Matches in SemOpenAlex for { <https://semopenalex.org/work/W4224991954> ?p ?o ?g. }
- W4224991954 endingPage "603" @default.
- W4224991954 startingPage "573" @default.
- W4224991954 abstract "This paper considers an $n$-player stochastic Nash equilibrium problem (NEP) in which the $i$th player minimizes a composite objective $f_i( bullet ,x_{-i}) + r_i( bullet )$, where $f_i$ is an expectation-valued smooth function, $x_{-i}$ is a tuple of rival decisions, and $r_i$ is a nonsmooth convex function with an efficient prox-evaluation. In this context, we make the following contributions. (I) Under suitable monotonicity assumptions on the redpseudogradient map, we derive optimal rate statements and oracle complexity bounds for the proposed variable sample-size proximal stochastic gradient-response (VS-PGR) scheme when the sample-size increases at a geometric rate. If the sample-size increases at a polynomial rate with degree $v > 0$, the mean-squared error of the iterates decays at a corresponding polynomial rate; in particular, we prove that the iteration and oracle complexities to obtain an $epsilon$-Nash equilibrium ($epsilon$-NE) are $mathcal{O}(1/epsilon^{1/v})$ and $mathcal{O}(1/epsilon^{1+1/v})$, respectively. redWhen the sample-size is held constant, the iterates converge geometrically to a neighborhood of the Nash equilibrium in an expected-value sense. (II) We then overlay bf VS-PGR with a consensus phase with a view towards developing distributed protocols for aggregative stochastic NEPs. In the resulting bf d-VS-PGR scheme, when the sample-size at each iteration grows at a geometric rate while the communication rounds per iteration grow at the rate of $ k+1 $, computing an $epsilon$-NE requires similar iteration and oracle complexities to bf VS-PGR with a communication complexity of $mathcal{O}(ln^2(1/epsilon))$. Notably, (I) and (II) rely on weaker oracle assumptions in that the conditionally unbiasedness assumption is relaxed while the bound on the conditional second moment may be state-dependent. (III) Under a suitable contractive property associated with the proximal best-response (BR) map, we design a variable sample-size proximal BR (VS-PBR) scheme, where each player solves a sample-average BR problem. When the sample-size increases at a suitable geometric rate, the resulting iterates converge at a geometric rate while the iteration and oracle complexity are, respectively, $mathcal{O}(ln(1/epsilon))$ and $mathcal{O}(1/epsilon)$. If the sample-size increases at a polynomial rate with degree $v$, the mean-squared error decays at a corresponding polynomial rate while the iteration and oracle complexities are $mathcal{O}(1/epsilon^{1/v})$ and $mathcal{O}(1/epsilon^{1+1/v})$, respectively. (IV) Akin to (II), the distributed variant bf d-VS-PBR achieves similar iteration and oracle complexities to the centralized VS-PBR with a communication complexity of $mathcal{O}(ln^2(1/epsilon))$ when the communication rounds per iteration increase at the rate of $ k+1 $. Finally, we present preliminary numerics to provide empirical support for the rate and complexity statements." @default.
- W4224991954 created "2022-04-28" @default.
- W4224991954 creator A5041336945 @default.
- W4224991954 creator A5047034022 @default.
- W4224991954 date "2022-04-27" @default.
- W4224991954 modified "2023-09-25" @default.
- W4224991954 title "Distributed Variable Sample-Size Gradient-Response and Best-Response Schemes for Stochastic Nash Equilibrium Problems" @default.
- W4224991954 cites W1972768959 @default.
- W4224991954 cites W1987083649 @default.
- W4224991954 cites W2007926026 @default.
- W4224991954 cites W2008796819 @default.
- W4224991954 cites W2012888164 @default.
- W4224991954 cites W2026355589 @default.
- W4224991954 cites W2029463628 @default.
- W4224991954 cites W2044212084 @default.
- W4224991954 cites W2066767736 @default.
- W4224991954 cites W2067050450 @default.
- W4224991954 cites W2118809092 @default.
- W4224991954 cites W2124181538 @default.
- W4224991954 cites W2129122308 @default.
- W4224991954 cites W2137435346 @default.
- W4224991954 cites W2146914418 @default.
- W4224991954 cites W2158898097 @default.
- W4224991954 cites W2266148951 @default.
- W4224991954 cites W2273889207 @default.
- W4224991954 cites W2345998142 @default.
- W4224991954 cites W2460240966 @default.
- W4224991954 cites W2485392636 @default.
- W4224991954 cites W2485473371 @default.
- W4224991954 cites W2501656778 @default.
- W4224991954 cites W2593248927 @default.
- W4224991954 cites W2608695873 @default.
- W4224991954 cites W2690123879 @default.
- W4224991954 cites W2892002891 @default.
- W4224991954 cites W2963550797 @default.
- W4224991954 cites W2981398825 @default.
- W4224991954 cites W3020058381 @default.
- W4224991954 cites W3039554471 @default.
- W4224991954 cites W3082629431 @default.
- W4224991954 cites W3100033291 @default.
- W4224991954 cites W3101495100 @default.
- W4224991954 cites W3102115099 @default.
- W4224991954 cites W3104258082 @default.
- W4224991954 doi "https://doi.org/10.1137/20m1340071" @default.
- W4224991954 hasPublicationYear "2022" @default.
- W4224991954 type Work @default.
- W4224991954 citedByCount "4" @default.
- W4224991954 countsByYear W42249919542022 @default.
- W4224991954 countsByYear W42249919542023 @default.
- W4224991954 crossrefType "journal-article" @default.
- W4224991954 hasAuthorship W4224991954A5041336945 @default.
- W4224991954 hasAuthorship W4224991954A5047034022 @default.
- W4224991954 hasConcept C105795698 @default.
- W4224991954 hasConcept C114614502 @default.
- W4224991954 hasConcept C126255220 @default.
- W4224991954 hasConcept C129848803 @default.
- W4224991954 hasConcept C134306372 @default.
- W4224991954 hasConcept C14036430 @default.
- W4224991954 hasConcept C140479938 @default.
- W4224991954 hasConcept C151730666 @default.
- W4224991954 hasConcept C182365436 @default.
- W4224991954 hasConcept C2779343474 @default.
- W4224991954 hasConcept C28826006 @default.
- W4224991954 hasConcept C32407928 @default.
- W4224991954 hasConcept C33923547 @default.
- W4224991954 hasConcept C46814582 @default.
- W4224991954 hasConcept C78458016 @default.
- W4224991954 hasConcept C86803240 @default.
- W4224991954 hasConcept C90119067 @default.
- W4224991954 hasConceptScore W4224991954C105795698 @default.
- W4224991954 hasConceptScore W4224991954C114614502 @default.
- W4224991954 hasConceptScore W4224991954C126255220 @default.
- W4224991954 hasConceptScore W4224991954C129848803 @default.
- W4224991954 hasConceptScore W4224991954C134306372 @default.
- W4224991954 hasConceptScore W4224991954C14036430 @default.
- W4224991954 hasConceptScore W4224991954C140479938 @default.
- W4224991954 hasConceptScore W4224991954C151730666 @default.
- W4224991954 hasConceptScore W4224991954C182365436 @default.
- W4224991954 hasConceptScore W4224991954C2779343474 @default.
- W4224991954 hasConceptScore W4224991954C28826006 @default.
- W4224991954 hasConceptScore W4224991954C32407928 @default.
- W4224991954 hasConceptScore W4224991954C33923547 @default.
- W4224991954 hasConceptScore W4224991954C46814582 @default.
- W4224991954 hasConceptScore W4224991954C78458016 @default.
- W4224991954 hasConceptScore W4224991954C86803240 @default.
- W4224991954 hasConceptScore W4224991954C90119067 @default.
- W4224991954 hasFunder F4320306076 @default.
- W4224991954 hasFunder F4320321001 @default.
- W4224991954 hasFunder F4320321885 @default.
- W4224991954 hasIssue "2" @default.
- W4224991954 hasLocation W42249919541 @default.
- W4224991954 hasOpenAccess W4224991954 @default.
- W4224991954 hasPrimaryLocation W42249919541 @default.
- W4224991954 hasRelatedWork W1511735024 @default.
- W4224991954 hasRelatedWork W1607392272 @default.
- W4224991954 hasRelatedWork W2166717043 @default.
- W4224991954 hasRelatedWork W2501714360 @default.
- W4224991954 hasRelatedWork W3119844974 @default.