Improved Complexities for Stochastic Conditional Gradient Methods under Interpolation-like Conditions
We analyze stochastic conditional gradient methods for constrained optimization problems arising in over-parametrized machine learning. We show that one could leverage the interpolation-like conditions satisfied by such models to obtain improved oracle complexities. Specifically, when the objective...
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext bestellen |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | |
|---|---|
| container_issue | |
| container_start_page | |
| container_title | |
| container_volume | |
| creator | Xiao, Tesi Balasubramanian, Krishnakumar Ghadimi, Saeed |
| description | We analyze stochastic conditional gradient methods for constrained
optimization problems arising in over-parametrized machine learning. We show
that one could leverage the interpolation-like conditions satisfied by such
models to obtain improved oracle complexities. Specifically, when the objective
function is convex, we show that the conditional gradient method requires
$\mathcal{O}(\epsilon^{-2})$ calls to the stochastic gradient oracle to find an
$\epsilon$-optimal solution. Furthermore, by including a gradient sliding step,
we show that the number of calls reduces to $\mathcal{O}(\epsilon^{-1.5})$. |
| doi_str_mv | 10.48550/arxiv.2006.08167 |
| format | Article |
| fullrecord | <record><control><sourceid>arxiv_GOX</sourceid><recordid>TN_cdi_arxiv_primary_2006_08167</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2006_08167</sourcerecordid><originalsourceid>FETCH-LOGICAL-a677-62a128a293f0d6a3c98a3a08ca57aa0c4f7b74906366a83ec82485fae27fac923</originalsourceid><addsrcrecordid>eNpFj7FOwzAURb0woMIHMOEfSHDsxHZGFEGJVMRA9-hhP6sWThw5pip_T1qQmO5w7r3SIeSuYmWtm4Y9QDr5Y8kZkyXTlVTXBPtxTvGIlnZxnAOefPa4UBcTfc_RHGDJ3qxssiuIEwS6TWA9Tpm-Yj5Eu9CvyWKi_ZQxzTHAuVYE_4n_q-WGXDkIC97-5Ybsn5_23Uuxe9v23eOuAKlUITlUXANvhWNWgjCtBgFMG2gUADO1Ux-qbpkUUoIWaDRftRwgVw5My8WG3P_eXjyHOfkR0vdw9h0uvuIHmcpSiw</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Improved Complexities for Stochastic Conditional Gradient Methods under Interpolation-like Conditions</title><source>arXiv.org</source><creator>Xiao, Tesi ; Balasubramanian, Krishnakumar ; Ghadimi, Saeed</creator><creatorcontrib>Xiao, Tesi ; Balasubramanian, Krishnakumar ; Ghadimi, Saeed</creatorcontrib><description>We analyze stochastic conditional gradient methods for constrained
optimization problems arising in over-parametrized machine learning. We show
that one could leverage the interpolation-like conditions satisfied by such
models to obtain improved oracle complexities. Specifically, when the objective
function is convex, we show that the conditional gradient method requires
$\mathcal{O}(\epsilon^{-2})$ calls to the stochastic gradient oracle to find an
$\epsilon$-optimal solution. Furthermore, by including a gradient sliding step,
we show that the number of calls reduces to $\mathcal{O}(\epsilon^{-1.5})$.</description><identifier>DOI: 10.48550/arxiv.2006.08167</identifier><language>eng</language><subject>Computer Science - Learning ; Mathematics - Optimization and Control ; Statistics - Machine Learning</subject><creationdate>2020-06</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,778,883</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2006.08167$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2006.08167$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Xiao, Tesi</creatorcontrib><creatorcontrib>Balasubramanian, Krishnakumar</creatorcontrib><creatorcontrib>Ghadimi, Saeed</creatorcontrib><title>Improved Complexities for Stochastic Conditional Gradient Methods under Interpolation-like Conditions</title><description>We analyze stochastic conditional gradient methods for constrained
optimization problems arising in over-parametrized machine learning. We show
that one could leverage the interpolation-like conditions satisfied by such
models to obtain improved oracle complexities. Specifically, when the objective
function is convex, we show that the conditional gradient method requires
$\mathcal{O}(\epsilon^{-2})$ calls to the stochastic gradient oracle to find an
$\epsilon$-optimal solution. Furthermore, by including a gradient sliding step,
we show that the number of calls reduces to $\mathcal{O}(\epsilon^{-1.5})$.</description><subject>Computer Science - Learning</subject><subject>Mathematics - Optimization and Control</subject><subject>Statistics - Machine Learning</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNpFj7FOwzAURb0woMIHMOEfSHDsxHZGFEGJVMRA9-hhP6sWThw5pip_T1qQmO5w7r3SIeSuYmWtm4Y9QDr5Y8kZkyXTlVTXBPtxTvGIlnZxnAOefPa4UBcTfc_RHGDJ3qxssiuIEwS6TWA9Tpm-Yj5Eu9CvyWKi_ZQxzTHAuVYE_4n_q-WGXDkIC97-5Ybsn5_23Uuxe9v23eOuAKlUITlUXANvhWNWgjCtBgFMG2gUADO1Ux-qbpkUUoIWaDRftRwgVw5My8WG3P_eXjyHOfkR0vdw9h0uvuIHmcpSiw</recordid><startdate>20200615</startdate><enddate>20200615</enddate><creator>Xiao, Tesi</creator><creator>Balasubramanian, Krishnakumar</creator><creator>Ghadimi, Saeed</creator><scope>AKY</scope><scope>AKZ</scope><scope>EPD</scope><scope>GOX</scope></search><sort><creationdate>20200615</creationdate><title>Improved Complexities for Stochastic Conditional Gradient Methods under Interpolation-like Conditions</title><author>Xiao, Tesi ; Balasubramanian, Krishnakumar ; Ghadimi, Saeed</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a677-62a128a293f0d6a3c98a3a08ca57aa0c4f7b74906366a83ec82485fae27fac923</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Computer Science - Learning</topic><topic>Mathematics - Optimization and Control</topic><topic>Statistics - Machine Learning</topic><toplevel>online_resources</toplevel><creatorcontrib>Xiao, Tesi</creatorcontrib><creatorcontrib>Balasubramanian, Krishnakumar</creatorcontrib><creatorcontrib>Ghadimi, Saeed</creatorcontrib><collection>arXiv Computer Science</collection><collection>arXiv Mathematics</collection><collection>arXiv Statistics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Xiao, Tesi</au><au>Balasubramanian, Krishnakumar</au><au>Ghadimi, Saeed</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Improved Complexities for Stochastic Conditional Gradient Methods under Interpolation-like Conditions</atitle><date>2020-06-15</date><risdate>2020</risdate><abstract>We analyze stochastic conditional gradient methods for constrained
optimization problems arising in over-parametrized machine learning. We show
that one could leverage the interpolation-like conditions satisfied by such
models to obtain improved oracle complexities. Specifically, when the objective
function is convex, we show that the conditional gradient method requires
$\mathcal{O}(\epsilon^{-2})$ calls to the stochastic gradient oracle to find an
$\epsilon$-optimal solution. Furthermore, by including a gradient sliding step,
we show that the number of calls reduces to $\mathcal{O}(\epsilon^{-1.5})$.</abstract><doi>10.48550/arxiv.2006.08167</doi><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext_linktorsrc |
| identifier | DOI: 10.48550/arxiv.2006.08167 |
| ispartof | |
| issn | |
| language | eng |
| recordid | cdi_arxiv_primary_2006_08167 |
| source | arXiv.org |
| subjects | Computer Science - Learning Mathematics - Optimization and Control Statistics - Machine Learning |
| title | Improved Complexities for Stochastic Conditional Gradient Methods under Interpolation-like Conditions |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-16T03%3A00%3A33IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-arxiv_GOX&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Improved%20Complexities%20for%20Stochastic%20Conditional%20Gradient%20Methods%20under%20Interpolation-like%20Conditions&rft.au=Xiao,%20Tesi&rft.date=2020-06-15&rft_id=info:doi/10.48550/arxiv.2006.08167&rft_dat=%3Carxiv_GOX%3E2006_08167%3C/arxiv_GOX%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true |