^{3/4})$ regret bound for convex losses and an $O(T^{2/3})$ regret bound for strongly convex losses. However, they assume that each gradient queried by OFW is revealed immediately, which may not hold in practice and limits the application of OFW. To address this limitation, we propose a delayed variant of OFW, which allows gradients to be delayed by arbitrary rounds. The main idea is to perform an update similar to OFW after receiving any delayed gradient, and play the latest decision for each round. Despite its simplicity, we prove that our delayed variant of OFW is able to achieve an $O(T^{3/4}+dT^{1/4})$ regret bound for convex losses and an $O(T^{2/3}+d\log T)$ regret bound for strongly convex losses, where $d$ is the maximum delay. This is quite surprising since under a relatively large amount of delay (e. g. , $d=O(\sqrt{T})$ for convex losses and $d=O(T^{2/3}/\log T)$ for strongly convex losses), the delayed variant of OFW enjoys the same regret bound as that of the original OFW.

JMLR Journal 2022 Journal Article

Projection-free Distributed Online Learning with Sublinear Communication Complexity

  • Yuanyu Wan
  • Guanghui Wang
  • Wei-Wei Tu
  • Lijun Zhang

To deal with complicated constraints via locally light computations in distributed online learning, a recent study has presented a projection-free algorithm called distributed online conditional gradient (D-OCG), and achieved an $O(T^{3/4})$ regret bound for convex losses, where $T$ is the number of total rounds. However, it requires $T$ communication rounds, and cannot utilize the strong convexity of losses. In this paper, we propose an improved variant of D-OCG, namely D-BOCG, which can attain the same $O(T^{3/4})$ regret bound with only $O(\sqrt{T})$ communication rounds for convex losses, and a better regret bound of $O(T^{2/3}(\log T)^{1/3})$ with fewer $O(T^{1/3}(\log T)^{2/3})$ communication rounds for strongly convex losses. The key idea is to adopt a delayed update mechanism that reduces the communication complexity, and redefine the surrogate loss function in D-OCG for exploiting the strong convexity. Furthermore, we provide lower bounds to demonstrate that the $O(\sqrt{T})$ communication rounds required by D-BOCG are optimal (in terms of $T$) for achieving the $O(T^{3/4})$ regret with convex losses, and the $O(T^{1/3}(\log T)^{2/3})$ communication rounds required by D-BOCG are near-optimal (in terms of $T$) for achieving the $O(T^{2/3}(\log T)^{1/3})$ regret with strongly convex losses up to polylogarithmic factors. Finally, to handle the more challenging bandit setting, in which only the loss value is available, we incorporate the classical one-point gradient estimator into D-BOCG, and obtain similar theoretical guarantees. [abs] [ pdf ][ bib ] &copy JMLR 2022. ( edit, beta )

NeurIPS Conference 2021 Conference Paper

Dual Adaptivity: A Universal Algorithm for Minimizing the Adaptive Regret of Convex Functions

  • Lijun Zhang
  • Guanghui Wang
  • Wei-Wei Tu
  • Wei Jiang
  • Zhi-Hua Zhou

To deal with changing environments, a new performance measure—adaptive regret, defined as the maximum static regret over any interval, was proposed in online learning. Under the setting of online convex optimization, several algorithms have been successfully developed to minimize the adaptive regret. However, existing algorithms lack universality in the sense that they can only handle one type of convex functions and need apriori knowledge of parameters. By contrast, there exist universal algorithms, such as MetaGrad, that attain optimal static regret for multiple types of convex functions simultaneously. Along this line of research, this paper presents the first universal algorithm for minimizing the adaptive regret of convex functions. Specifically, we borrow the idea of maintaining multiple learning rates in MetaGrad to handle the uncertainty of functions, and utilize the technique of sleeping experts to capture changing environments. In this way, our algorithm automatically adapts to the property of functions (convex, exponentially concave, or strongly convex), as well as the nature of environments (stationary or changing). As a by product, it also allows the type of functions to switch between rounds.

AAAI Conference 2021 Conference Paper

Explanation Consistency Training: Facilitating Consistency-Based Semi-Supervised Learning with Interpretability

  • Tao Han
  • Wei-Wei Tu
  • Yu-Feng Li

Unlabeled data exploitation and interpretability are usually both required in reality. They, however, are conducted independently, and very few works try to connect the two. For unlabeled data exploitation, state-of-the-art semi-supervised learning (SSL) results have been achieved via encouraging the consistency of model output on data perturbation, that is, consistency assumption. However, it remains hard for users to understand how particular decisions are made by state-ofthe-art SSL models. To this end, in this paper we first disclose that the consistency assumption is closely related to causality invariance, where causality invariance lies in the main reason why the consistency assumption is valid. We then propose ECT (Explanation Consistency Training) which encourages a consistent reason of model decision under data perturbation. ECT employs model explanation as a surrogate of the causality of model output, which is able to bridge state-of-the-art interpretability to SSL models and alleviate the high complexity of causality. We realize ECT-SM for vision and ECT- ATT for NLP tasks. Experimental results on real-world data sets validate the highly competitive performance and better explanation of the proposed algorithms.

NeurIPS Conference 2021 Conference Paper

OmniPrint: A Configurable Printed Character Synthesizer

  • Haozhe Sun
  • Wei-Wei Tu
  • Isabelle Guyon

We introduce OmniPrint, a synthetic data generator of isolated printed characters, geared toward machine learning research. It draws inspiration from famous datasets such as MNIST, SVHN and Omniglot, but offers the capability of generating a wide variety of printed characters from various languages, fonts and styles, with customized distortions. We include 935 fonts from 27 scripts and many types of distortions. As a proof of concept, we show various use cases, including an example of meta-learning dataset designed for the upcoming MetaDL NeurIPS 2021 competition. OmniPrint is available at https: //github. com/SunHaozhe/OmniPrint.

AAAI Conference 2020 Conference Paper

Efficient Neural Architecture Search via Proximal Iterations

  • Quanming Yao
  • Ju Xu
  • Wei-Wei Tu
  • Zhanxing Zhu

Neural architecture search (NAS) attracts much research attention because of its ability to identify better architectures than handcrafted ones. Recently, differentiable search methods become the state-of-the-arts on NAS, which can obtain highperformance architectures in several days. However, they still suffer from huge computation costs and inferior performance due to the construction of the supernet. In this paper, we propose an efficient NAS method based on proximal iterations (denoted as NASP). Different from previous works, NASP reformulates the search process as an optimization problem with a discrete constraint on architectures and a regularizer on model complexity. As the new objective is hard to solve, we further propose an efficient algorithm inspired by proximal iterations for optimization. In this way, NASP is not only much faster than existing differentiable search methods, but also can find better architectures and balance the model complexity. Finally, extensive experiments on various tasks demonstrate that NASP can obtain high-performance architectures with more than 10 times speedup over the state-of-the-arts.

ICML Conference 2020 Conference Paper

Projection-free Distributed Online Convex Optimization with $O(\sqrt{T})$ Communication Complexity

  • Yuanyu Wan
  • Wei-Wei Tu
  • Lijun Zhang 0005

To deal with complicated constraints via locally light computations in distributed online learning, a recent study has presented a projection-free algorithm called distributed online conditional gradient (D-OCG), and achieved an $O(T^{3/4})$ regret bound, where $T$ is the number of prediction rounds. However, in each round, the local learners of D-OCG need to communicate with their neighbors to share the local gradients, which results in a high communication complexity of $O(T)$. In this paper, we first propose an improved variant of D-OCG, namely D-BOCG, which enjoys an $O(T^{3/4})$ regret bound with only $O(\sqrt{T})$ communication complexity. The key idea is to divide the total prediction rounds into $\sqrt{T}$ equally-sized blocks, and only update the local learners at the beginning of each block by performing iterative linear optimization steps. Furthermore, to handle the more challenging bandit setting, in which only the loss value is available, we incorporate the classical one-point gradient estimator into D-BOCG, and obtain similar theoretical guarantees.

ICLR Conference 2020 Conference Paper

SAdam: A Variant of Adam for Strongly Convex Functions

  • Guanghui Wang 0006
  • Shiyin Lu
  • Quan Cheng 0001
  • Wei-Wei Tu
  • Lijun Zhang 0005

The Adam algorithm has become extremely popular for large-scale machine learning. Under convexity condition, it has been proved to enjoy a data-dependent $O(\sqrt{T})$ regret bound where $T$ is the time horizon. However, whether strong convexity can be utilized to further improve the performance remains an open problem. In this paper, we give an affirmative answer by developing a variant of Adam (referred to as SAdam) which achieves a data-dependent $O(\log T)$ regret bound for strongly convex functions. The essential idea is to maintain a faster decaying yet under controlled step size for exploiting strong convexity. In addition, under a special configuration of hyperparameters, our SAdam reduces to SC-RMSprop, a recently proposed variant of RMSprop for strongly convex functions, for which we provide the first data-dependent logarithmic regret bound. Empirical results on optimizing strongly convex functions and training deep networks demonstrate the effectiveness of our method.

IJCAI Conference 2019 Conference Paper

Learning for Tail Label Data: A Label-Specific Feature Approach

  • Tong Wei
  • Wei-Wei Tu
  • Yu-Feng Li

Tail label data (TLD) is prevalent in real-world tasks, and large-scale multi-label learning (LMLL) is its major learning scheme. Previous LMLL studies typically need to additionally take into account extensive head label data (HLD), and thus fail to guide the learning behavior of TLD. In many applications such as recommender systems, however, the prediction of tail label is very necessary, since it provides very important supplementary information. We call this kind of problem as \emph{tail label learning}. In this paper, we propose a novel method for the tail label learning problem. Based on the observation that the raw feature representation in LMLL data usually benefits HLD, which may not be suitable for TLD, we construct effective and rich label-specific features through exploring labeled data distribution and leveraging label correlations. Specifically, we employ clustering analysis to explore discriminative features for each tail label replacing the original high-dimensional and sparse features. In addition, due to the scarcity of positive examples of TLD, we encode knowledge from HLD by exploiting label correlations to enhance the label-specific features. Experimental results verify the superiority of the proposed method in terms of performance on TLD.

AAAI Conference 2019 Conference Paper

Multi-Fidelity Automatic Hyper-Parameter Tuning via Transfer Series Expansion

  • Yi-Qi Hu
  • Yang Yu
  • Wei-Wei Tu
  • Qiang Yang
  • Yuqiang Chen
  • Wenyuan Dai

Automatic machine learning (AutoML) aims at automatically choosing the best configuration for machine learning tasks. However, a configuration evaluation can be very time consuming particularly on learning tasks with large datasets. This limitation usually restrains derivative-free optimization from releasing its full power for a fine configuration search using many evaluations. To alleviate this limitation, in this paper, we propose a derivative-free optimization framework for AutoML using multi-fidelity evaluations. It uses many lowfidelity evaluations on small data subsets and very few highfidelity evaluations on the full dataset. However, the lowfidelity evaluations can be badly biased, and need to be corrected with only a very low cost. We thus propose the Transfer Series Expansion (TSE) that learns the low-fidelity correction predictor efficiently by linearly combining a set of base predictors. The base predictors can be obtained cheaply from down-scaled and experienced tasks. Experimental results on real-world AutoML problems verify that the proposed framework can accelerate derivative-free configuration search significantly by making use of the multi-fidelity evaluations.

AAAI Conference 2019 Conference Paper

Towards Automated Semi-Supervised Learning

  • Yu-Feng Li
  • Hai Wang
  • Tong Wei
  • Wei-Wei Tu

Automated Machine Learning (AutoML) aims to build an appropriate machine learning model for any unseen dataset automatically, i. e. , without human intervention. Great efforts have been devoted on AutoML while they typically focus on supervised learning. In many applications, however, semisupervised learning (SSL) are widespread and current AutoML systems could not well address SSL problems. In this paper, we propose to present an automated learning system for SSL (AUTO-SSL). First, meta-learning with enhanced meta-features is employed to quickly suggest some instantiations of the SSL techniques which are likely to perform quite well. Second, a large margin separation method is proposed to fine-tune the hyperparameters and more importantly, alleviate performance deterioration. The basic idea is that, if a certain hyperparameter owns a high quality, its predictive results on unlabeled data may have a large margin separation. Extensive empirical results over 200 cases demonstrate that our proposal on one side achieves highly competitive or better performance compared to the state-of-the-art AutoML system AUTO-SKLEARN and classical SSL techniques, on the other side unlike classical SSL techniques which often significantly degenerate performance, our proposal seldom suffers from such deficiency.