An adaptive algorithm for gradient-based optimization of stochastic objective functions, often used to train deep neural networks.

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### Stochastic objective function in Adam [duplicate]

Relating to the question What is a stochastic objective function?. In the paper of the Adam Algorithm they also mention a Stochastic objective function when explaining the algorithm. In this context I ...
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Line of thought The weight updates in RMSprop gradient descent can be considered as normalizing a gradient $d\Theta_i$ by the factor $1/(\sqrt{Sd\Theta_i} + \epsilon)$. If $\nabla_\Theta J$ of the ...
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### What is a random variable in ADAM optimizer?

Look at the definition of ADAM optimizer, from the original paper of Kingma and Ba (paper): See algorithm $1$ for pseudo-code of our proposed algorithm Adam. Let $f(\theta)$ be a noisy objective ...
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### Why Exponential Weighted Average in RMSProp

In optimization algorithms such as RMSProp, Adam, etc. why is an exponential weighted average used over a straight sum and divide? Seemingly an exponential weighted average would be useful when the ...
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### Shrinkage / L1 regularization as a loss term versus a constraint (post-process step) with momentum optimizers

I have a complex model with very non-linear operations (divisions, exponentials, matrix inversions, square roots, Cholesky decompositions, etc...) for which I want to optimize the parameters. However, ...
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### spikes in training CNN using Adam

I have an instability issue when training CNN on high dimensional data. I train Unet-3D model (https://arxiv.org/pdf/1505.04597.pdf) with batch normalization layer before each convolution layer. My ...
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I'm reading Hands-On Machine Learning with Scikit-Learn, Keras & Tensorflow and on page 325 (follows up on 326) there's a following piece of text on learning-rate: The learning is arguably the ...
1 vote
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### Pathological curvature

How common is the issue of pathological curvature? I have been reading a post on the internet about it, and I would like to know how common this happens with deep learning models. Could you also ...
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### Training a neural network on chess data

I have been writing a chess engine with a friend and the engine itself is really good already (2700+ CCRL). We had the idea to use a neural network to have a better evaluation of positions. Input to ...
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### Momentum vs Polyak averaging

I'm going through this deck but don't quite get the difference between momentum and Polyak averaging, and what role Polyak averaging plays in modern optimizers. For example, is it correct to say that ...
1 vote
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### What is a stochastic objective function?

In the paper "ADAM: A METHOD FOR STOCHASTIC OPTIMIZATION" they write in the introduction "Often, objective functions are stochastic." I know what a stochastic gradient descent is, but what does it ...
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### Adam converges while SGD does not improve at all

I am trying to build a model based movie recommendation system with a neural network. The architecture looks as follows: ...
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### Do we have guarantees about Adam's convergence when we reach an region with gradient $0$?

Recall the Adam update rule: $$m_t = \beta_1 m_{t-1} + (1 - \beta_1) g_t$$ $$v_t = \beta_2 v_{t-1} + (1 - \beta_2) g_t^2$$ $$\hat{m}_t = \dfrac{m_t}{1 - \beta^t_1}$$ \hat{v}_t = \dfrac{v_t}{1 - \...
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### step size in the first epochs of adam are too large [closed]

When I train models in keras with keras.optimizers.Adam(learning_rate=0.001), I typically get a history of the training error over the training time in epochs like in the plot below. This looks like ...
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### understanding bias correction in ADAM algorithm [duplicate]

why is possible to approximate E[gi^2] with E[gt^2]? by the time we go to the t timestamp, we've already made weight updates, which mean gradients should be different as they are taken from different ...
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### Different optimization behaviours on delta vs non-delta targets

I built a simple classification model that is required to predict a probability distribution for a set of two available classes. The target distributions are not necessarily delta distributions. i.e ...
1 vote
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### SGD versus Adamax on XOR operator

I am trying to resolve the xor operator using neural networks, and to accomplish that this is my code: ...
1 vote
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There is no "gradient" in the standard Random Forest formulation, but can I combine random Forests with an optimisation method like Gradient Descent or SGD? Can I use Adam (Adaptive moment estimation)...
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### How well should I expect Adam to work?

I've been coding up a neural network package for my own amusement, and it seems to work. I've been reading about Adam and from what I've seen it's very difficult to beat. Well, when I implement the ...
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### What does decay_steps mean in Tensorflow tf.train.exponential_decay?

I am trying to implement an exponential learning rate decay with the Adam optimizer for a LSTM. I do not want the 'staircase = true' version. The decay_steps for me feels like the number of steps that ...
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### Why we call ADAM an a adaptive learning rate algorithm if the step size is a constant

In the book "Deep Learning" by Goodfellow et.al, the ADAM algorithm is described in sub-chapter 8.5 "Algorithm with Adaptive Learning Rate". To my understanding an adaptive learning rate should ...
1 vote
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### Adam optimizer's escape from local minima [duplicate]

I noticed some interesting behaviour in my loss history while training my model. Please note the sudden change in test loss at around epoch 106. A similar drop will appear around epoch ~1000. It ...
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I am using ADAM for performing gradient descent. I am having difficulty in setting the learning rate, $\beta_1$ and $\beta_2$. Along with gradient descent, I am projecting the paramters on $L_1$ ball ...
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### what is the mistake of convergence proof in Adam

Sashank J. Reddi et. al in their paper "On the convergence of Adam and beyond" say that, Adam's proof of convergence as stated in original paper is wrong. More than that, they point out that the value ...
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### Understanding a derivation of bias correction for the Adam optimizer

I'm reading paper about the Adam optimizer and went up until the bias-correction section; in the paper they estimate the bias of the moving average of the squared gradient. These are the equations ...
1 vote
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### Adaptive Moment Estimate - What is meant by parameters of Adam optimizer are biased towards zero initially? [duplicate]

Let us consider the Adam optimizer with the equation given below: $w_{t + 1} = w_{t} - \frac{\eta \times \bar{m_t}} {\sqrt{\bar{v_t} + \epsilon}}$ Here $w$ denotes weight (in time $t$ and $t + 1$) ...
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### What does Diagonal Rescaling of the gradients mean in ADAM paper?

I was reading the original paper on ADAM (Adam: A Method for Stochastic Optimization), which mentions: [...] invariant to diagonal rescaling of the gradients, [...] What does it mean? Also, ...
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### Two large decreses in loss function with ADAM optimizer

I am training an RNN with tensorflow using the ADAM optimizer. The loss with respect to iteration has a sort of "two stage" decrease. As shown in the image below. The task itself if just trying to ...
1 vote
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### Decreasing accuracy of neural network after long training

I trained a MLP network in Tensorflow which reached at some point 98.66 % accuracy. I used the MNIST data set and five hidden layers of the following size: 4096, 2048, 4096, 2048, 4096. In Tensorflow ...
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What is the history behind the choice of the name "Adam" as used in Adam: A Method for Stochastic Optimization?
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### Do we need to normalize inputs when using adaptive learning rate optimizers?

As stated in this thread Why do we need to normalize the images before we put them into CNN?, normalization of the inputs to a deep network to have zero mean and unit-deviation will make SGD more ...
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### Difference between Stochastic Approximation (SA) and Stochastic Gradient Descent (SGD)

I understand the intended use cases for both stochastic approximation algorithms like SPSA or FDSA, and for SGD algorithms like Adam. SPSA is intended for noisy objective functions, and Adam for ...
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### What should we do when changing SGD optimizer to Adam optimizer?

Adam is one popular method of the optimization policies with adaptive learning rate. I'm focusing on a image segmentation project using fully convolutional networks. All weights were initialized by ...