2024-06-30-jambulapati24b.md

title	section	abstract	layout	series	publisher	issn	id	month	tex_title	firstpage	lastpage	page	order	cycles	bibtex_author	author	date	address	container-title	volume	genre	issued	pdf	extras
Closing the Computational-Query Depth Gap in Parallel Stochastic Convex Optimization	Original Papers	We develop a new parallel algorithm for minimizing Lipschitz, convex functions with a stochastic subgradient oracle. The total number of queries made and the query depth, i.e., the number of parallel rounds of queries, match the prior state-of-the-art, [CJJLLST23], while improving upon the computational depth by a polynomial factor for sufficiently small accuracy. When combined with previous state-of-the-art methods our result closes a gap between the best-known query depth and the best-known computational depth of parallel algorithms. Our method starts with a \emph{ball acceleration} framework of previous parallel methods, i.e., [CJJJLST20, ACJJS21], which reduce the problem to minimizing a regularized Gaussian convolution of the function constrained to Euclidean balls. By developing and leveraging new stability properties of the Hessian of this induced function, we depart from prior parallel algorithms and reduce these ball-constrained optimization problems to stochastic unconstrained quadratic minimization problems. Although we are unable to prove concentration of the asymmetric matrices that we use to approximate this Hessian, we nevertheless develop an efficient parallel method for solving these quadratics. Interestingly, our algorithms can be improved using fast matrix multiplication and run in nearly-linear time if the matrix multiplication exponent is 2.	inproceedings	Proceedings of Machine Learning Research	PMLR	2640-3498	jambulapati24b	0	Closing the Computational-Query Depth Gap in Parallel Stochastic Convex Optimization	2608	2643	2608-2643	2608	false	Jambulapati, Arun and Sidford, Aaron and Tian, Kevin	given family Arun Jambulapati given family Aaron Sidford given family Kevin Tian	2024-06-30		Proceedings of Thirty Seventh Conference on Learning Theory	247	inproceedings	date-parts 2024 6 30	https://proceedings.mlr.press/v247/jambulapati24b/jambulapati24b.pdf