uni:8:ml:start
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- | - Learner is not told what to do | + | |
- | - Trial and error search | + | - Trial and error search |
- | - Delayed reward | + | - Delayed reward |
- | - We need to explore round exploit | + | - 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 feedback ==== | ||
+ | * 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 | ||
+ | == Action Value Methods == | ||
+ | Suppose by the ??? play actions $a$ had been choosen $k_a$ times, producing rewards $r_1, r_2, \dots r_{k,a}$ | ||
+ | $$Q_t(a) = \frac{r_1, r_2, \dots r_{k, | ||
+ | $$\lim_{k \rightarrow \infty} Q_t(a) = Q^*(a)$$ | ||
+ | |||
+ | == \epsilon-feeding action selection == | ||
+ | * feeding: $a_t = a_t^* = avg_a max Q_t(a)$ | ||
+ | * $\epsilon$-feeding = $a_t^*$???? | ||
+ | == In the 10-Armed test bed == | ||
+ | * $n=10$ possible actions | ||
+ | * Each Q^*(a) is chosen rounding from N(0,1) | ||
+ | * 1000 plays, avergage our 2000 experiments | ||
+ | |||
+ | == Softmax action selection == | ||
+ | * Softmax grade action probabilities by estimated values $Q_t$ | ||
+ | * Bolzmann-distribution: | ||
+ | |||
+ | ===== Something else ===== | ||
+ | $$ Q_k = \frac{r_1, r_2, \ldots, r_k}{k}$$ | ||
+ | |||
+ | ==== Incremental implementation ==== | ||
+ | $$Q_{k+1} = Q_k+\frac{1}{k+1}\[r_{k+1} - Q_k\]$$ | ||
+ | |||
+ | Common form: NewEstimate == OldEstimate + StepSize[Target - OldEstimate] | ||
+ | |||
+ | ==== Agent-Estimation??? | ||
+ | Learn a policy: | ||
+ | Policy at step t, $\pi_t$ is a mapping from states to action probabilities $\pi_t(s, | ||
+ | |||
+ | Return: | ||
+ | $$r_{t+1}, r_{t+2}, | ||
+ | |||
+ | 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 \} |
uni/8/ml/start.txt · Last modified: 2020-11-18 18:11 by 127.0.0.1