Due to a growing interest in deep learning applications [5], compute-intensive and long-running (hours to days) training jobs have become a significant component of datacenter workloads. A large fraction of these jobs is often exploratory, with the goal of determining the best model structure (e.g., the number of layers and channels in a convolutional neural network), hyperparameters (e.g., the learning rate), and data augmentation strategies for the target application. Notably, training jobs are often terminated early if their learning metrics (e.g., training and validation accuracy) are not converging, with only a few completing successfully. For this motivating application, we consider the problem of scheduling a set of jobs that can be terminated at predetermined checkpoints with known probabilities estimated from historical data. We prove that, in order to minimize the time to complete the first K successful jobs on a single server, optimal scheduling does not require preemption (even when preemption overhead is negligible) and provide an optimal policy; advantages of this policy are quantified through simulation. Related Work. While job scheduling has been investigated extensively in many scenarios (see [6] and [2] for a survey of recent result), most policies require that the cost of waiting times of each job be known at scheduling time; in contrast, in our setting the scheduler does not know which job will be the K-th successful job, and sojourn times of subsequent jobs do not contribute to the target metric. For example, [4, 3] minimize makespan (i.e., the time to complete all jobs) for known execution times and waiting time costs; similarly, Gittins index [1] and SR rank [7] minimize expected sojourn time of all jobs, i.e., both successfully completed jobs and jobs terminated early. Unfortunately, scheduling policies not distinguishing between these two types of jobs may favor jobs where the next stage is short and leads to early termination with high probability, which is an undesirable outcome in our applications of interest.
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Maximal Initial Learning Rates in Deep ReLU Networks
Training a neural network requires choosing a suitable learning rate, which involves a trade-off between speed and effectiveness of convergence. While there has been considerable theoretical and empirical analysis of how large the learning rate can be, most prior work focuses only on late-stage training. In this work, we introduce the maximal initial learning rate - the largest learning rate at which a randomly initialized neural network can successfully begin training and achieve (at least) a given threshold accuracy. Using a simple approach to estimate the maximal initial learning rate, we observe that in constant-width fully-connected ReLU networks, the maximal initial learning rate behaves differently from the maximum learning rate later in training. Specifically, we find that the maximal initial learning rate is well predicted as a power of depth times width, provided that (i) the width of the network is sufficiently large compared to the depth, and (ii) the input layer is trained at a relatively small learning rate. We further analyze the relationship between the maximal initial learning rate and the sharpness of the network at initialization, indicating they are closely though not inversely related. We formally prove bounds for the maximal initial learning rate in terms of depth times width that align with our empirical results.
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- NSF-PAR ID:
- 10479889
- Publisher / Repository:
- Proceedings of Machine Learning Research
- Date Published:
- Journal Name:
- Proceedings of Machine Learning Research
- ISSN:
- 2640-3498
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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