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3

Question 1 The taylor expansion of $\frac{1}{1-\gamma}$ at $\gamma= 0$ is as follows $$\frac{1}{1-\gamma} = 1 + \gamma + \gamma^2 + \dots$$ When you multiply by $1-\gamma$ you get $$1 = (1-\gamma)(1 + \gamma + \gamma^2 + \dots)$$ Which can be equivalently written as $$1 = (1-\gamma)\sum_\limits{i=0}^{\infty}\gamma^i$$ Hence we can see that by multiplying ...

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There are two relevant neural network designs for DQN: Model q function directly $Q(s,a): \mathcal{S} \times \mathcal{A} \rightarrow \mathbb{R}$, so neural network has concatenated input of state and action, and outputs a single real value. This is arguably the more natural fit to Q learning, but can be inefficient. Model all q values for given state \$Q(s,\...

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Genetic Algorithm is not the best approach here: GA is a stochastic methods and therefore will never guarantee the best possible solution. Your solution (GA individual) is modeled as a simple integer. GA is optimal to find a solution modeled as an array (like our genomes), so it can do mutation and crossover. Good Approach: The set |S|=N can be around ...

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