Biased Stochastic First-Order Methods for Conditional Stochastic Optimization and Applications in Meta Learning
- URL: http://arxiv.org/abs/2002.10790v2
- Date: Sun, 2 Jun 2024 12:38:17 GMT
- Title: Biased Stochastic First-Order Methods for Conditional Stochastic Optimization and Applications in Meta Learning
- Authors: Yifan Hu, Siqi Zhang, Xin Chen, Niao He,
- Abstract summary: We propose a biased gradient descent (BSGD) for Conditional optimization problems.
Our lower bound analysis shows that BSGD cannot be improved for general convex objectives non objectives.
For this special setting, we propose an accelerated algorithm called biased SpiderBoost (BSpiderBoost) that matches the lower bound.
- Score: 24.12941820827126
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Conditional stochastic optimization covers a variety of applications ranging from invariant learning and causal inference to meta-learning. However, constructing unbiased gradient estimators for such problems is challenging due to the composition structure. As an alternative, we propose a biased stochastic gradient descent (BSGD) algorithm and study the bias-variance tradeoff under different structural assumptions. We establish the sample complexities of BSGD for strongly convex, convex, and weakly convex objectives under smooth and non-smooth conditions. Our lower bound analysis shows that the sample complexities of BSGD cannot be improved for general convex objectives and nonconvex objectives except for smooth nonconvex objectives with Lipschitz continuous gradient estimator. For this special setting, we propose an accelerated algorithm called biased SpiderBoost (BSpiderBoost) that matches the lower bound complexity. We further conduct numerical experiments on invariant logistic regression and model-agnostic meta-learning to illustrate the performance of BSGD and BSpiderBoost.
Related papers
- Non-asymptotic Analysis of Biased Adaptive Stochastic Approximation [0.8192907805418583]
We show that biased gradients converge to critical points for smooth non- functions.
We show how the effect of bias can be reduced by appropriate tuning.
arXiv Detail & Related papers (2024-02-05T10:17:36Z) - Robust Stochastic Optimization via Gradient Quantile Clipping [6.2844649973308835]
We introduce a quant clipping strategy for Gradient Descent (SGD)
We use gradient new outliers as norm clipping chains.
We propose an implementation of the algorithm using Huberiles.
arXiv Detail & Related papers (2023-09-29T15:24:48Z) - Enhancing Generalization of Universal Adversarial Perturbation through
Gradient Aggregation [40.18851174642427]
Deep neural networks are vulnerable to universal adversarial perturbation (UAP)
In this paper, we examine the serious dilemma of UAP generation methods from a generalization perspective.
We propose a simple and effective method called Gradient Aggregation (SGA)
SGA alleviates the gradient vanishing and escapes from poor local optima at the same time.
arXiv Detail & Related papers (2023-08-11T08:44:58Z) - Adaptive Zeroth-Order Optimisation of Nonconvex Composite Objectives [1.7640556247739623]
We analyze algorithms for zeroth-order entropy composite objectives, focusing on dependence on dimensionality.
This is achieved by exploiting low dimensional structure of the decision set using the mirror descent method with an estimation alike function.
To improve the gradient, we replace the classic sampling method based on Rademacher and show that the mini-batch method copes with non-Eucli geometry.
arXiv Detail & Related papers (2022-08-09T07:36:25Z) - Clipped Stochastic Methods for Variational Inequalities with
Heavy-Tailed Noise [64.85879194013407]
We prove the first high-probability results with logarithmic dependence on the confidence level for methods for solving monotone and structured non-monotone VIPs.
Our results match the best-known ones in the light-tails case and are novel for structured non-monotone problems.
In addition, we numerically validate that the gradient noise of many practical formulations is heavy-tailed and show that clipping improves the performance of SEG/SGDA.
arXiv Detail & Related papers (2022-06-02T15:21:55Z) - The Power of Adaptivity in SGD: Self-Tuning Step Sizes with Unbounded
Gradients and Affine Variance [46.15915820243487]
We show that AdaGrad-Norm exhibits an order optimal convergence of $mathcalOleft.
We show that AdaGrad-Norm exhibits an order optimal convergence of $mathcalOleft.
arXiv Detail & Related papers (2022-02-11T17:37:54Z) - Differentiable Annealed Importance Sampling and the Perils of Gradient
Noise [68.44523807580438]
Annealed importance sampling (AIS) and related algorithms are highly effective tools for marginal likelihood estimation.
Differentiability is a desirable property as it would admit the possibility of optimizing marginal likelihood as an objective.
We propose a differentiable algorithm by abandoning Metropolis-Hastings steps, which further unlocks mini-batch computation.
arXiv Detail & Related papers (2021-07-21T17:10:14Z) - Efficient Semi-Implicit Variational Inference [65.07058307271329]
We propose an efficient and scalable semi-implicit extrapolational (SIVI)
Our method maps SIVI's evidence to a rigorous inference of lower gradient values.
arXiv Detail & Related papers (2021-01-15T11:39:09Z) - Zeroth-Order Hybrid Gradient Descent: Towards A Principled Black-Box
Optimization Framework [100.36569795440889]
This work is on the iteration of zero-th-order (ZO) optimization which does not require first-order information.
We show that with a graceful design in coordinate importance sampling, the proposed ZO optimization method is efficient both in terms of complexity as well as as function query cost.
arXiv Detail & Related papers (2020-12-21T17:29:58Z) - Cogradient Descent for Bilinear Optimization [124.45816011848096]
We introduce a Cogradient Descent algorithm (CoGD) to address the bilinear problem.
We solve one variable by considering its coupling relationship with the other, leading to a synchronous gradient descent.
Our algorithm is applied to solve problems with one variable under the sparsity constraint.
arXiv Detail & Related papers (2020-06-16T13:41:54Z) - Towards Better Understanding of Adaptive Gradient Algorithms in
Generative Adversarial Nets [71.05306664267832]
Adaptive algorithms perform gradient updates using the history of gradients and are ubiquitous in training deep neural networks.
In this paper we analyze a variant of OptimisticOA algorithm for nonconcave minmax problems.
Our experiments show that adaptive GAN non-adaptive gradient algorithms can be observed empirically.
arXiv Detail & Related papers (2019-12-26T22:10:10Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.