Policy Optimization Using Semiparametric Models for Dynamic Pricing
In this article, we study the contextual dynamic pricing problem where the market value of a product is linear in its observed features plus some market noise. Products are sold one at a time, and only a binary response indicating success or failure of a sale is observed. Our model setting is simila...
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Veröffentlicht in: | Journal of the American Statistical Association 2024-01, Vol.119 (545), p.552-564 |
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description | In this article, we study the contextual dynamic pricing problem where the market value of a product is linear in its observed features plus some market noise. Products are sold one at a time, and only a binary response indicating success or failure of a sale is observed. Our model setting is similar to the work by? except that we expand the demand curve to a semiparametric model and learn dynamically both parametric and nonparametric components. We propose a dynamic statistical learning and decision making policy that minimizes regret (maximizes revenue) by combining semiparametric estimation for a generalized linear model with unknown link and online decision making. Under mild conditions, for a market noise cdf
F
(
·
)
with mth order derivative (
m
≥
2
), our policy achieves a regret upper bound of
O
˜
d
(
T
2
m
+
1
4
m
−
1
)
, where T is the time horizon and
O
˜
d
is the order hiding logarithmic terms and the feature dimension d. The upper bound is further reduced to
O
˜
d
(
T
)
if F is super smooth. These upper bounds are close to
Ω
(
T
)
, the lower bound where F belongs to a parametric class. We further generalize these results to the case with dynamic dependent product features under the strong mixing condition.
Supplementary materials
for this article are available online. |
doi_str_mv | 10.1080/01621459.2022.2128359 |
format | Article |
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F
(
·
)
with mth order derivative (
m
≥
2
), our policy achieves a regret upper bound of
O
˜
d
(
T
2
m
+
1
4
m
−
1
)
, where T is the time horizon and
O
˜
d
is the order hiding logarithmic terms and the feature dimension d. The upper bound is further reduced to
O
˜
d
(
T
)
if F is super smooth. These upper bounds are close to
Ω
(
T
)
, the lower bound where F belongs to a parametric class. We further generalize these results to the case with dynamic dependent product features under the strong mixing condition.
Supplementary materials
for this article are available online.</description><identifier>ISSN: 0162-1459</identifier><identifier>ISSN: 1537-274X</identifier><identifier>EISSN: 1537-274X</identifier><identifier>DOI: 10.1080/01621459.2022.2128359</identifier><language>eng</language><publisher>Alexandria: Taylor & Francis</publisher><subject>Contextual dynamic pricing ; Decision making ; Decision theory ; Demand curves ; Generalized linear model with unknown link ; Generalized linear models ; income ; issues and policy ; Linear analysis ; linear models ; Lower bounds ; Market value ; markets ; Noise ; Nonparametric statistics ; Optimization ; Policy optimization ; Pricing ; Product specifications ; Regret ; Statistical models ; Statistics ; Upper bounds</subject><ispartof>Journal of the American Statistical Association, 2024-01, Vol.119 (545), p.552-564</ispartof><rights>2022 American Statistical Association 2022</rights><rights>2022 American Statistical Association</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c404t-13675a4af3eb4eb6d1a34ebdfa298c7df08a82f2544c0f60f97d02b1d47c7cc13</citedby><cites>FETCH-LOGICAL-c404t-13675a4af3eb4eb6d1a34ebdfa298c7df08a82f2544c0f60f97d02b1d47c7cc13</cites><orcidid>0000-0002-6818-4083</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.tandfonline.com/doi/pdf/10.1080/01621459.2022.2128359$$EPDF$$P50$$Ginformaworld$$H</linktopdf><linktohtml>$$Uhttps://www.tandfonline.com/doi/full/10.1080/01621459.2022.2128359$$EHTML$$P50$$Ginformaworld$$H</linktohtml><link.rule.ids>314,776,780,27901,27902,59620,60409</link.rule.ids></links><search><creatorcontrib>Fan, Jianqing</creatorcontrib><creatorcontrib>Guo, Yongyi</creatorcontrib><creatorcontrib>Yu, Mengxin</creatorcontrib><title>Policy Optimization Using Semiparametric Models for Dynamic Pricing</title><title>Journal of the American Statistical Association</title><description>In this article, we study the contextual dynamic pricing problem where the market value of a product is linear in its observed features plus some market noise. Products are sold one at a time, and only a binary response indicating success or failure of a sale is observed. Our model setting is similar to the work by? except that we expand the demand curve to a semiparametric model and learn dynamically both parametric and nonparametric components. We propose a dynamic statistical learning and decision making policy that minimizes regret (maximizes revenue) by combining semiparametric estimation for a generalized linear model with unknown link and online decision making. Under mild conditions, for a market noise cdf
F
(
·
)
with mth order derivative (
m
≥
2
), our policy achieves a regret upper bound of
O
˜
d
(
T
2
m
+
1
4
m
−
1
)
, where T is the time horizon and
O
˜
d
is the order hiding logarithmic terms and the feature dimension d. The upper bound is further reduced to
O
˜
d
(
T
)
if F is super smooth. These upper bounds are close to
Ω
(
T
)
, the lower bound where F belongs to a parametric class. We further generalize these results to the case with dynamic dependent product features under the strong mixing condition.
Supplementary materials
for this article are available online.</description><subject>Contextual dynamic pricing</subject><subject>Decision making</subject><subject>Decision theory</subject><subject>Demand curves</subject><subject>Generalized linear model with unknown link</subject><subject>Generalized linear models</subject><subject>income</subject><subject>issues and policy</subject><subject>Linear analysis</subject><subject>linear models</subject><subject>Lower bounds</subject><subject>Market value</subject><subject>markets</subject><subject>Noise</subject><subject>Nonparametric statistics</subject><subject>Optimization</subject><subject>Policy optimization</subject><subject>Pricing</subject><subject>Product specifications</subject><subject>Regret</subject><subject>Statistical models</subject><subject>Statistics</subject><subject>Upper bounds</subject><issn>0162-1459</issn><issn>1537-274X</issn><issn>1537-274X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><recordid>eNp9kE1LxDAQhoMouK7-BKHgxUvXfDbpTVk_QdkFXfAWsmkiWdqmJl2k_npTdr14cC4DwzMzLw8A5wjOEBTwCqICI8rKGYYYzzDCgrDyAEwQIzzHnL4fgsnI5CN0DE5i3MBUXIgJmC997fSQLbreNe5b9c632Sq69iN7NY3rVFCN6YPT2YuvTB0z60N2O7SqSaNlmifyFBxZVUdztu9TsLq_e5s_5s-Lh6f5zXOuKaR9jkjBmaLKErOmZl1USJHUK6twKTSvLBRKYIsZpRraAtqSVxCvUUW55lojMgWXu7td8J9bE3vZuKhNXavW-G2UBKY_nCIqEnrxB934bWhTOolLwpMYUbJEsR2lg48xGCu74BoVBomgHNXKX7VyVCv3atPe9W7PtUlHo758qCvZq6H2wQbVapfC_H_iB8Q0f5g</recordid><startdate>20240102</startdate><enddate>20240102</enddate><creator>Fan, Jianqing</creator><creator>Guo, Yongyi</creator><creator>Yu, Mengxin</creator><general>Taylor & Francis</general><general>Taylor & Francis Ltd</general><scope>AAYXX</scope><scope>CITATION</scope><scope>8BJ</scope><scope>FQK</scope><scope>JBE</scope><scope>K9.</scope><scope>7S9</scope><scope>L.6</scope><orcidid>https://orcid.org/0000-0002-6818-4083</orcidid></search><sort><creationdate>20240102</creationdate><title>Policy Optimization Using Semiparametric Models for Dynamic Pricing</title><author>Fan, Jianqing ; Guo, Yongyi ; Yu, Mengxin</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c404t-13675a4af3eb4eb6d1a34ebdfa298c7df08a82f2544c0f60f97d02b1d47c7cc13</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Contextual dynamic pricing</topic><topic>Decision making</topic><topic>Decision theory</topic><topic>Demand curves</topic><topic>Generalized linear model with unknown link</topic><topic>Generalized linear models</topic><topic>income</topic><topic>issues and policy</topic><topic>Linear analysis</topic><topic>linear models</topic><topic>Lower bounds</topic><topic>Market value</topic><topic>markets</topic><topic>Noise</topic><topic>Nonparametric statistics</topic><topic>Optimization</topic><topic>Policy optimization</topic><topic>Pricing</topic><topic>Product specifications</topic><topic>Regret</topic><topic>Statistical models</topic><topic>Statistics</topic><topic>Upper bounds</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Fan, Jianqing</creatorcontrib><creatorcontrib>Guo, Yongyi</creatorcontrib><creatorcontrib>Yu, Mengxin</creatorcontrib><collection>CrossRef</collection><collection>International Bibliography of the Social Sciences (IBSS)</collection><collection>International Bibliography of the Social Sciences</collection><collection>International Bibliography of the Social Sciences</collection><collection>ProQuest Health & Medical Complete (Alumni)</collection><collection>AGRICOLA</collection><collection>AGRICOLA - Academic</collection><jtitle>Journal of the American Statistical Association</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Fan, Jianqing</au><au>Guo, Yongyi</au><au>Yu, Mengxin</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Policy Optimization Using Semiparametric Models for Dynamic Pricing</atitle><jtitle>Journal of the American Statistical Association</jtitle><date>2024-01-02</date><risdate>2024</risdate><volume>119</volume><issue>545</issue><spage>552</spage><epage>564</epage><pages>552-564</pages><issn>0162-1459</issn><issn>1537-274X</issn><eissn>1537-274X</eissn><abstract>In this article, we study the contextual dynamic pricing problem where the market value of a product is linear in its observed features plus some market noise. Products are sold one at a time, and only a binary response indicating success or failure of a sale is observed. Our model setting is similar to the work by? except that we expand the demand curve to a semiparametric model and learn dynamically both parametric and nonparametric components. We propose a dynamic statistical learning and decision making policy that minimizes regret (maximizes revenue) by combining semiparametric estimation for a generalized linear model with unknown link and online decision making. Under mild conditions, for a market noise cdf
F
(
·
)
with mth order derivative (
m
≥
2
), our policy achieves a regret upper bound of
O
˜
d
(
T
2
m
+
1
4
m
−
1
)
, where T is the time horizon and
O
˜
d
is the order hiding logarithmic terms and the feature dimension d. The upper bound is further reduced to
O
˜
d
(
T
)
if F is super smooth. These upper bounds are close to
Ω
(
T
)
, the lower bound where F belongs to a parametric class. We further generalize these results to the case with dynamic dependent product features under the strong mixing condition.
Supplementary materials
for this article are available online.</abstract><cop>Alexandria</cop><pub>Taylor & Francis</pub><doi>10.1080/01621459.2022.2128359</doi><tpages>13</tpages><orcidid>https://orcid.org/0000-0002-6818-4083</orcidid></addata></record> |
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source | Taylor & Francis:Master (3349 titles) |
subjects | Contextual dynamic pricing Decision making Decision theory Demand curves Generalized linear model with unknown link Generalized linear models income issues and policy Linear analysis linear models Lower bounds Market value markets Noise Nonparametric statistics Optimization Policy optimization Pricing Product specifications Regret Statistical models Statistics Upper bounds |
title | Policy Optimization Using Semiparametric Models for Dynamic Pricing |
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