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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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Penalty (barrier function) is perfectly valid and simplest method for simplex type constraint (L1 norm is simplex constraint on absolute values). Any type of barrier function may work, logarithmic, reciprocal or quadratic. All of them supported by any major framework(pytorch, tensorflow), just add them to loss function. You would need some hyperparameter ...

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The thing is, the decoder samples from a latent mu and sigma, so you cant sample from a raw image directly. But if you’re trying to put a random image into the encoder of a trained VAE to match it to some sample image (via reconstruction loss), then your random input image will converge to the target sample. This will work when the following VAE ...

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If I understood correctly, your problem is about finding the optimal way to execute a series of tasks in order to maximize the results, using Genetic Algorithms. In few words, you're trying to solve the salesman problem. If I am correct, you're looking for Crossover and Mutation algorithms that allow you to work with ordered sets of elements. For these ...

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You have two broad categories of options, prevention and repair. Prevention means defining a crossover and mutation operator that try to be more intelligent about respecting the constraints. Suppose you have an encoding where each individual is a list of integers, and the constraint is that there can't be duplicates. You might define a crossover operator ...

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