Questions tagged [objective-functions]

For questions related to the concept of loss (or cost) function in the context of machine learning.

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2
votes
3answers
243 views

Where does the so-called 'loss' / 'loss function' fit into the idea of a perceptron / artificial neuron (as presented in the figure)?

I am currently studying the textbook Neural Networks and Deep Learning by Charu C. Aggarwal. Chapter 1.2.1.3 Choice of Activation and Loss Functions presents the following figure: $\overline{X}$ is ...
4
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1answer
292 views

Why is the evidence equal to the KL divergence plus the loss?

Why is the equation $$\log p_{\theta}(x^1,...,x^N)=D_{KL}(q_{\theta}(z|x^i)||p_{\phi}(z|x^i))+\mathbb{L}(\phi,\theta;x^i)$$ true, where $x^i$ are data points and $z$ are latent variables? I was ...
6
votes
1answer
222 views

What is the formula used to calculate the loss in the FaceNet model?

The FaceNet model returns the loss of the predictions and ground-truth classes. How is this loss calculated?
5
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1answer
69 views

Why is the mean used to compute the expectation in the GAN loss?

From Goodfellow et al. (2014), we have the adversarial loss: $$ \min_G \, \max_D V (D, G) = \mathbb{E}_{x∼p_{data}(x)} \, [\log \, D(x)] \\ \quad\quad\quad\quad\quad\quad\quad + \, \mathbb{E}_{z∼p_z(...
3
votes
1answer
57 views

What are the necessary mathematical properties to be a loss function in gradient based optimizations?

Loss functions are used in training neural networks. I am interested in knowing the mathematical properties that are necessary for a loss function to participate in gradient descent optimization. I ...
0
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1answer
57 views

An explanation involving the sign activation, its affect on the loss function, and the perceptron and perceptron criterion: what is this saying?

I am currently studying the textbook Neural Networks and Deep Learning by Charu C. Aggarwal. Chapter 1.2.1.3 Choice of Activation and Loss Functions says the following: The classical activation ...
20
votes
3answers
25k views

How can we process the data from both the true distribution and the generator?

I'm struggling to understand the GAN loss function as provided in Understanding Generative Adversarial Networks (a blog post written by Daniel Seita). In the standard cross-entropy loss, we have an ...
3
votes
1answer
9k views

What is an objective function?

Local search algorithms are useful for solving pure optimization problems, in which the aim is to find the best state according to an objective function. My question is what is the objective function?
3
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1answer
222 views

What is the difference between a fitness function and a reward function?

In reinforcement learning (RL), the reward function (RF), which can be denoted as $r(s)$, $r(s, a)$, $r(s, a, s')$, $r(s, s')$ depending on its specific definition, provides the learning signal, which ...
3
votes
0answers
252 views

Understanding log probabilities of actions in the PPO objective

I'm trying to implement the Proximal Policy Optimization (PPO) algorithm (code here), but I am confused about certain concepts. What is the correct way to implement log probability of a policy (...
3
votes
2answers
1k views

What are the major differences between cost, loss, error, fitness, utility, objective, criterion functions?

I find the terms cost, loss, error, fitness, utility, objective, criterion functions to be interchangeable, but any kind of minor difference explained is appreciated.
3
votes
1answer
3k views

How do I calculate the gradient of the hinge loss function?

With reference to the research paper entitled Sentiment Embeddings with Applications to Sentiment Analysis, I am trying to implement its sentiment ranking model in Python, for which I am required to ...
2
votes
1answer
128 views

Generation of 'new log probabilities' in continuous action space PPO

I have a conceptual question for you all that hopefully I can convey clearly. I am building an RL agent in Keras using continuous PPO to control a laser attached to a pan/tilt turret for target ...
1
vote
1answer
119 views

In logistic regression, why is the binary cross-entropy loss function convex?

I am studying logistic regression for binary classification. The loss function used is cross-entropy. For a given input $x$, if our model outputs $\hat{y}$ instead of $y$, the loss is given by $$\text{...
1
vote
1answer
139 views

What is the best loss function for convolution neural network and autoencoder?

What is the best choice for loss function in Convolution Neural Network and in Autoencoder in particular - and why? I understand that the MSE is probably not the best choice, because little ...
0
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1answer
42 views

Does average loss function in GAN training is just an approximation of value function and does not ensure convergence of generator and discriminator?

The value function on which convergence has been proved by the original paper of GAN is $$\min_G \max_DV(D, G) = \mathbb{E}_{x ∼ P_{data}}[\log D(x)] + \mathbb{E}_{z ∼ p_z}[log (1 - D(G(z)))]$$ and ...
0
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1answer
624 views

Why is this PyTorch implementation of the actor-critic algorithm inconsistent with the mathematical formulas?

This PyTorch implementation of the actor-critic algorithm calculates the losses like so: ...