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--- uni:8:ml:start [2015-06-11 10:27] – skrupellos
+++ uni:8:ml:start [2015-06-11 11:16] – [Evaluating feedback] skrupellos
@@ 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 \}