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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

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

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2020

Kód důvěrnosti údajů

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

Název periodika

SIAM Journal on Computing

ISSN

0097-5397

e-ISSN

—

Svazek periodika

49

Číslo periodika v rámci svazku

6

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

45

Strana od-do

1128-1172

Kód UT WoS článku

000600680900004

EID výsledku v databázi Scopus

2-s2.0-85098653670