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Title: A Resizable Mini-batch Gradient Descent based on a Multi-Armed Bandit

Paper content:
Determining the appropriate batch size for mini-batch gradient descent is always time consuming as it often relies on grid search.
This paper considers a resizable mini-batch gradient descent (RMGD) algorithm based on a multi-armed bandit that achieves performance equivalent to that of best fixed batch-size.
At each epoch, the RMGD samples a batch size according to a certain probability distribution proportional to a batch being successful in reducing the loss function.
Sampling from this probability provides a mechanism for exploring different batch size and exploiting batch sizes with history of success.
After obtaining the validation loss at each epoch with the sampled batch size, the probability distribution is updated to incorporate the effectiveness of the sampled batch size.
Experimental results show that the RMGD achieves performance better than the best performing single batch size.
It is surprising that the RMGD achieves better performance than grid search.
Furthermore, it attains this performance in a shorter amount of time than grid search.
Gradient descent (GD) is a common optimization algorithm for finding the minimum of the expected loss.
It takes iterative steps proportional to the negative gradient of the loss function at each iteration.
It is based on the observation that if the multi-variable loss functions f (w) is differentiable at point w, then f (w) decreases fastest in the direction of the negative gradient of f at w, i.e., −∇f (w).
The model parameters are updated iteratively in GD as follows: DISPLAYFORM0 where w t , g t , and η t are the model parameters, gradients of f with respect to w, and learning rate at time t respectively.
For small enough η t , f (w t ) ≥ f (w t+1 ) and ultimately the sequence of w t will move down toward a local minimum.
For a convex loss function, GD is guaranteed to converge to a global minimum with an appropriate learning rate.There are various issues to consider in gradient-based optimization.
First, GD can be extremely slow and impractical for large dataset: gradients of all the data have to be evaluated for each iteration.
With larger data size, the convergence rate, the computational cost and memory become critical, and special care is required to minimize these factors.
Second, for non-convex function which is often encountered in deep learning, GD can get stuck in a local minimum without the hope of escaping.
Third, stochastic gradient descent (SGD), which is based on the gradient of a single training sample, has large gradient variance, and it requires a large number of iterations.
This ultimately translates to slow convergence.
Mini-batch gradient descent (MGD), which is based on the gradient over a small batch of training data, trades off between the robustness of SGD and the stability of GD.
There are three advantages for using MGD over GD and SGD:
1) The batching allows both the efficiency of memory usage and implementations;
2) The model update frequency is higher than GD which allows for a more robust convergence avoiding local minimum;
3) MGD requires less iteration per epoch and provides a more stable update than SGD.
For these reasons, MGD has been a popular algorithm for machine learning.
However, selecting an appropriate batch size is difficult.
Various studies suggest that there is a close link between performance and batch size used in MGD Breuel (2015) ; Keskar et al. (2016) ; Wilson & Martinez (2003) .There
are various guidelines for selecting a batch size but have not been completely practical BID1 . Grid
search is a popular method but it comes at the expense of search time. There
are a small number of adaptive MGD algorithms to replace grid search BID3 ; BID4 Friedlander & Schmidt (2012) . These
algorithms increase the batch size gradually according to their own criterion. However
, these algorithms are based on convex loss function and hard to be applied to deep learning. For non-convex
optimization, it is difficult to determine the optimal batch size for best performance.This paper considers a resizable mini-batch gradient descent (RMGD) algorithm based on a multi-armed bandit for achieving best performance in grid search by selecting an appropriate batch size at each epoch with a probability defined as a function of its previous success/failure. At each epoch,
RMGD samples a batch size from its probability distribution, then uses the selected batch size for mini-batch gradient descent. After obtaining
the validation loss at each epoch, the probability distribution is updated to incorporate the effectiveness of the sampled batch size. The benefit of
RMGD is that it avoids the need for cumbersome grid search to achieve best performance and that it is simple enough to apply to any optimization algorithm using MGD. The detailed algorithm
of RMGD are described in Section 4, and experimental results are presented in Section 5.
Selecting batch size affects the model quality and training efficiency, and determining the appropriate batch size is time consuming and requires considerable resources as it often relies on grid search.
The focus of this paper is to design a simple robust algorithm that is theoretically sound and applicable in many situations.
This paper considers a resizable mini-batch gradient descent (RMGD) algorithm based on a multiarmed bandit that achieves equivalent performance to that of best fixed batch-size.
At each epoch, the RMGD samples a batch size according to certain probability distribution of a batch being successful in reducing the loss function.
Sampling from this probability provides a mechanism for exploring different batch size and exploiting batch sizes with history of success.
After obtaining the validation loss at each epoch with the sampled batch size, the probability distribution is updated to incorporate the effectiveness of the sampled batch size.The goal of this algorithm is not to achieve state-of-the-art accuracy but rather to select appropriate batch size which leads low misupdating and performs better.
The RMGD essentially assists the learning process to explore the possible domain of the batch size and exploit successful batch size.
The benefit of RMGD is that it avoids the need for cumbersome grid search to achieve best performance and that it is simple enough to apply to various field of machine learning including deep learning using MGD.
Experimental results show that the RMGD achieves the best grid search performance on various dataset, networks, and optimizers.
Furthermore, it, obviously, attains this performance in a shorter amount of time than the grid search.
Also, there is no need to worry about which batch size set or cost function to choose when setting RMGD.
In conclusion, the RMGD is effective and flexible mini-batch gradient descent algorithm.

assistant: text: An optimization algorithm that explores various batch sizes based on probability and automatically exploits successful batch size which minimizes validation loss.