Update Rule for
Nondeterministic Case
• Q(s,a) = E[r(s,a)] + g Sums'[P(s'|s,a) maxa'[Q(s',a')]]
• Our previous update rule fails to converge.
– Suppose we start with the correct Q function.
– Nondeterminism will change Q forever.
• Need to slow change to Q over time:
• Let an = 1/(1+visitsn(s,a)) (including current visit)
• Qn(s,a) ß (1-an)(old estimate) + an(new estimate)
• Qn(s,a) ß (1-an)Qn-1(s,a) + an(r + g maxa'[Qn-1(s',a')])