Trust-Region Minimization Algorithm for Training Responses (TRMinATR): The Rise of Machine Learning Techniques

Rafati, Jacob; DeGuchy, Omar; Marcia, Roummel F.

doi:10.23919/eusipco.2018.8553243

Cited by 4 publications

(5 citation statements)

References 16 publications

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“…is already computed when we computed the gradient in (26). The line search multi-batch L-BFGS optimization algorithm for deep Q-Leaning is provided in Algorithm 4.…”

Section: L-bfgs Line-search Deep Q-learning Methodsmentioning

confidence: 99%

“…These methods not only have the benefit of being independent from the fine-tuning of hyperaparameters, but they may improve upon the training performance and the convergence robustness of the line-search methods. Furthermore, trust-region L-BFGS methods can easily reject the search directions if the curvature condition is not satisfied in order to preserve the positive definiteness of the L-BFGS matrices [26]. The computational bottleneck of trust-region methods is the solution of the trust-region subproblem.…”

Section: Motivationmentioning

confidence: 99%

“…First, we introduce novel large-scale L-BFGS optimization methods using the trust-region strategy -as an alternative to the gradient descent methods. This method is called Trust-Region Minimization Algorithm for Training Responses (TRMinATR) [26]. We implement practical computational algorithms to solve the Empirical Risk Minimization (ERM) problems that arise in machine learning and deep learning applications.…”

Section: Applications and Objectivesmentioning

confidence: 99%

“…As the number of multi batches increase, the size of each batch decreases. Both methods were tested using different values of the memory parameter m[26].…”

mentioning

confidence: 99%

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Quasi-Newton Optimization Methods for Deep Learning Applications

Rafati

Marica

2020

Advances in Intelligent Systems and Computing

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Deep learning algorithms often require solving a highly non-linear and nonconvex unconstrained optimization problem. Methods for solving optimization problems in large-scale machine learning, such as deep learning and deep reinforcement learning (RL), are generally restricted to the class of first-order algorithms, like stochastic gradient descent (SGD). While SGD iterates are inexpensive to compute, they have slow theoretical convergence rates. Furthermore, they require exhaustive trial-and-error to fine-tune many learning parameters. Using second-order curvature information to find search directions can help with more robust convergence for non-convex optimization problems. However, computing Hessian matrices for large-scale problems is not computationally practical. Alternatively, quasi-Newton methods construct an approximate of the Hessian matrix to build a quadratic model of the objective function. Quasi-Newton methods, like SGD, require only first-order gradient information, but they can result in superlinear convergence, which makes them attractive alternatives to SGD. The limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) approach is one of the most popular quasi-Newton methods that construct positive definite Hessian approximations. In this chapter, we propose efficient optimization methods based on L-BFGS quasi-Newton methods using line search and trust-region strategies. Our methods bridge the disparity between first-and second-order methods by using gradient information to calculate low-rank updates to Hessian approximations. We provide formal convergence analysis of these methods as well as empirical results on deep learning applications, such as image classification tasks and deep reinforcement learning on a set of ATARI 2600 video games. Our results show a robust convergence with preferred generalization characteristics as well as fast training time.

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“…is already computed when we computed the gradient in (26). The line search multi-batch L-BFGS optimization algorithm for deep Q-Leaning is provided in Algorithm 4.…”

Section: L-bfgs Line-search Deep Q-learning Methodsmentioning

confidence: 99%

Section: Motivationmentioning

confidence: 99%

Section: Applications and Objectivesmentioning

confidence: 99%

“…As the number of multi batches increase, the size of each batch decreases. Both methods were tested using different values of the memory parameter m[26].…”

mentioning

confidence: 99%

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Quasi-Newton Optimization Methods for Deep Learning Applications

Rafati

Marica

2020

Advances in Intelligent Systems and Computing

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“…While line search and trust-region methods have already been applied to ML, as demonstrated by Rafati et al (2018), they have not yet been used in combination with adaptive batch size. Also, Lederrey et al (2018a,b) have demonstrated that the use of a full batch data is required at the end of the optimization process to achieve the appropriate precision for DCMs.…”

Section: Adaptive Batch Sizementioning

confidence: 99%

Estimation of discrete choice models with hybrid stochastic adaptive batch size algorithms

Lederrey,

Lurkin,

Hillel

et al. 2020

Preprint

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The emergence of Big Data has enabled new research perspectives in the discrete choice community. While the techniques to estimate Machine Learning models on a massive amount of data are well established, these have not yet been fully explored for the estimation of statistical Discrete Choice Models based on the random utility framework. In this article, we provide new ways of dealing with large datasets in the context of Discrete Choice Models. We achieve this by proposing new efficient stochastic optimization algorithms and extensively testing them alongside existing approaches. We develop these algorithms based on three main contributions: the use of a stochastic Hessian, the modification of the batch size, and a change of optimization algorithm depending on the batch size. A comprehensive experimental comparison of fifteen optimization algorithms is conducted across ten benchmark Discrete Choice Model cases. The results indicate that the HAMABS algorithm, a hybrid adaptive batch size stochastic method, is the best performing algorithm across the optimization benchmarks. This algorithm speeds up the optimization time by a factor of 23 on the largest model compared to existing algorithms used in practice. The integration of the new algorithms in Discrete Choice Models estimation software will significantly reduce the time required for model estimation and therefore enable researchers and practitioners to explore new approaches for the specification of choice models.

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Improving L-BFGS Initialization for Trust-Region Methods in Deep Learning

Rafati

Marcia

2018

2018 17th IEEE International Conference on Machine Learning and Applications (ICMLA)

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Trust-Region Minimization Algorithm for Training Responses (TRMinATR): The Rise of Machine Learning Techniques

Cited by 4 publications

References 16 publications

Quasi-Newton Optimization Methods for Deep Learning Applications

Quasi-Newton Optimization Methods for Deep Learning Applications

Estimation of discrete choice models with hybrid stochastic adaptive batch size algorithms

Improving L-BFGS Initialization for Trust-Region Methods in Deep Learning

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