A Constrained Mechanism for Procedural Learning

The p r o b l e m s t u d i e d i s t h a t o f l e a r n i n g p r o b l e m s o l v i n g h e u r i s t i c s b y d o i n g . The pu rpose i s t o e x p l o r e t h e l e a r n i n g b e h a v i o r o f a h i g h l y c o n s t r a i n e d mechan ism. The c o n s t r a i n t s a r e choosen o n t h e b a s i s o f D s y c h o l o g i c a l c o n s i d e r a t i o n s . Computer r u n s show t h a t t h e c o n s t r a i n t s d o n o t p r e v e n t s u c c e s s f u l l e a r n i n g . T h e l e a r n i n g s t y l e o f t h e p rog ram t u r n s o u t t o b e a f u n c t i o n o f t h e s t r u c t u r e o f t h e p r o b l e m s p a c e . I HEURISTICS LEARNING The t a s k s t u d i e d i n t h i s paper i s t h a t o f d i s c o v e r i n g p r o b l e m s o l v i n g h e u r i s t i c s b y d o i n g . We p resuppose a t a s k i n d e p e n d e n t , weak p r o b l e m s o l v e r w h i c h can t a k e a p r o b l e m space and a p r o b l e m a s i n o u t , and s e a r c h f o r t h e s o l u t i o n t o t h e l a t t e r . We add a s e t o f l e a r n i n g mechanisms w h i c h s p e c i f y how t h e i n f o r m a t i o n g e n e r a t e d d u r i n g s e a r c h s h o u l d b e encoded f o r f u t u r e u s e . The t a s k o f t h e sys tem i s t o c o n s t r u c t a s t r a t e g y f o r s e a r c h i n g a p r o b l e m space on t h e b a s i s o f r e p e a t e d p r o b l e m s o l v i n g t r i a l s i n t h a t s p a c e . Systems o f t h i s k i n d have been d e s c r i b e d by Anza i & Simon ( 1 9 7 9 ) , by L a n g l e v ( 1 9 8 ? ) , by O h l s s o n ( 1 9 8 2 ; 1983), a s w e l l a s b y o t h e r s . They w i l l h e r e b e c a l l e d h e u r i s t i c s l e a r n e r s . The pu rpose o f t h e work r e p o r t e d he re i s n o t t o c o n s t r u c t t h e most i n t e l l i g e n t l e a r n i n g sys tem w h i c h t h e s t a t e o f t h e a r t a l l o w s , b u t t o s t u d y how a p a r t i c u l a r s e t o f c o n s t r a i n t s on an i n f o r m a t i o n p r o c e s s i n g sys tem a f f e c t s i t s l e a r n i n g b e h a v i o r . The c o n s t r a i n t s chosen f o r s t u d y a r e based o n p s y c h o l o g i c a l c o n s i d e r a t i o n s , a l t h o u g h n o d e t a i l e d c o m p a r i s o n between t h e Drogram and human b e h a v i o r w i l l b e made i n t h i s p a p e r . II THE UNIVERSAL PUZZLE LEARNER A n e a r l i e r v e r s i o n o f t h e U n i v e r s a l P u z z l e L e a r n e r (UPL) p rogram has been d e s c r i b e d i n O h l s s o n ( 1 9 8 2 ; 1 9 8 3 ) . The t h i r d and c u r r e n t v e r s i o n c o n s i s t s o f t h r e e l a y e r s : t h e i m p l e m e n t a t i o n l a n g u a g e , t h e p rob lem s o l v e r , and t h e l e a r n i n g mechan isms . A . I m p l e m e n t a t i o n Language UPL i s w r i t t e n i n PSS, a n e o c l a s s i c a l p r o d u c t i o n sys tem language ( O h l s s o n , 1979 ) . I t a l l o w s t h e u s e r t o o r g a n i z e p r o d u c t i o n memory i n t o n o d e s , each node c o n t a i n i n g one o r more p r o d u c t i o n s . When PSS i s " i n " a node , i t w i l l t r y t o f i r e a p r o d u c t i o n f r om t h a t node b e f o r e i t c o n s i d e s p r o d u c t i o n s f r om o t h e r n o d e s . C o n t r o l can be t r a n s f e r r e d f r o m one node to a n o t h e r by t h e f i r i n g o f a p r o d u c t i o n . The PSS c o n d i t i o n ma tche r r e c o g n i z e s a c o n s t r u c t c a l l e d sequence v a r i a b l e s , w h i c h f u l f i l l t h e same f u n c t i o n a s t h e " t h r e e d o t s " o f i n f o r m a l m a t h e m a t i c s ; t h e e x p r e s s i o n " ( A B ) " i n w h i c h i s a sequence v a r i a b l e i s i n t e r p r e t e d a s "any l i s t c o n t a i n i n g A , f o l l o w e d b y any number o f e x p r e s s i o n s , f o l l o w e d b y B " . Sequence v a r i a b l e s match a g a i n s t t h e empty sequence , s o t h a t " ( A B ) " i s a n I n s t a n c e o f " ( A B ) " . A s a n example o f t h e use o f sequence v a r i a b l e s , t h e e x p r e s s i o n " ( X 1 ) " w i l l b i n d t h e v a r i a b l e X 1 t o t h e l a s t e x p r e s s i o n i n any l i s t w h i c h has a t l e a s t one e l e m e n t . As a second e x a m p l e , t h e e x p r e s s i o n "(ALTERNATIVES: X1 )" w i l l r e c o g n i z e a l i s t w i t h one o r more a l t e r n a t i v e s . The sequence v a r i a b l e s a r e bound t o t h e sequences t h e y match a g a i n s t . The PSS sequence v a r i a b l e s can be seen as a deve lopmen t o f t h e " r e m a i n i n g segment " f e a t u r e ( " ! " ) o f t h e OPS language f a m i l y ( F o r g y & M c D e r m o t t , 1 9 7 7 ) . B. The Prob lem S o l v e r The n e x t l a y e r o f UPL i s a t a s k i n d e p e n d e n t , weak p r o b l e m s o l v e r c o n s i s t i n g o f 1 3 nodes w i t h v a r i o u s t a s k s , such a s s e t t i n g g o a l s , m a i n t a i n i n g t h e g o a l s t a c k , g e n e r a t i n g a c t i o n s , c e n s o r i n g a c t i o n s , d o i n g c o n f l i c t r e s o l u t i o n , e x e c u t i n g a c t i o n s , e v a l u a t i n g r e s u l t s o f a c t i o n s , b a c k i n g u p , and r e s t a r t i n g . The p rogram t a k e s a p r o b l e m space and a p r o b l e m as i n p u t . A p r o b l e m space is g i v e n to t h e p rogram in two p a r t s , a BNF grammar d e f i n i n g a k n o w l e d g e s t a t e , and a l i s t o f o p e r a t o r d e f i n i t i o n s . A p r o b l e m i s p r e s e n t e d a s a n o r d e r e d p a i r o f s t a t e s , t h e i n i t i a l s t a t e and t h e g o a l s t a t e . The p r o b l e m s o l v e r i s t a s k i n d e p e n d e n t i n t h e sense t h a t i t does n o t make any a s s u m p t i o n s a b o u t t h e e x p r e s s i o n s w h i c h a r e used a s t h e k n o w l e d g e e l e m e n t s o f t h e p r o b l e m s p a c e .