1. Learner is not told what to do
2. Trial and error search
3. Delayed reward
4. We need to explore round exploit

• Policy what to do
• Reward what is good
• Value what is good because it predicts reward
• Model what follows what

• Evaluating actions vs. inst???
• Example: n-armed bandit
  • evaluate feedback
• after each play $a_t$ we got a reward r_t where $ E\{r_t \mid a_t \} = Q^*(a_t)$
• optimize reward ??? 1000 plays
• Exploration/
  • ??? $Q_t(a) = Q^*(a)$ action value estimate
  • ???
• $a_t = a_t^*$ ⇒ exploitation
• $a_t \ne a_t^*$ ⇒ exploration

Suppose by the ??? play actions $a$ had been choosen $k_a$ times, producing rewards $r_1, r_2, \dots r_{k,a}$ $$Q_t(a) = \frac{r_1, r_2, \dots r_{k,a}}{k_a}$$ $$\lim_{k \rightarrow \infty} Q_t(a) = Q^*(a)$$

• feeding: $a_t = a_t^* = avg_a max Q_t(a)$
• $\epsilon$-feeding = $a_t^*$????

• $n=10$ possible actions
• Each Q^*(a) is chosen rounding from N(0,1)
• 1000 plays, avergage our 2000 experiments

• Softmax grade action probabilities by estimated values $Q_t$
• Bolzmann-distribution: $$\pi(a_t) = \frac{e^{Q_t(a)/\tau}}{\sum^n_{b=1} e^{Q_t(b)/\tau}}$$