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Understanding Short-Horizon Bias in Stochastic Meta-Optimization



Careful tuning of the learning rate, or even schedules thereof, can be crucial to effective neural net training. There has been much recent interest in gradient-based meta-optimization, where one tunes hyperparameters, or even learns an optimizer, in order to minimize the expected loss when the training procedure is unrolled. But because the training procedure must be unrolled thousands of times, the metaobjective must be defined with an orders-of-magnitude shorter time horizon than is typical for neural net training. We show that such short-horizon meta-objectives cause a serious bias towards small step sizes, an effect we term short-horizon bias. We introduce a toy problem, a noisy quadratic cost function, on which we analyze short-horizon bias by deriving and comparing the optimal schedules for short and long time horizons. We then run meta-optimization experiments (both offline and online) on standard benchmark datasets, showing that meta-optimization chooses too small a learning rate by multiple orders of magnitude, even when run with a moderately long time horizon (100 steps) typical of work in the area. We believe short-horizon bias is a fundamental problem that needs to be addressed if metaoptimization is to scale to practical neural net training regimes.


Yuhuai Wu, Mengye Ren, Renjie Liao, Roger B. Grosse


ICLR 2018

Full Paper

‘Understanding Short-Horizon Bias in Stochastic Meta-Optimization’ (PDF)

Uber ATG

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Mengye Ren
Mengye Ren is a research scientist at Uber ATG Toronto. He is also a PhD student in the machine learning group of the Department of Computer Science at the University of Toronto. He studied Engineering Science in his undergrad at the University of Toronto. His research interests are machine learning, neural networks, and computer vision. He is originally from Shanghai, China.
Renjie Liao
Renjie Liao is a PhD student in Machine Learning Group, Department of Computer Science, University of Toronto, supervised by Prof. Raquel Urtasun and Prof. Richard Zemel. He is also a Research Scientist in Uber Advanced Technology Group Toronto. He is also affiliated with Vector Institute. He received M.Phil. degree from Department of Computer Science and Engineering, Chinese University of Hong Kong, under the supervision of Prof. Jiaya Jia. He got B.Eng. degree from School of Automation Science and Electrical Engineering in Beihang University (former Beijing University of Aeronautics and Astronautics).