From Kingma and Ba (2015): "We introduce Adam, an algorithm for first-order gradient-based optimization of stochastic objective functions, based on adaptive estimates of lower-order moments. The method is straightforward to implement, is computationally efficient, has little memory requirements, is invariant to diagonal rescaling of the gradients, and is well suited for problems that are large in terms of data and/or parameters. The method is also appropriate for non-stationary objectives and problems with very noisy and/or sparse gradients. The hyper-parameters have intuitive interpretations and typically require little tuning. Some connections to related algorithms, on which Adam was inspired, are discussed. We also analyze the theoretical convergence properties of the algorithm and provide a regret bound on the convergence rate that is comparable to the best known results under the online convex optimization framework. Empirical results demonstrate that Adam works well in practice and compares favorably to other stochastic optimization methods. Finally, we discuss AdaMax, a variant of Adam based on the infinity norm."
adam(f, p, x, y, w, tau, ..., iterlim=5000, iterbreak=iterlim,
alpha=0.01, minibatch=nrow(x), beta1=0.9, beta2=0.999,
epsilon=1e-8, print.level=10)A list with elements:
The best set of parameters found.
The value of f corresponding to estimate.
the function to be minimized, including gradient information
contained in the gradient attribute.
the starting parameters for the minimization.
covariate matrix with number of rows equal to the number of samples and number of columns equal to the number of variables.
response column matrix with number of rows equal to the number of samples.
vector of weights with length equal to the number of samples.
vector of desired tau-quantile(s) with length equal to the number of samples.
additional parameters passed to the f cost function.
the maximum number of iterations before the optimization is stopped.
the maximum number of iterations without progress before the optimization is stopped.
size of the learning rate.
number of samples in each minibatch.
controls the exponential decay rate used to scale the biased first moment estimate.
controls the exponential decay rate used to scale the biased second raw moment estimate.
smoothing term to avoid division by zero.
the level of printing which is done during optimization. A value of
0 suppresses any progress reporting, whereas positive values
report the value of f every print.level iterations.
Kingma, D.P. and J. Ba, 2015. Adam: A method for stochastic optimization. The International Conference on Learning Representations (ICLR) 2015. http://arxiv.org/abs/1412.6980