Risk-Sensitive Reinforcement Learning: A Constrained Optimization Viewpoint. Article Swipe
The classic objective in a reinforcement learning (RL) problem is to find a policy that minimizes, in expectation, a long-run objective such as the infinite-horizon discounted or long-run average cost. In many practical applications, optimizing the expected value alone is not sufficient, and it may be necessary to include a risk measure in the optimization process, either as the objective or as a constraint. Various risk measures have been proposed in the literature, e.g., mean-variance tradeoff, exponential utility, the percentile performance, value at risk, conditional value at risk, prospect theory and its later enhancement, cumulative prospect theory. In this article, we focus on the combination of risk criteria and reinforcement learning in a constrained optimization framework, i.e., a setting where the goal to find a policy that optimizes the usual objective of infinite-horizon discounted/average cost, while ensuring that an explicit risk constraint is satisfied. We introduce the risk-constrained RL framework, cover popular risk measures based on variance, conditional value-at-risk and cumulative prospect theory, and present a template for a risk-sensitive RL algorithm. We survey some of our recent work on this topic, covering problems encompassing discounted cost, average cost, and stochastic shortest path settings, together with the aforementioned risk measures in a constrained framework. This non-exhaustive survey is aimed at giving a flavor of the challenges involved in solving a risk-sensitive RL problem, and outlining some potential future research directions.
Related Topics
Concepts
Cumulative prospect theory
Reinforcement learning
Risk measure
Mathematical optimization
Expected shortfall
Computer science
Time horizon
Variance (accounting)
Exponential utility
Constraint (computer-aided design)
Value at risk
Risk management
Expected utility hypothesis
Mathematics
Mathematical economics
Economics
Artificial intelligence
Management
Geometry
Financial economics
Accounting
Portfolio
Metadata
- Type
- preprint
- Language
- en
- Landing Page
- https://arxiv.org/pdf/1810.09126.pdf
- OA Status
- green
- Cited By
- 26
- References
- 59
- Related Works
- 20
- OpenAlex ID
- https://openalex.org/W2896408693
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
-
https://openalex.org/W2896408693Canonical identifier for this work in OpenAlex
- Title
-
Risk-Sensitive Reinforcement Learning: A Constrained Optimization Viewpoint.Work title
- Type
-
preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2018Year of publication
- Publication date
-
2018-10-22Full publication date if available
- Authors
-
L. A. Prashanth, Michael C. FuList of authors in order
- Landing page
-
https://arxiv.org/pdf/1810.09126.pdfPublisher landing page
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
-
https://arxiv.org/pdf/1810.09126.pdfDirect OA link when available
- Concepts
-
Cumulative prospect theory, Reinforcement learning, Risk measure, Mathematical optimization, Expected shortfall, Computer science, Time horizon, Variance (accounting), Exponential utility, Constraint (computer-aided design), Value at risk, Risk management, Expected utility hypothesis, Mathematics, Mathematical economics, Economics, Artificial intelligence, Management, Geometry, Financial economics, Accounting, PortfolioTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
26Total citation count in OpenAlex
- Citations by year (recent)
-
2025: 1, 2024: 2, 2023: 3, 2022: 3, 2021: 5Per-year citation counts (last 5 years)
- References (count)
-
59Number of works referenced by this work
- Related works (count)
-
20Other works algorithmically related by OpenAlex
Full payload
| id | https://openalex.org/W2896408693 |
|---|---|
| doi | |
| ids.mag | 2896408693 |
| ids.openalex | https://openalex.org/W2896408693 |
| fwci | |
| type | preprint |
| title | Risk-Sensitive Reinforcement Learning: A Constrained Optimization Viewpoint. |
| biblio.issue | |
| biblio.volume | |
| biblio.last_page | |
| biblio.first_page | |
| topics[0].id | https://openalex.org/T11413 |
| topics[0].field.id | https://openalex.org/fields/18 |
| topics[0].field.display_name | Decision Sciences |
| topics[0].score | 0.9975000023841858 |
| topics[0].domain.id | https://openalex.org/domains/2 |
| topics[0].domain.display_name | Social Sciences |
| topics[0].subfield.id | https://openalex.org/subfields/1803 |
| topics[0].subfield.display_name | Management Science and Operations Research |
| topics[0].display_name | Risk and Portfolio Optimization |
| topics[1].id | https://openalex.org/T12101 |
| topics[1].field.id | https://openalex.org/fields/18 |
| topics[1].field.display_name | Decision Sciences |
| topics[1].score | 0.9962999820709229 |
| topics[1].domain.id | https://openalex.org/domains/2 |
| topics[1].domain.display_name | Social Sciences |
| topics[1].subfield.id | https://openalex.org/subfields/1803 |
| topics[1].subfield.display_name | Management Science and Operations Research |
| topics[1].display_name | Advanced Bandit Algorithms Research |
| topics[2].id | https://openalex.org/T10462 |
| topics[2].field.id | https://openalex.org/fields/17 |
| topics[2].field.display_name | Computer Science |
| topics[2].score | 0.9936000108718872 |
| topics[2].domain.id | https://openalex.org/domains/3 |
| topics[2].domain.display_name | Physical Sciences |
| topics[2].subfield.id | https://openalex.org/subfields/1702 |
| topics[2].subfield.display_name | Artificial Intelligence |
| topics[2].display_name | Reinforcement Learning in Robotics |
| is_xpac | False |
| apc_list | |
| apc_paid | |
| concepts[0].id | https://openalex.org/C2779449553 |
| concepts[0].level | 3 |
| concepts[0].score | 0.7591113448143005 |
| concepts[0].wikidata | https://www.wikidata.org/wiki/Q5194187 |
| concepts[0].display_name | Cumulative prospect theory |
| concepts[1].id | https://openalex.org/C97541855 |
| concepts[1].level | 2 |
| concepts[1].score | 0.7468242645263672 |
| concepts[1].wikidata | https://www.wikidata.org/wiki/Q830687 |
| concepts[1].display_name | Reinforcement learning |
| concepts[2].id | https://openalex.org/C2781472820 |
| concepts[2].level | 3 |
| concepts[2].score | 0.5928972959518433 |
| concepts[2].wikidata | https://www.wikidata.org/wiki/Q2154759 |
| concepts[2].display_name | Risk measure |
| concepts[3].id | https://openalex.org/C126255220 |
| concepts[3].level | 1 |
| concepts[3].score | 0.5854555368423462 |
| concepts[3].wikidata | https://www.wikidata.org/wiki/Q141495 |
| concepts[3].display_name | Mathematical optimization |
| concepts[4].id | https://openalex.org/C5496284 |
| concepts[4].level | 3 |
| concepts[4].score | 0.5579007863998413 |
| concepts[4].wikidata | https://www.wikidata.org/wiki/Q5420856 |
| concepts[4].display_name | Expected shortfall |
| concepts[5].id | https://openalex.org/C41008148 |
| concepts[5].level | 0 |
| concepts[5].score | 0.5008828639984131 |
| concepts[5].wikidata | https://www.wikidata.org/wiki/Q21198 |
| concepts[5].display_name | Computer science |
| concepts[6].id | https://openalex.org/C28761237 |
| concepts[6].level | 2 |
| concepts[6].score | 0.4938576817512512 |
| concepts[6].wikidata | https://www.wikidata.org/wiki/Q7805321 |
| concepts[6].display_name | Time horizon |
| concepts[7].id | https://openalex.org/C196083921 |
| concepts[7].level | 2 |
| concepts[7].score | 0.4836250841617584 |
| concepts[7].wikidata | https://www.wikidata.org/wiki/Q7915758 |
| concepts[7].display_name | Variance (accounting) |
| concepts[8].id | https://openalex.org/C2778475510 |
| concepts[8].level | 2 |
| concepts[8].score | 0.4765917956829071 |
| concepts[8].wikidata | https://www.wikidata.org/wiki/Q5421533 |
| concepts[8].display_name | Exponential utility |
| concepts[9].id | https://openalex.org/C2776036281 |
| concepts[9].level | 2 |
| concepts[9].score | 0.42746254801750183 |
| concepts[9].wikidata | https://www.wikidata.org/wiki/Q48769818 |
| concepts[9].display_name | Constraint (computer-aided design) |
| concepts[10].id | https://openalex.org/C94128290 |
| concepts[10].level | 3 |
| concepts[10].score | 0.4104287922382355 |
| concepts[10].wikidata | https://www.wikidata.org/wiki/Q963287 |
| concepts[10].display_name | Value at risk |
| concepts[11].id | https://openalex.org/C32896092 |
| concepts[11].level | 2 |
| concepts[11].score | 0.3440236449241638 |
| concepts[11].wikidata | https://www.wikidata.org/wiki/Q189447 |
| concepts[11].display_name | Risk management |
| concepts[12].id | https://openalex.org/C205706631 |
| concepts[12].level | 2 |
| concepts[12].score | 0.2950694262981415 |
| concepts[12].wikidata | https://www.wikidata.org/wiki/Q2319304 |
| concepts[12].display_name | Expected utility hypothesis |
| concepts[13].id | https://openalex.org/C33923547 |
| concepts[13].level | 0 |
| concepts[13].score | 0.2926667630672455 |
| concepts[13].wikidata | https://www.wikidata.org/wiki/Q395 |
| concepts[13].display_name | Mathematics |
| concepts[14].id | https://openalex.org/C144237770 |
| concepts[14].level | 1 |
| concepts[14].score | 0.19265815615653992 |
| concepts[14].wikidata | https://www.wikidata.org/wiki/Q747534 |
| concepts[14].display_name | Mathematical economics |
| concepts[15].id | https://openalex.org/C162324750 |
| concepts[15].level | 0 |
| concepts[15].score | 0.19108444452285767 |
| concepts[15].wikidata | https://www.wikidata.org/wiki/Q8134 |
| concepts[15].display_name | Economics |
| concepts[16].id | https://openalex.org/C154945302 |
| concepts[16].level | 1 |
| concepts[16].score | 0.16218647360801697 |
| concepts[16].wikidata | https://www.wikidata.org/wiki/Q11660 |
| concepts[16].display_name | Artificial intelligence |
| concepts[17].id | https://openalex.org/C187736073 |
| concepts[17].level | 1 |
| concepts[17].score | 0.0 |
| concepts[17].wikidata | https://www.wikidata.org/wiki/Q2920921 |
| concepts[17].display_name | Management |
| concepts[18].id | https://openalex.org/C2524010 |
| concepts[18].level | 1 |
| concepts[18].score | 0.0 |
| concepts[18].wikidata | https://www.wikidata.org/wiki/Q8087 |
| concepts[18].display_name | Geometry |
| concepts[19].id | https://openalex.org/C106159729 |
| concepts[19].level | 1 |
| concepts[19].score | 0.0 |
| concepts[19].wikidata | https://www.wikidata.org/wiki/Q2294553 |
| concepts[19].display_name | Financial economics |
| concepts[20].id | https://openalex.org/C121955636 |
| concepts[20].level | 1 |
| concepts[20].score | 0.0 |
| concepts[20].wikidata | https://www.wikidata.org/wiki/Q4116214 |
| concepts[20].display_name | Accounting |
| concepts[21].id | https://openalex.org/C2780821815 |
| concepts[21].level | 2 |
| concepts[21].score | 0.0 |
| concepts[21].wikidata | https://www.wikidata.org/wiki/Q5340806 |
| concepts[21].display_name | Portfolio |
| keywords[0].id | https://openalex.org/keywords/cumulative-prospect-theory |
| keywords[0].score | 0.7591113448143005 |
| keywords[0].display_name | Cumulative prospect theory |
| keywords[1].id | https://openalex.org/keywords/reinforcement-learning |
| keywords[1].score | 0.7468242645263672 |
| keywords[1].display_name | Reinforcement learning |
| keywords[2].id | https://openalex.org/keywords/risk-measure |
| keywords[2].score | 0.5928972959518433 |
| keywords[2].display_name | Risk measure |
| keywords[3].id | https://openalex.org/keywords/mathematical-optimization |
| keywords[3].score | 0.5854555368423462 |
| keywords[3].display_name | Mathematical optimization |
| keywords[4].id | https://openalex.org/keywords/expected-shortfall |
| keywords[4].score | 0.5579007863998413 |
| keywords[4].display_name | Expected shortfall |
| keywords[5].id | https://openalex.org/keywords/computer-science |
| keywords[5].score | 0.5008828639984131 |
| keywords[5].display_name | Computer science |
| keywords[6].id | https://openalex.org/keywords/time-horizon |
| keywords[6].score | 0.4938576817512512 |
| keywords[6].display_name | Time horizon |
| keywords[7].id | https://openalex.org/keywords/variance |
| keywords[7].score | 0.4836250841617584 |
| keywords[7].display_name | Variance (accounting) |
| keywords[8].id | https://openalex.org/keywords/exponential-utility |
| keywords[8].score | 0.4765917956829071 |
| keywords[8].display_name | Exponential utility |
| keywords[9].id | https://openalex.org/keywords/constraint |
| keywords[9].score | 0.42746254801750183 |
| keywords[9].display_name | Constraint (computer-aided design) |
| keywords[10].id | https://openalex.org/keywords/value-at-risk |
| keywords[10].score | 0.4104287922382355 |
| keywords[10].display_name | Value at risk |
| keywords[11].id | https://openalex.org/keywords/risk-management |
| keywords[11].score | 0.3440236449241638 |
| keywords[11].display_name | Risk management |
| keywords[12].id | https://openalex.org/keywords/expected-utility-hypothesis |
| keywords[12].score | 0.2950694262981415 |
| keywords[12].display_name | Expected utility hypothesis |
| keywords[13].id | https://openalex.org/keywords/mathematics |
| keywords[13].score | 0.2926667630672455 |
| keywords[13].display_name | Mathematics |
| keywords[14].id | https://openalex.org/keywords/mathematical-economics |
| keywords[14].score | 0.19265815615653992 |
| keywords[14].display_name | Mathematical economics |
| keywords[15].id | https://openalex.org/keywords/economics |
| keywords[15].score | 0.19108444452285767 |
| keywords[15].display_name | Economics |
| keywords[16].id | https://openalex.org/keywords/artificial-intelligence |
| keywords[16].score | 0.16218647360801697 |
| keywords[16].display_name | Artificial intelligence |
| language | en |
| locations[0].id | mag:2896408693 |
| locations[0].is_oa | True |
| locations[0].source.id | https://openalex.org/S4306400194 |
| locations[0].source.issn | |
| locations[0].source.type | repository |
| locations[0].source.is_oa | True |
| locations[0].source.issn_l | |
| locations[0].source.is_core | False |
| locations[0].source.is_in_doaj | False |
| locations[0].source.display_name | arXiv (Cornell University) |
| locations[0].source.host_organization | https://openalex.org/I205783295 |
| locations[0].source.host_organization_name | Cornell University |
| locations[0].source.host_organization_lineage | https://openalex.org/I205783295 |
| locations[0].license | |
| locations[0].pdf_url | |
| locations[0].version | submittedVersion |
| locations[0].raw_type | |
| locations[0].license_id | |
| locations[0].is_accepted | False |
| locations[0].is_published | False |
| locations[0].raw_source_name | arXiv (Cornell University) |
| locations[0].landing_page_url | https://arxiv.org/pdf/1810.09126.pdf |
| authorships[0].author.id | https://openalex.org/A5068379567 |
| authorships[0].author.orcid | |
| authorships[0].author.display_name | L. A. Prashanth |
| authorships[0].author_position | first |
| authorships[0].raw_author_name | L A Prashanth |
| authorships[0].is_corresponding | False |
| authorships[1].author.id | https://openalex.org/A5000889975 |
| authorships[1].author.orcid | https://orcid.org/0000-0003-2105-4932 |
| authorships[1].author.display_name | Michael C. Fu |
| authorships[1].author_position | last |
| authorships[1].raw_author_name | Michael C. Fu |
| authorships[1].is_corresponding | False |
| has_content.pdf | False |
| has_content.grobid_xml | False |
| is_paratext | False |
| open_access.is_oa | True |
| open_access.oa_url | https://arxiv.org/pdf/1810.09126.pdf |
| open_access.oa_status | green |
| open_access.any_repository_has_fulltext | False |
| created_date | 2025-10-10T00:00:00 |
| display_name | Risk-Sensitive Reinforcement Learning: A Constrained Optimization Viewpoint. |
| has_fulltext | False |
| is_retracted | False |
| updated_date | 2025-10-10T17:16:08.811792 |
| primary_topic.id | https://openalex.org/T11413 |
| primary_topic.field.id | https://openalex.org/fields/18 |
| primary_topic.field.display_name | Decision Sciences |
| primary_topic.score | 0.9975000023841858 |
| primary_topic.domain.id | https://openalex.org/domains/2 |
| primary_topic.domain.display_name | Social Sciences |
| primary_topic.subfield.id | https://openalex.org/subfields/1803 |
| primary_topic.subfield.display_name | Management Science and Operations Research |
| primary_topic.display_name | Risk and Portfolio Optimization |
| related_works | https://openalex.org/W2965585060, https://openalex.org/W3157409643, https://openalex.org/W2963082979, https://openalex.org/W2257979135, https://openalex.org/W2145339207, https://openalex.org/W2121863487, https://openalex.org/W1845972764, https://openalex.org/W3106238320, https://openalex.org/W2795609531, https://openalex.org/W2783797945, https://openalex.org/W2783782435, https://openalex.org/W2583582904, https://openalex.org/W2561666900, https://openalex.org/W2556121307, https://openalex.org/W2462780152, https://openalex.org/W2167696704, https://openalex.org/W2027591506, https://openalex.org/W1841951819, https://openalex.org/W1823979212, https://openalex.org/W1818156433 |
| cited_by_count | 26 |
| counts_by_year[0].year | 2025 |
| counts_by_year[0].cited_by_count | 1 |
| counts_by_year[1].year | 2024 |
| counts_by_year[1].cited_by_count | 2 |
| counts_by_year[2].year | 2023 |
| counts_by_year[2].cited_by_count | 3 |
| counts_by_year[3].year | 2022 |
| counts_by_year[3].cited_by_count | 3 |
| counts_by_year[4].year | 2021 |
| counts_by_year[4].cited_by_count | 5 |
| counts_by_year[5].year | 2020 |
| counts_by_year[5].cited_by_count | 11 |
| counts_by_year[6].year | 2019 |
| counts_by_year[6].cited_by_count | 1 |
| locations_count | 1 |
| best_oa_location.id | mag:2896408693 |
| best_oa_location.is_oa | True |
| best_oa_location.source.id | https://openalex.org/S4306400194 |
| best_oa_location.source.issn | |
| best_oa_location.source.type | repository |
| best_oa_location.source.is_oa | True |
| best_oa_location.source.issn_l | |
| best_oa_location.source.is_core | False |
| best_oa_location.source.is_in_doaj | False |
| best_oa_location.source.display_name | arXiv (Cornell University) |
| best_oa_location.source.host_organization | https://openalex.org/I205783295 |
| best_oa_location.source.host_organization_name | Cornell University |
| best_oa_location.source.host_organization_lineage | https://openalex.org/I205783295 |
| best_oa_location.license | |
| best_oa_location.pdf_url | |
| best_oa_location.version | submittedVersion |
| best_oa_location.raw_type | |
| best_oa_location.license_id | |
| best_oa_location.is_accepted | False |
| best_oa_location.is_published | False |
| best_oa_location.raw_source_name | arXiv (Cornell University) |
| best_oa_location.landing_page_url | https://arxiv.org/pdf/1810.09126.pdf |
| primary_location.id | mag:2896408693 |
| primary_location.is_oa | True |
| primary_location.source.id | https://openalex.org/S4306400194 |
| primary_location.source.issn | |
| primary_location.source.type | repository |
| primary_location.source.is_oa | True |
| primary_location.source.issn_l | |
| primary_location.source.is_core | False |
| primary_location.source.is_in_doaj | False |
| primary_location.source.display_name | arXiv (Cornell University) |
| primary_location.source.host_organization | https://openalex.org/I205783295 |
| primary_location.source.host_organization_name | Cornell University |
| primary_location.source.host_organization_lineage | https://openalex.org/I205783295 |
| primary_location.license | |
| primary_location.pdf_url | |
| primary_location.version | submittedVersion |
| primary_location.raw_type | |
| primary_location.license_id | |
| primary_location.is_accepted | False |
| primary_location.is_published | False |
| primary_location.raw_source_name | arXiv (Cornell University) |
| primary_location.landing_page_url | https://arxiv.org/pdf/1810.09126.pdf |
| publication_date | 2018-10-22 |
| publication_year | 2018 |
| referenced_works | https://openalex.org/W1557270667, https://openalex.org/W1998147290, https://openalex.org/W3122620151, https://openalex.org/W2082261506, https://openalex.org/W1569296262, https://openalex.org/W75119881, https://openalex.org/W2235056388, https://openalex.org/W2313791856, https://openalex.org/W2025611071, https://openalex.org/W2007181101, https://openalex.org/W2160769068, https://openalex.org/W2962951833, https://openalex.org/W2128347943, https://openalex.org/W2559703049, https://openalex.org/W89883662, https://openalex.org/W2088413745, https://openalex.org/W2119567691, https://openalex.org/W2150552447, https://openalex.org/W2161270100, https://openalex.org/W2462780152, https://openalex.org/W1576452626, https://openalex.org/W2108888882, https://openalex.org/W1979085877, https://openalex.org/W2162849300, https://openalex.org/W1647779468, https://openalex.org/W2060248504, https://openalex.org/W2094387729, https://openalex.org/W2138740914, https://openalex.org/W2100677568, https://openalex.org/W2086304253, https://openalex.org/W2031764013, https://openalex.org/W2070570138, https://openalex.org/W2173945562, https://openalex.org/W2019291268, https://openalex.org/W3125094392, https://openalex.org/W1585575029, https://openalex.org/W2001009060, https://openalex.org/W1825688215, https://openalex.org/W594357522, https://openalex.org/W2057510529, https://openalex.org/W2057338828, https://openalex.org/W1895872655, https://openalex.org/W2141203641, https://openalex.org/W2124289529, https://openalex.org/W1970303738, https://openalex.org/W2107431923, https://openalex.org/W2056158656, https://openalex.org/W88312990, https://openalex.org/W2170923204, https://openalex.org/W2140282437, https://openalex.org/W1518931405, https://openalex.org/W1985077192, https://openalex.org/W1593140824, https://openalex.org/W2133469585, https://openalex.org/W3122851459, https://openalex.org/W2796289712, https://openalex.org/W2121863487, https://openalex.org/W2128723253, https://openalex.org/W2139418546 |
| referenced_works_count | 59 |
| abstract_inverted_index.a | 4, 12, 18, 49, 62, 112, 117, 124, 165, 168, 201, 211, 219 |
| abstract_inverted_index.In | 30, 97 |
| abstract_inverted_index.RL | 148, 170, 221 |
| abstract_inverted_index.We | 144, 172 |
| abstract_inverted_index.an | 138 |
| abstract_inverted_index.as | 22, 57, 61 |
| abstract_inverted_index.at | 82, 86, 209 |
| abstract_inverted_index.be | 45 |
| abstract_inverted_index.in | 3, 16, 52, 70, 111, 200, 217 |
| abstract_inverted_index.is | 9, 39, 142, 207 |
| abstract_inverted_index.it | 43 |
| abstract_inverted_index.of | 105, 131, 175, 213 |
| abstract_inverted_index.on | 102, 155, 179 |
| abstract_inverted_index.or | 26, 60 |
| abstract_inverted_index.to | 10, 47, 122 |
| abstract_inverted_index.we | 100 |
| abstract_inverted_index.The | 0 |
| abstract_inverted_index.and | 42, 90, 108, 159, 163, 189, 223 |
| abstract_inverted_index.for | 167 |
| abstract_inverted_index.its | 91 |
| abstract_inverted_index.may | 44 |
| abstract_inverted_index.not | 40 |
| abstract_inverted_index.our | 176 |
| abstract_inverted_index.the | 23, 35, 53, 58, 71, 78, 103, 120, 128, 146, 196, 214 |
| abstract_inverted_index.(RL) | 7 |
| abstract_inverted_index.This | 204 |
| abstract_inverted_index.been | 68 |
| abstract_inverted_index.find | 11, 123 |
| abstract_inverted_index.goal | 121 |
| abstract_inverted_index.have | 67 |
| abstract_inverted_index.many | 31 |
| abstract_inverted_index.path | 192 |
| abstract_inverted_index.risk | 50, 65, 106, 140, 152, 198 |
| abstract_inverted_index.some | 174, 225 |
| abstract_inverted_index.such | 21 |
| abstract_inverted_index.that | 14, 126, 137 |
| abstract_inverted_index.this | 98, 180 |
| abstract_inverted_index.with | 195 |
| abstract_inverted_index.work | 178 |
| abstract_inverted_index.aimed | 208 |
| abstract_inverted_index.alone | 38 |
| abstract_inverted_index.based | 154 |
| abstract_inverted_index.cost, | 134, 186, 188 |
| abstract_inverted_index.cost. | 29 |
| abstract_inverted_index.cover | 150 |
| abstract_inverted_index.e.g., | 73 |
| abstract_inverted_index.focus | 101 |
| abstract_inverted_index.i.e., | 116 |
| abstract_inverted_index.later | 92 |
| abstract_inverted_index.risk, | 83, 87 |
| abstract_inverted_index.usual | 129 |
| abstract_inverted_index.value | 37, 81, 85 |
| abstract_inverted_index.where | 119 |
| abstract_inverted_index.while | 135 |
| abstract_inverted_index.either | 56 |
| abstract_inverted_index.flavor | 212 |
| abstract_inverted_index.future | 227 |
| abstract_inverted_index.giving | 210 |
| abstract_inverted_index.policy | 13, 125 |
| abstract_inverted_index.recent | 177 |
| abstract_inverted_index.survey | 173, 206 |
| abstract_inverted_index.theory | 89 |
| abstract_inverted_index.topic, | 181 |
| abstract_inverted_index.Various | 64 |
| abstract_inverted_index.average | 28, 187 |
| abstract_inverted_index.classic | 1 |
| abstract_inverted_index.include | 48 |
| abstract_inverted_index.measure | 51 |
| abstract_inverted_index.popular | 151 |
| abstract_inverted_index.present | 164 |
| abstract_inverted_index.problem | 8 |
| abstract_inverted_index.setting | 118 |
| abstract_inverted_index.solving | 218 |
| abstract_inverted_index.theory, | 162 |
| abstract_inverted_index.theory. | 96 |
| abstract_inverted_index.article, | 99 |
| abstract_inverted_index.covering | 182 |
| abstract_inverted_index.criteria | 107 |
| abstract_inverted_index.ensuring | 136 |
| abstract_inverted_index.expected | 36 |
| abstract_inverted_index.explicit | 139 |
| abstract_inverted_index.involved | 216 |
| abstract_inverted_index.learning | 6, 110 |
| abstract_inverted_index.long-run | 19, 27 |
| abstract_inverted_index.measures | 66, 153, 199 |
| abstract_inverted_index.problem, | 222 |
| abstract_inverted_index.problems | 183 |
| abstract_inverted_index.process, | 55 |
| abstract_inverted_index.proposed | 69 |
| abstract_inverted_index.prospect | 88, 95, 161 |
| abstract_inverted_index.research | 228 |
| abstract_inverted_index.shortest | 191 |
| abstract_inverted_index.template | 166 |
| abstract_inverted_index.together | 194 |
| abstract_inverted_index.utility, | 77 |
| abstract_inverted_index.introduce | 145 |
| abstract_inverted_index.necessary | 46 |
| abstract_inverted_index.objective | 2, 20, 59, 130 |
| abstract_inverted_index.optimizes | 127 |
| abstract_inverted_index.outlining | 224 |
| abstract_inverted_index.potential | 226 |
| abstract_inverted_index.practical | 32 |
| abstract_inverted_index.settings, | 193 |
| abstract_inverted_index.tradeoff, | 75 |
| abstract_inverted_index.variance, | 156 |
| abstract_inverted_index.algorithm. | 171 |
| abstract_inverted_index.challenges | 215 |
| abstract_inverted_index.constraint | 141 |
| abstract_inverted_index.cumulative | 94, 160 |
| abstract_inverted_index.discounted | 25, 185 |
| abstract_inverted_index.framework, | 115, 149 |
| abstract_inverted_index.framework. | 203 |
| abstract_inverted_index.minimizes, | 15 |
| abstract_inverted_index.optimizing | 34 |
| abstract_inverted_index.percentile | 79 |
| abstract_inverted_index.satisfied. | 143 |
| abstract_inverted_index.stochastic | 190 |
| abstract_inverted_index.combination | 104 |
| abstract_inverted_index.conditional | 84, 157 |
| abstract_inverted_index.constrained | 113, 202 |
| abstract_inverted_index.constraint. | 63 |
| abstract_inverted_index.directions. | 229 |
| abstract_inverted_index.exponential | 76 |
| abstract_inverted_index.literature, | 72 |
| abstract_inverted_index.sufficient, | 41 |
| abstract_inverted_index.encompassing | 184 |
| abstract_inverted_index.enhancement, | 93 |
| abstract_inverted_index.expectation, | 17 |
| abstract_inverted_index.optimization | 54, 114 |
| abstract_inverted_index.performance, | 80 |
| abstract_inverted_index.applications, | 33 |
| abstract_inverted_index.mean-variance | 74 |
| abstract_inverted_index.reinforcement | 5, 109 |
| abstract_inverted_index.value-at-risk | 158 |
| abstract_inverted_index.aforementioned | 197 |
| abstract_inverted_index.non-exhaustive | 205 |
| abstract_inverted_index.risk-sensitive | 169, 220 |
| abstract_inverted_index.infinite-horizon | 24, 132 |
| abstract_inverted_index.risk-constrained | 147 |
| abstract_inverted_index.discounted/average | 133 |
| cited_by_percentile_year | |
| countries_distinct_count | 0 |
| institutions_distinct_count | 2 |
| sustainable_development_goals[0].id | https://metadata.un.org/sdg/17 |
| sustainable_development_goals[0].score | 0.4300000071525574 |
| sustainable_development_goals[0].display_name | Partnerships for the goals |
| citation_normalized_percentile |