Flattened one-bit stochastic gradient descent: compressed distributed optimization with controlled variance
<|reference_start|>Flattened one-bit stochastic gradient descent: compressed distributed optimization with controlled variance: We propose a novel algorithm for distributed stochastic gradient descent (SGD) with compressed gradient communication in the parameter-server framework. Our gradient compression technique, named flattened one-bit stochastic gradient descent (FO-SGD), relies on two simple algorithmic ideas: (i) a one-bit quantization procedure leveraging the technique of dithering, and (ii) a randomized fast Walsh-Hadamard transform to flatten the stochastic gradient before quantization. As a result, the approximation of the true gradient in this scheme is biased, but it prevents commonly encountered algorithmic problems, such as exploding variance in the one-bit compression regime, deterioration of performance in the case of sparse gradients, and restrictive assumptions on the distribution of the stochastic gradients. In fact, we show SGD-like convergence guarantees under mild conditions. The compression technique can be used in both directions of worker-server communication, therefore admitting distributed optimization with full communication compression.<|reference_end|>
@article{stollenwerk2024flattened,
    title={Flattened one-bit stochastic gradient descent: compressed distributed
  optimization with controlled variance},
    author={Alexander Stollenwerk and Laurent Jacques},
    journal={arXiv preprint arXiv:2405.11095},
    year={2024},
    number={TR.2024.01},
    archivePrefix={arXiv},
    eprint={2405.11095},
    primaryClass={cs.LG cs.NA math.NA math.OC}
}