Minimal Communication-Cost Statistical Learning
<|reference_start|>Minimal Communication-Cost Statistical Learning: A client device which has access to $n$ training data samples needs to obtain a statistical hypothesis or model $W$ and then to send it to a remote server. The client and the server devices share some common randomness sequence as well as a prior on the hypothesis space. In this problem a suitable hypothesis or model $W$ should meet two distinct design criteria simultaneously: (i) small (population) risk during the inference phase and (ii) small 'complexity' for it to be conveyed to the server with minimum communication cost. In this paper, we propose a joint training and source coding scheme with provable in-expectation guarantees, where the expectation is over the encoder's output message. Specifically, we show that by imposing a constraint on a suitable Kullback-Leibler divergence between the conditional distribution induced by a compressed learning model $\widehat{W}$ given $W$ and the prior, one guarantees simultaneously small average empirical risk (aka training loss), small average generalization error and small average communication cost. We also consider a one-shot scenario in which the guarantees on the empirical risk and generalization error are obtained for every encoder's output message.<|reference_end|>
@article{sefidgaran2024minimal,
    title={Minimal Communication-Cost Statistical Learning},
    author={Milad Sefidgaran, Abdellatif Zaidi, Piotr Krasnowski},
    journal={arXiv preprint arXiv:2406.08193},
    year={2024},
    archivePrefix={arXiv},
    eprint={2406.08193},
    primaryClass={stat.ML cs.IT cs.LG math.IT}
}