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Nth Teacher Rn - • jth Teacher Rj -'• 1st Teacher R1 . . I i'i t %1i ......... w r ) Figure 9 Stochastic automaton D operating in the nonstationary multi-teacher environment (NMT) 58 n si" E (t,~0)/n, holds j=l j for some state w , some 8 > O, all time t, all j ( # a ), and all m ( ~ ) . where Fi,t(s ) (i=l .... (t,m)} j=l ] the expectation of the sum of the penalty strengths. Therefore, condition (I) means that the ~th action y~ is the best among r actions Yi' .... Yr since y~ receives the least sum of the penalty strengths in the sense of mathematical expectation.

Nth Teacher Rn - • jth Teacher Rj -'• 1st Teacher R1 . . I i'i t %1i ......... w r ) Figure 9 Stochastic automaton D operating in the nonstationary multi-teacher environment (NMT) 58 n si" E (t,~0)/n, holds j=l j for some state w , some 8 > O, all time t, all j ( # a ), and all m ( ~ ) . where Fi,t(s ) (i=l .... (t,m)} j=l ] the expectation of the sum of the penalty strengths. Therefore, condition (I) means that the ~th action y~ is the best among r actions Yi' .... Yr since y~ receives the least sum of the penalty strengths in the sense of mathematical expectation.

R ; i # B ) 468) ) 54 In the above inequality i im 2XOl2exp (201 x] x+O = 0 and ,v_(6 nz c _ -6 n- j= 1 J n~ C"~ ) j=i J > 0 Consequently, there exists some small positive number z such that M(z,P) < 1 Hence, from (75) E{hz,o(P~(t+l))/P(t)} for all < hz,0(P~(t)) t and P(t). D. 1 Introduction In the previous chapter, the GAE reinforcement scheme has been introduced and it has been shown that this scheme has several desirable learning performances such as g-optimality and absolute expediency in the general n-teacher environment.