On Traceability in Stochastic Convex Optimization

In this paper, we investigate the necessity of traceability for accurate learning in stochastic convex optimization (SCO) under geometries. Informally, we say a learning algorithm is -traceable if, by analyzing its output, it is possible to identify at least of its training samples. Our main results uncover a fundamental tradeoff between traceability and excess risk in SCO. For every , we establish the existence of an excess risk threshold below which every sample-efficient learner is traceable with the number of samples which is a constant fraction of its training sample. For , this threshold coincides with the best excess risk of differentially private (DP) algorithms, i.e., above this threshold, there exist algorithms that are not traceable, which corresponds to a sharp phase transition. For , this threshold instead gives novel lower bounds for DP learning, partially closing an open problem in this setup. En route to establishing these results, we prove a sparse variant of the fingerprinting lemma, which is of independent interest to the community.
View on arXiv@article{voitovych2025_2502.17384, title={ On Traceability in $\ell_p$ Stochastic Convex Optimization }, author={ Sasha Voitovych and Mahdi Haghifam and Idan Attias and Gintare Karolina Dziugaite and Roi Livni and Daniel M. Roy }, journal={arXiv preprint arXiv:2502.17384}, year={ 2025 } }