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--- uni:8:ml:start [2015-06-11 10:27] – skrupellos
+++ uni:8:ml:start [2020-11-18 18:11] (current) – external edit 127.0.0.1
@@ Line 43: / Line 43: @@
   * Softmax grade action probabilities by estimated values  $Q_t$
   * Bolzmann-distribution:  $\pi(a_t) = \frac{e^{Q_t(a)/\tau}}{\sum^n_{b=1} e^{Q_t(b)/\tau}}$
+===== Something else =====
+ $Q_k = \frac{r_1, r_2, \ldots, r_k}{k}$
+==== Incremental implementation ====
+ $Q_{k+1} = Q_k+\frac{1}{k+1}\[r_{k+1} - Q_k\]$
+Common form: NewEstimate == OldEstimate + StepSize[Target - OldEstimate]
+==== Agent-Estimation??? ====
+Learn a policy:
+Policy at step t,  $\pi_t$  is a mapping from states to action probabilities  $\pi_t(s,a)$ =probability that  $a_k=a$  when  $S_k = S$
+Return:
+ $r_{t+1}, r_{t+2},  \ldots$
+We want to maximize the expected reward,  $E\{R_t\}$  for each t
+ $R_t = r_{t+1} + r_{t+2} +  \ldots + r_T$
+Discounted reward
+ $R_t = r_{t+1} + \gamma r_{t+2} + \gamma^2 r_{t+3} + \ldots = \sum_{k=0}^\infty \gamma^k r_{t+k+1} \text{where} 0 \le \gamma \le 1$
+ $\text{shortsited} 0 \leftarrow \gamma \rightarrow 1 \text{farsited}$
+==== Markov Property ====
+$$Pr\{s_{t+1} = s', r_{t+1} = r \mid s_t, a_t, r_t, s_{t-1}, a_{t-1}, r_{t-1}, \ldots s_0, a_0, r_0 \} = Pr \{s_{t+1} = s', r_{t+1} = 1 \mid s_t, a_t \}