Conditions for Convergence
• If:
– rewards are bounded (as before)
– the training rule is:
Qn(s,a) ß (1-an)Qn-1(s,a) + an(r + g maxa'[Qn-1(s',a')])
– 0 £ g < 1
– Sumi=1à¥(an(i,s,a)) = ¥ where n(i,s,a) is the iteration corresponding
to the ith time a is applied to s
– Sumi=1à¥(an(i,s,a))2 < ¥
• Then Q will converge correctly as n à ¥ with probability
1.