{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/error-feedback-shines-when-features-are-rare","title":"Error Feedback Shines when Features are Rare","arxiv_id":"2305.15264","date":"2023-05-24","proceeding":null,"authors":["Peter Richtárik","Elnur Gasanov","Konstantin Burlachenko"],"abstract":"We provide the first proof that gradient descent $\\left({\\color{green}\\sf GD}\\right)$ with greedy sparsification $\\left({\\color{green}\\sf TopK}\\right)$ and error feedback $\\left({\\color{green}\\sf EF}\\right)$ can obtain better communication complexity than vanilla ${\\color{green}\\sf GD}$ when solving the distributed optimization problem $\\min_{x\\in \\mathbb{R}^d} {f(x)=\\frac{1}{n}\\sum_{i=1}^n f_i(x)}$, where $n$ = # of clients, $d$ = # of features, and $f_1,\\dots,f_n$ are smooth nonconvex functions. Despite intensive research since 2014 when ${\\color{green}\\sf EF}$ was first proposed by Seide et al., this problem remained open until now. We show that ${\\color{green}\\sf EF}$ shines in the regime when features are rare, i.e., when each feature is present in the data owned by a small number of clients only. To illustrate our main result, we show that in order to find a random vector $\\hat{x}$ such that $\\lVert {\\nabla f(\\hat{x})} \\rVert^2 \\leq \\varepsilon$ in expectation, ${\\color{green}\\sf GD}$ with the ${\\color{green}\\sf Top1}$ sparsifier and ${\\color{green}\\sf EF}$ requires ${\\cal O} \\left(\\left( L+{\\color{blue}r} \\sqrt{ \\frac{{\\color{red}c}}{n} \\min \\left( \\frac{{\\color{red}c}}{n} \\max_i L_i^2, \\frac{1}{n}\\sum_{i=1}^n L_i^2 \\right) }\\right) \\frac{1}{\\varepsilon} \\right)$ bits to be communicated by each worker to the server only, where $L$ is the smoothness constant of $f$, $L_i$ is the smoothness constant of $f_i$, ${\\color{red}c}$ is the maximal number of clients owning any feature ($1\\leq {\\color{red}c} \\leq n$), and ${\\color{blue}r}$ is the maximal number of features owned by any client ($1\\leq {\\color{blue}r} \\leq d$). Clearly, the communication complexity improves as ${\\color{red}c}$ decreases (i.e., as features become more rare), and can be much better than the ${\\cal O}({\\color{blue}r} L \\frac{1}{\\varepsilon})$ communication complexity of ${\\color{green}\\sf GD}$ in the same regime.","url_abs":"https://arxiv.org/abs/2305.15264v1","url_pdf":"https://arxiv.org/pdf/2305.15264v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"error-feedback-shines-when-features-are-rare","repo_url":"https://github.com/burlachenkok/ef21_with_rare_features","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"distributed-optimization","task_name":"Distributed Optimization"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}