Asymptotic Optimality of Finite Models for Witsenhausen’s Counterexample and Beyond View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

2018

AUTHORS

Naci Saldi , Tamás Linder , Serdar Yüksel

ABSTRACT

In this chapter, we study the approximation of Witsenhausen’s counterexample and the Gaussian relay channel problem by using the results of the previous chapter. In particular, our goal is to establish that finite models obtained through the uniform quantization of the observation and action spaces result in a sequence of policies whose costs converge to the value function. We note that the operation of quantization has typically been the method to show that a non-linear policy can perform better than an optimal linear policy, both for Witsenhausen’s counterexample [10, 86] and the Gaussian relay channel problem [88, 152]. Our findings show that for a large class of problems, quantized policies not only may perform better than linear policies, but that they are actually almost optimal. More... »

PAGES

177-188

Book

TITLE

Finite Approximations in Discrete-Time Stochastic Control

ISBN

978-3-319-79032-9
978-3-319-79033-6

Author Affiliations

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-3-319-79033-6_9

DOI

http://dx.doi.org/10.1007/978-3-319-79033-6_9

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1103951463


Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
Incoming Citations Browse incoming citations for this publication using opencitations.net

JSON-LD is the canonical representation for SciGraph data.

TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

[
  {
    "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
    "about": [
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/1402", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Applied Economics", 
        "type": "DefinedTerm"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/14", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Economics", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "\u00d6zye\u011fin University", 
          "id": "https://www.grid.ac/institutes/grid.28009.33", 
          "name": [
            "Ozyegin University"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Saldi", 
        "givenName": "Naci", 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "name": [
            "Queen\u2019s University"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Linder", 
        "givenName": "Tam\u00e1s", 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "name": [
            "Queen\u2019s University"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Y\u00fcksel", 
        "givenName": "Serdar", 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "https://doi.org/10.1016/j.automatica.2013.06.011", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1007324662"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/j.automatica.2010.12.001", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1009574832"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s11590-011-0339-6", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1032847206", 
          "https://doi.org/10.1007/s11590-011-0339-6"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s11590-011-0339-6", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1032847206", 
          "https://doi.org/10.1007/s11590-011-0339-6"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/j.automatica.2015.02.026", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1047013701"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1109/9.911416", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1061246661"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1109/9.948480", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1061246818"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1109/tac.1987.1104636", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1061474827"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1109/tac.2016.2613902", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1061480279"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1137/0306011", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1062842740"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1137/0324038", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1062843882"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "2018", 
    "datePublishedReg": "2018-01-01", 
    "description": "In this chapter, we study the approximation of Witsenhausen\u2019s counterexample and the Gaussian relay channel problem by using the results of the previous chapter. In particular, our goal is to establish that finite models obtained through the uniform quantization of the observation and action spaces result in a sequence of policies whose costs converge to the value function. We note that the operation of quantization has typically been the method to show that a non-linear policy can perform better than an optimal linear policy, both for Witsenhausen\u2019s counterexample [10, 86] and the Gaussian relay channel problem [88, 152]. Our findings show that for a large class of problems, quantized policies not only may perform better than linear policies, but that they are actually almost optimal.", 
    "genre": "chapter", 
    "id": "sg:pub.10.1007/978-3-319-79033-6_9", 
    "inLanguage": [
      "en"
    ], 
    "isAccessibleForFree": false, 
    "isPartOf": {
      "isbn": [
        "978-3-319-79032-9", 
        "978-3-319-79033-6"
      ], 
      "name": "Finite Approximations in Discrete-Time Stochastic Control", 
      "type": "Book"
    }, 
    "name": "Asymptotic Optimality of Finite Models for Witsenhausen\u2019s Counterexample and Beyond", 
    "pagination": "177-188", 
    "productId": [
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/978-3-319-79033-6_9"
        ]
      }, 
      {
        "name": "readcube_id", 
        "type": "PropertyValue", 
        "value": [
          "82875f4e7c24fab9d9b3459fddbadd97bec8b5355cb23847769ad1185655f509"
        ]
      }, 
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1103951463"
        ]
      }
    ], 
    "publisher": {
      "location": "Cham", 
      "name": "Springer International Publishing", 
      "type": "Organisation"
    }, 
    "sameAs": [
      "https://doi.org/10.1007/978-3-319-79033-6_9", 
      "https://app.dimensions.ai/details/publication/pub.1103951463"
    ], 
    "sdDataset": "chapters", 
    "sdDatePublished": "2019-04-15T18:24", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-uberresearch-data-dimensions-target-20181106-alternative/cleanup/v134/2549eaecd7973599484d7c17b260dba0a4ecb94b/merge/v9/a6c9fde33151104705d4d7ff012ea9563521a3ce/jats-lookup/v90/0000000001_0000000264/records_8681_00000384.jsonl", 
    "type": "Chapter", 
    "url": "http://link.springer.com/10.1007/978-3-319-79033-6_9"
  }
]
 

Download the RDF metadata as:  json-ld nt turtle xml License info

HOW TO GET THIS DATA PROGRAMMATICALLY:

JSON-LD is a popular format for linked data which is fully compatible with JSON.

curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/978-3-319-79033-6_9'

N-Triples is a line-based linked data format ideal for batch operations.

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/978-3-319-79033-6_9'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/978-3-319-79033-6_9'

RDF/XML is a standard XML format for linked data.

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/978-3-319-79033-6_9'


 

This table displays all metadata directly associated to this object as RDF triples.

105 TRIPLES      22 PREDICATES      36 URIs      19 LITERALS      7 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/978-3-319-79033-6_9 schema:about anzsrc-for:14
2 anzsrc-for:1402
3 schema:author Na2afe6ff7d9745c3a513affe4fda1b9a
4 schema:citation sg:pub.10.1007/s11590-011-0339-6
5 https://doi.org/10.1016/j.automatica.2010.12.001
6 https://doi.org/10.1016/j.automatica.2013.06.011
7 https://doi.org/10.1016/j.automatica.2015.02.026
8 https://doi.org/10.1109/9.911416
9 https://doi.org/10.1109/9.948480
10 https://doi.org/10.1109/tac.1987.1104636
11 https://doi.org/10.1109/tac.2016.2613902
12 https://doi.org/10.1137/0306011
13 https://doi.org/10.1137/0324038
14 schema:datePublished 2018
15 schema:datePublishedReg 2018-01-01
16 schema:description In this chapter, we study the approximation of Witsenhausen’s counterexample and the Gaussian relay channel problem by using the results of the previous chapter. In particular, our goal is to establish that finite models obtained through the uniform quantization of the observation and action spaces result in a sequence of policies whose costs converge to the value function. We note that the operation of quantization has typically been the method to show that a non-linear policy can perform better than an optimal linear policy, both for Witsenhausen’s counterexample [10, 86] and the Gaussian relay channel problem [88, 152]. Our findings show that for a large class of problems, quantized policies not only may perform better than linear policies, but that they are actually almost optimal.
17 schema:genre chapter
18 schema:inLanguage en
19 schema:isAccessibleForFree false
20 schema:isPartOf Nd656c54c930e485a859b8ecd7e5f9bd4
21 schema:name Asymptotic Optimality of Finite Models for Witsenhausen’s Counterexample and Beyond
22 schema:pagination 177-188
23 schema:productId N86070e981e944f4a9455892c66500fad
24 N8edabc99044241cca492b3be053ec649
25 N9ed609fbc66d41efb177a9e440bc9d06
26 schema:publisher N85ce18b9f6734fcd92495d745e2dc8e5
27 schema:sameAs https://app.dimensions.ai/details/publication/pub.1103951463
28 https://doi.org/10.1007/978-3-319-79033-6_9
29 schema:sdDatePublished 2019-04-15T18:24
30 schema:sdLicense https://scigraph.springernature.com/explorer/license/
31 schema:sdPublisher Nd85a28d7e7f74afab7504bc374855a68
32 schema:url http://link.springer.com/10.1007/978-3-319-79033-6_9
33 sgo:license sg:explorer/license/
34 sgo:sdDataset chapters
35 rdf:type schema:Chapter
36 N767e967e492e41a3bd3576d325ddf2e1 schema:affiliation https://www.grid.ac/institutes/grid.28009.33
37 schema:familyName Saldi
38 schema:givenName Naci
39 rdf:type schema:Person
40 N85ce18b9f6734fcd92495d745e2dc8e5 schema:location Cham
41 schema:name Springer International Publishing
42 rdf:type schema:Organisation
43 N86070e981e944f4a9455892c66500fad schema:name readcube_id
44 schema:value 82875f4e7c24fab9d9b3459fddbadd97bec8b5355cb23847769ad1185655f509
45 rdf:type schema:PropertyValue
46 N8edabc99044241cca492b3be053ec649 schema:name doi
47 schema:value 10.1007/978-3-319-79033-6_9
48 rdf:type schema:PropertyValue
49 N94e3d7f312784b1abc73bada71568c22 rdf:first N97630a8e3a644b38b60f47d6baa65d17
50 rdf:rest rdf:nil
51 N97630a8e3a644b38b60f47d6baa65d17 schema:affiliation Nb857464c422042549956d1bb83772b50
52 schema:familyName Yüksel
53 schema:givenName Serdar
54 rdf:type schema:Person
55 N9ed609fbc66d41efb177a9e440bc9d06 schema:name dimensions_id
56 schema:value pub.1103951463
57 rdf:type schema:PropertyValue
58 Na2afe6ff7d9745c3a513affe4fda1b9a rdf:first N767e967e492e41a3bd3576d325ddf2e1
59 rdf:rest Nec2a14e5d4c24dbb8481803ec1df1831
60 Nb857464c422042549956d1bb83772b50 schema:name Queen’s University
61 rdf:type schema:Organization
62 Nc98bfcb68e38410c84be9759e496411b schema:name Queen’s University
63 rdf:type schema:Organization
64 Nd656c54c930e485a859b8ecd7e5f9bd4 schema:isbn 978-3-319-79032-9
65 978-3-319-79033-6
66 schema:name Finite Approximations in Discrete-Time Stochastic Control
67 rdf:type schema:Book
68 Nd85a28d7e7f74afab7504bc374855a68 schema:name Springer Nature - SN SciGraph project
69 rdf:type schema:Organization
70 Nec2a14e5d4c24dbb8481803ec1df1831 rdf:first Nfee39d55af5f4736acd002021a360997
71 rdf:rest N94e3d7f312784b1abc73bada71568c22
72 Nfee39d55af5f4736acd002021a360997 schema:affiliation Nc98bfcb68e38410c84be9759e496411b
73 schema:familyName Linder
74 schema:givenName Tamás
75 rdf:type schema:Person
76 anzsrc-for:14 schema:inDefinedTermSet anzsrc-for:
77 schema:name Economics
78 rdf:type schema:DefinedTerm
79 anzsrc-for:1402 schema:inDefinedTermSet anzsrc-for:
80 schema:name Applied Economics
81 rdf:type schema:DefinedTerm
82 sg:pub.10.1007/s11590-011-0339-6 schema:sameAs https://app.dimensions.ai/details/publication/pub.1032847206
83 https://doi.org/10.1007/s11590-011-0339-6
84 rdf:type schema:CreativeWork
85 https://doi.org/10.1016/j.automatica.2010.12.001 schema:sameAs https://app.dimensions.ai/details/publication/pub.1009574832
86 rdf:type schema:CreativeWork
87 https://doi.org/10.1016/j.automatica.2013.06.011 schema:sameAs https://app.dimensions.ai/details/publication/pub.1007324662
88 rdf:type schema:CreativeWork
89 https://doi.org/10.1016/j.automatica.2015.02.026 schema:sameAs https://app.dimensions.ai/details/publication/pub.1047013701
90 rdf:type schema:CreativeWork
91 https://doi.org/10.1109/9.911416 schema:sameAs https://app.dimensions.ai/details/publication/pub.1061246661
92 rdf:type schema:CreativeWork
93 https://doi.org/10.1109/9.948480 schema:sameAs https://app.dimensions.ai/details/publication/pub.1061246818
94 rdf:type schema:CreativeWork
95 https://doi.org/10.1109/tac.1987.1104636 schema:sameAs https://app.dimensions.ai/details/publication/pub.1061474827
96 rdf:type schema:CreativeWork
97 https://doi.org/10.1109/tac.2016.2613902 schema:sameAs https://app.dimensions.ai/details/publication/pub.1061480279
98 rdf:type schema:CreativeWork
99 https://doi.org/10.1137/0306011 schema:sameAs https://app.dimensions.ai/details/publication/pub.1062842740
100 rdf:type schema:CreativeWork
101 https://doi.org/10.1137/0324038 schema:sameAs https://app.dimensions.ai/details/publication/pub.1062843882
102 rdf:type schema:CreativeWork
103 https://www.grid.ac/institutes/grid.28009.33 schema:alternateName Özyeğin University
104 schema:name Ozyegin University
105 rdf:type schema:Organization
 




Preview window. Press ESC to close (or click here)


...