{"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/accelerated-bregman-proximal-gradient-methods","title":"Accelerated Bregman Proximal Gradient Methods for Relatively Smooth Convex Optimization","arxiv_id":"1808.03045","date":"2018-08-09","proceeding":null,"authors":["Filip Hanzely","Peter Richtarik","Lin Xiao"],"abstract":"We consider the problem of minimizing the sum of two convex functions: one is differentiable and relatively smooth with respect to a reference convex function, and the other can be nondifferentiable but simple to optimize. We investigate a triangle scaling property of the Bregman distance generated by the reference convex function and present accelerated Bregman proximal gradient (ABPG) methods that attain an $O(k^{-\\gamma})$ convergence rate, where $\\gamma\\in(0,2]$ is the triangle scaling exponent (TSE) of the Bregman distance. For the Euclidean distance, we have $\\gamma=2$ and recover the convergence rate of Nesterov's accelerated gradient methods. For non-Euclidean Bregman distances, the TSE can be much smaller (say $\\gamma\\leq 1$), but we show that a relaxed definition of intrinsic TSE is always equal to 2. We exploit the intrinsic TSE to develop adaptive ABPG methods that converge much faster in practice. Although theoretical guarantees on a fast convergence rate seem to be out of reach in general, our methods obtain empirical $O(k^{-2})$ rates in numerical experiments on several applications and provide posterior numerical certificates for the fast rates.","url_abs":"https://arxiv.org/abs/1808.03045v3","url_pdf":"https://arxiv.org/pdf/1808.03045v3.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":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"accelerated-bregman-proximal-gradient-methods","repo_url":"https://github.com/Microsoft/accbpg","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"MIT"}},{"paper_slug":"accelerated-bregman-proximal-gradient-methods","repo_url":"https://github.com/linxiaolx/accbpg","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1808.03045","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1808.03045"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. Samples come from repositories linked to the paper, official or community; repo_kind says which.","repos":[{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/linxiaolx/accbpg","reach":null},{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/Microsoft/accbpg","reach":{"status":"ok","spdx":"MIT"}}],"summary":{"ran_fixture":2,"ran_honours":1,"unverified":8},"by_repo_kind":{"official":{"samples":11,"ran":3,"repositories":2}},"repo_kind_vocabulary":{"official":"The archive marks this repository official for the paper","named_in_paper":"The archive records that the paper mentions this repository; it is not marked official","listed":"In the archive's code links for this paper, not marked official and not recorded as mentioned in the paper","found_in_text":"Syntology found this repository in the paper's own text; whether it is the authors' implementation is not asserted","community":"Not in the archive's code links for this paper; a community repository Syntology harvested"},"n_pointer_only_for_licence":0,"samples":[{"code_sha256_prefix":"9a55fc3fd11346ec","entry":"ABPG","repo":"linxiaolx/accbpg","repo_kind":"official","path":"accbpg/algorithms.py","file_url":"https://github.com/linxiaolx/accbpg/blob/HEAD/accbpg/algorithms.py","link_basis":"first_harvest_node","language":"python","status":"ran_fixture","verification_level":1,"contract_check":"RAISES","metamorphic_tier":"none","behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"9a55fc3fd11346ec"}},{"code_sha256_prefix":"70d648a19e9e5f2a","entry":"BPG","repo":"linxiaolx/accbpg","repo_kind":"official","path":"accbpg/algorithms.py","file_url":"https://github.com/linxiaolx/accbpg/blob/HEAD/accbpg/algorithms.py","link_basis":"first_harvest_node","language":"python","status":"ran_fixture","verification_level":1,"contract_check":"RAISES","metamorphic_tier":"none","behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"70d648a19e9e5f2a"}},{"code_sha256_prefix":"5aabc13a3b3cb060","entry":"solve_theta","repo":"linxiaolx/accbpg","repo_kind":"official","path":"accbpg/algorithms.py","file_url":"https://github.com/linxiaolx/accbpg/blob/HEAD/accbpg/algorithms.py","link_basis":"first_harvest_node","language":"python","status":"ran_honours","verification_level":1,"contract_check":"HONOURS","metamorphic_tier":"well_formed","behaviour_fingerprint":true,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"5aabc13a3b3cb060"}},{"code_sha256_prefix":"6d3542f113696500","entry":"D_opt_FW","repo":"Microsoft/accbpg","repo_kind":"official","path":"accbpg/D_opt_alg.py","file_url":"https://github.com/Microsoft/accbpg/blob/HEAD/accbpg/D_opt_alg.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"6d3542f113696500"}},{"code_sha256_prefix":"ebb43079607596cc","entry":"D_opt_FW_away","repo":"Microsoft/accbpg","repo_kind":"official","path":"accbpg/D_opt_alg.py","file_url":"https://github.com/Microsoft/accbpg/blob/HEAD/accbpg/D_opt_alg.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"ebb43079607596cc"}},{"code_sha256_prefix":"87864de3167417a5","entry":"D_opt_KYinit","repo":"Microsoft/accbpg","repo_kind":"official","path":"accbpg/applications.py","file_url":"https://github.com/Microsoft/accbpg/blob/HEAD/accbpg/applications.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"87864de3167417a5"}},{"code_sha256_prefix":"5ff255477435bde3","entry":"D_opt_design","repo":"Microsoft/accbpg","repo_kind":"official","path":"accbpg/applications.py","file_url":"https://github.com/Microsoft/accbpg/blob/HEAD/accbpg/applications.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"5ff255477435bde3"}},{"code_sha256_prefix":"0779cc54868c0714","entry":"D_opt_libsvm","repo":"Microsoft/accbpg","repo_kind":"official","path":"accbpg/applications.py","file_url":"https://github.com/Microsoft/accbpg/blob/HEAD/accbpg/applications.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"0779cc54868c0714"}},{"code_sha256_prefix":"8097e49b7557dfbf","entry":"load_libsvm_file","repo":"Microsoft/accbpg","repo_kind":"official","path":"accbpg/utils.py","file_url":"https://github.com/Microsoft/accbpg/blob/HEAD/accbpg/utils.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"8097e49b7557dfbf"}},{"code_sha256_prefix":"39b1e2f7bd6e45fb","entry":"mnist_2digits","repo":"Microsoft/accbpg","repo_kind":"official","path":"accbpg/utils.py","file_url":"https://github.com/Microsoft/accbpg/blob/HEAD/accbpg/utils.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"39b1e2f7bd6e45fb"}},{"code_sha256_prefix":"fb69d5f3793a0e5b","entry":"shuffle_data","repo":"Microsoft/accbpg","repo_kind":"official","path":"accbpg/utils.py","file_url":"https://github.com/Microsoft/accbpg/blob/HEAD/accbpg/utils.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"fb69d5f3793a0e5b"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}