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1

The route/trajectory followed by the optimization algorithm basically depends your dataset and the loss function. However, what really matters, for the purpose of final accuracy performance, is the final point which the trajectory converges to.

2

I see why you might be confused. First, the logistic-loss or log-loss is technically called cross-entropy loss. This function is very simple: $CE = -[y \log(p) + (1 - y) \log(1 - p)]$ This tells basically if the predicted class $y$ was right $y=1$ then the loss is $CE=-\log(p)$, if the predicted class was not the right one then the loss is $CE=-\log(1-p)$. ...

1

Yes, you're interpreting the $\max$ there wrongly. In your second formula $$\operatorname{Regret}_{T}(\mathcal{H})=\max _{h^{\star} \in \mathcal{H}} \operatorname{Regret}_{T}\left(h^{\star}\right) \label{1}\tag{1}$$ The sign $=$ means "is defined as", so maybe the following notation is less confusing  \operatorname{Regret}_{T}(\mathcal{H}) \...

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In general it's better to not use sigmoid function in any hidden layer. There are many other great options such as ReLU and ELU. However, if for any reason you have to use sigmoid-like function, then go with Tanh function, at least it has ~0 mean.

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After diving deeper into the material I am able to answer my own question: Simulated Annealing tries to optimize a energy (cost) function by stochastically searching for minima at different temparatures via a Markov Chain Monte Carlo method. The stochasticity comes from the fact that we always accept a new state $c'$ with lower energy ($\Delta E < 0$), ...

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The term REINFORCE actually corresponds to a method of estimating gradients, it is not particular to reinforcement learning. The paper you linked doesn't appear to deal with RL at all, so the issue they're describing is not one that you should expect to find in a policy gradient application. If you're using REINFORCE to estimate policy gradients in RL (this ...

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