We give a simple, fast algorithm for hyperparameter optimization inspired by techniques from the analysis of Boolean functions. We focus on the high-dimensional regime where the canonical example is training a neural network with a large number of hyperparameters. The algorithm --- an iterative application of compressed sensing techniques for orthogonal polynomials --- requires only uniform sampling of the hyperparameters and is thus easily parallelizable.
Experiments for training deep neural networks on Cifar-10 show that compared to state-of-the-art tools (e.g., Hyperband and Spearmint), our algorithm finds significantly improved solutions, in some cases better than what is attainable by hand-tuning. In terms of overall running time (i.e., time required to sample various settings of hyperparameters plus additional computation time), we are at least an order of magnitude faster than Hyperband and Bayesian Optimization. We also outperform Random Search 8x.
Additionally, our method comes with provable guarantees and yields the first improvements on the sample complexity of learning decision trees in over two decades. In particular, we obtain the first quasi-polynomial time algorithm for learning noisy decision trees with polynomial sample complexity.
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PolarAir: A Compressed Sensing Scheme for Over-the-Air Federated Learning
We explore a scheme that enables the training of a deep neural network in a Federated Learning configuration over an additive white Gaussian noise channel. The goal is to create a low complexity, linear compression strategy, called PolarAir, that reduces the size of the gradient at the user side to lower the number of channel uses needed to transmit it. The suggested approach belongs to the family of compressed sensing techniques, yet it constructs the sensing matrix and the recovery procedure using multiple access techniques. Simulations show that it can reduce the number of channel uses by ∼30% when compared to conveying the gradient without compression. The main advantage of the proposed scheme over other schemes in the literature is its low time complexity. We also investigate the behavior of gradient updates and the performance of PolarAir throughout the training process to obtain insight on how best to construct this compression scheme based on compressed sensing.
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- NSF-PAR ID:
- 10443177
- Date Published:
- Journal Name:
- IEEE Information Theory Workshop (ITW)
- Page Range / eLocation ID:
- 136 to 141
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1109/ITW55543.2023.10161691
