arXiv subjects

Shangqian Gao

Publications and source records attributed to Shangqian Gao.

42 records · Page 3Linked to original sources

arXiv2022

Enhanced Bilevel Optimization via Bregman Distance

Bilevel optimization has been recently used in many machine learning problems such as hyperparameter optimization, policy optimization, and meta learning. Although many bilevel optimization methods have been proposed, they still suffer from the high computational complexities and do not consider the more general bilevel problems with nonsmooth regularization. In the paper, thus, we propose a class of enhanced bilevel optimization methods with using Bregman distance to solve bilevel optimization problems, where the outer subproblem is nonconvex and possibly nonsmooth, and the inner subproblem is strongly convex. Specifically, we propose a bilevel optimization method based on Bregman distance (BiO-BreD) to solve deterministic bilevel problems, which achieves a lower computational complexity than the best known results. Meanwhile, we also propose a stochastic bilevel optimization method (SBiO-BreD) to solve stochastic bilevel problems based on stochastic approximated gradients and Bregman distance. Moreover, we further propose an accelerated version of SBiO-BreD method (ASBiO-BreD) using the variance-reduced technique, which can achieve a lower computational complexity than the best known computational complexities with respect to condition number $κ$ and target accuracy $ε$ for finding an $ε$-stationary point. We conduct data hyper-cleaning task and hyper-representation learning task to demonstrate that our new algorithms outperform related bilevel optimization approaches.

math.OC↗

arXiv2022

Interpretations Steered Network Pruning via Amortized Inferred Saliency Maps

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}

cs.CV↗

arXiv2022

Bregman Gradient Policy Optimization

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.

cs.LG↗

arXiv2022

Accelerated Zeroth-Order and First-Order Momentum Methods from Mini to Minimax Optimization

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.

math.OC↗

arXiv2020

Momentum-Based Policy Gradient Methods

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.

cs.LG↗

arXiv2019

Zeroth-Order Stochastic Alternating Direction Method of Multipliers for Nonconvex Nonsmooth Optimization

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.

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