GPU Memory Usage Optimization for Backward Propagation in Deep Network Training

In modern Deep Learning, it has been a trend to design larger Deep Neural Networks (DNNs) for the execution of more complex tasks and better accuracy. On the other hand, Convolutional Neural Networks (CNNs) have become the standard method for most of computer vision tasks. However, the memory allocation for the intermediate data in convolution layers can cause severe memory pressure during model training. Many solutions have been proposed to resolve the problem. Besides hardware-dependent solutions, a general methodology rematerialization can reduce GPU memory usage by trading computation for memory efficiently. The idea is to select a set of intermediate results during the forward phase as checkpoints, and only save them in memory to reduce memory usage. The backward phase recomputes the intermediate data from the closest checkpoints in memory as needed. This recomputation increases execution time but saves memory by not storing all intermediate results in memory during the forward phase. In this paper, we will focus on efficiently finding the optimal checkpoint subset to achieve the least peak memory usage during the model training. We first describe the theoretical background of the training of a neural network using mathematical equations. We use these equations to identify all essential data required during both forward and backward phases to compute the gradient of weights of the model. We first identify the checkpoint selection problem and propose a dynamic programming algorithm with time complexity O(n3) to solve the problem of finding the optimal checkpoint subset. With extensive experiments, we formulate a more accurate description of the problem using our theoretical analysis and revise the objective function based on the tracing, and propose an O(n)-time algorithm for finding the optimal checkpoint subset.

lil'HDoC: An Algorithm for Good Arm Identification under Small Threshold Gap

Good arm identification (GAI) is a pure-exploration bandit problem in which a single learner outputs an arm as soon as it is identified as a good arm. A good arm is defined as an arm with an expected reward greater than or equal to a given threshold. This paper focuses on the GAI problem under a small threshold gap, which refers to the distance between the expected rewards of arms and the given threshold. We propose a new algorithm called lil'HDoC to significantly improve the total sample complexity of the HDoC algorithm. We demonstrate that the sample complexity of the first $\lambda$ output arm in lil'HDoC is bounded by the original HDoC algorithm, except for one negligible term, when the distance between the expected reward and threshold is small. Extensive experiments confirm that our algorithm outperforms the state-of-the-art algorithms in both synthetic and real-world datasets.

Differential Good Arm Identification

This paper targets a variant of the stochastic multi-armed bandit problem called good arm identification (GAI). GAI is a pure-exploration bandit problem with the goal to output as many good arms using as few samples as possible, where a good arm is defined as an arm whose expected reward is greater than a given threshold. In this work, we propose DGAI - a differentiable good arm identification algorithm to improve the sample complexity of the state-of-the-art HDoC algorithm in a data-driven fashion. We also showed that the DGAI can further boost the performance of a general multi-arm bandit (MAB) problem given a threshold as a prior knowledge to the arm set. Extensive experiments confirm that our algorithm outperform the baseline algorithms significantly in both synthetic and real world datasets for both GAI and MAB tasks.