HARDNESS OF CONTINUOUS LOCAL SEARCH: QUERY COMPLEXITY AND CRYPTOGRAPHIC LOWER BOUNDS

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F20%3A10422409" target="_blank" >RIV/00216208:11320/20:10422409 - isvavai.cz</a>

Result on the web

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=S.~4IGyEkb" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=S.~4IGyEkb</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1137/17M1118014" target="_blank" >10.1137/17M1118014</a>

Result language

angličtina

Original language name

HARDNESS OF CONTINUOUS LOCAL SEARCH: QUERY COMPLEXITY AND CRYPTOGRAPHIC LOWER BOUNDS

Original language description

Local search proved to be an extremely useful tool when facing hard optimization problems (e.g., via the simplex algorithm, simulated annealing, or genetic algorithms). Although powerful, it has its limitations: there are functions for which exponentially many queries are needed to find a local optimum. In many contexts, the optimization problem is defined by a continuous function which might offer an advantage when performing the local search. This leads us to study the following natural question: How hard is continuous local search? The computational complexity of such search problems is captured by the complexity class CLS [C. Daskalakis and C. H. Papadimitriou, Proceedings of SODA&apos;11, 2011], which is contained in the intersection of PLS and PPAD, two important subclasses of TFNP (the class of NP search problems with a guaranteed solution). In this work, we show the first hardness results for CLS (the smallest nontrivial class among the currently defined subclasses of TFNP). Our hardness results are in terms of black-box (where only oracle access to the function is given) and white-box (where the function is represented succinctly by a circuit). In the black-box case, we show instances for which any (computationally unbounded) randomized algorithm must perform exponentially many queries in order to find a local optimum. In the white-box case, we show hardness for computationally bounded algorithms under cryptographic assumptions. Our results demonstrate a strong conceptual barrier precluding design of efficient algorithms for solving local search problems even over continuous domains. As our main technical contribution we introduce a new total search problem which we call END-OF-METERED-LINE. The special structure of END-OF-METERED-LINE enables us to (1) show that it is contained in CLS, (2) prove hardness for it in both the black-box and the white-box setting, and (3) extend to CLS a variety of results previously known only for PPAD.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Project

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Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2020

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

SIAM Journal on Computing

ISSN

0097-5397

e-ISSN

—

Volume of the periodical

49

Issue of the periodical within the volume

6

Country of publishing house

US - UNITED STATES

Number of pages

45

Pages from-to

1128-1172

UT code for WoS article

000600680900004

EID of the result in the Scopus database

2-s2.0-85098653670