Federal gosudarstvennoe uchebnoe predpriyatie Chair of the System of Artificial Intelligence

3.1 Optimization methods
vybora shaga. Ispolzovanie optimalnogo shaga v zadachax
For training on oddnym primeram, t.e. without postranichnoy
H w ÿ H w
k ÿ1
42
k ÿ1
k
ÿ ÿ
ÿ
ÿ
k ww hS ÿ ÿ
k ÿ1
k
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ÿ
tochku mojno nayti, esli s nekotorÿm shagom (postoyannÿm ili peremennÿm) dvigatsya vdol
napravleniya minimizatsii v obe storony i analizirovat
minimizirovat funktsiyu H. The simplest, what can be done - go to
minimum funktsii H. Togda tochku minimum mojno nayti iteratsionnymi
Empty set nachalnoe znachenie parameters w i vÿchislena function
zaranee neizvesten i mojet imet gorby i vpadiny, to bolee effektivno
The simplest method is half-division (dichotomy). In etom
vtoroy tochkoy otrezka minimizatsii budet tochka, v kotoroy funktsiya nachala
znacheniyami funktsii na krayax otrezka H (a) i H (b) i vybiraetsya odin iz
,
novÿm otrezkom povtoryayutsya te je operatsii. Protsess zavershaet rabotu, kogda dlina
otrezka ÿ ÿ a, b stanet menshe zaranee zadannoy tochnosti
tselevaya funktsiya umenshaetsya dostatochno bÿstro, to shag na posleduyushchix
k tochke minimum, tem menshe doljen byt shag. V
obshchem sluchae shag mojno nayti, ispolzuya standartnÿe metody
.
Sushchestvuet neskolko metodov vÿbora napravleniya dvijeniya pri
imeem ne otrezok ÿ ÿ a, b a vsego lish odnu ego granichnuyu tochku. Vtoruyu
Pust nam na kajdoy iteratsii izvestno napravlenie, v kotorom nujno
peremennoy - shaga h. Pust izvesten otrezok ÿa, bÿ, na kotorom naxoditsya
etomu napravleniyu s postoyannym shagom. Odnako, t.k. relief functions
methods with zaranee zadannoy tochnostyu.
vÿchislyaetsya znachenie funktsii H (c). It znachenie sravnivaetsya with
povedenie funktsii H. Esli, naprimer, funktsiya H snachala umenshalas, to
otrezkov ÿ ÿ a, c or ÿ ÿ c,
b , vnutri kotorogo naxoditsya minimum funktsii. S
budet avtomaticheski podbirat shag na kajdoy iteratsii. K primer, esli
rosti. Esli je funktsiya rastet srazu je na pervom shage ot nachalnoy tochki, to mojno
poprobovat idti v protivopolojnom napravlenii.
opredelit napravlenie S i nachalnÿy shag.
3.1.2 Mnogoparametricheskaya optimization
iteratsiyax mojno ostavit bolshim. Chem blije argument funktsii podkhodit
i
otsenki
optimizations. Imeem tselevuyu funktsiyu H (h), zavisyashchuyu ot odnoy
3.1.1 Odnoparametricheskaya optimization
method na kajdom shage otrezok ÿa, bÿ delitsya popolam tochkoy
Odnako, na vxode protsedurÿ odnoparametricheskoy optimizatsii my
minimization tselevoy funktsii.
43
0
ÿ ÿ 0 . Odnomernaya optimization dast priblijennoe polojenie
ab
c
H ÿ H w
ÿ
minimum hÿ ÿ x ÿ Hÿw ÿ xSÿ 0 (voobshche govorya, lokalnogo). Teper nujno
ÿ
2
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1
k
2
2
5
0
0
4
2
k
0
4
3
10
2
2
ÿÿ ÿ2
1
w -
vychislim gradient H i t.d. This is a method of short-term descent, primitive of gradient methods. Inogda
rabotaet xorosho.
Iteratsionnyy partan-metod (k-partan) stoitsya tak. In nachalnoy tochke
w uje ne
gde z
optimizations. Poluchaemÿy method requires bolshogo chisla shagov, no zato
ispolzuetsya odnomernaya optimization. Dalee - snova naiskoreyshiy spusk i
pryamoe funktsionirovanie s vychisleniem otsenki. Krome togo, vstrechayutsya
. Poluchaem