stochQN (version 0.1.2-1)

adaQN: adaQN guided optimizer

Description

Optimizes an empirical (possibly non-convex) loss function over batches of sample data.

Usage

adaQN(x0, grad_fun, obj_fun = NULL, pred_fun = NULL,
  initial_step = 0.01, step_fun = function(iter) 1/sqrt((iter/100) +
  1), callback_iter = NULL, args_cb = NULL, verbose = TRUE,
  mem_size = 10, fisher_size = 100, bfgs_upd_freq = 20,
  max_incr = 1.01, min_curvature = 1e-04, y_reg = NULL,
  scal_reg = 1e-04, rmsprop_weight = 0.9, use_grad_diff = FALSE,
  check_nan = TRUE, nthreads = -1, X_val = NULL, y_val = NULL,
  w_val = NULL)

Arguments

x0

Initial values for the variables to optimize.

grad_fun

Function taking as unnamed arguments `x_curr` (variable values), `X` (covariates), `y` (target variable), and `w` (weights), plus additional arguments (`...`), and producing the expected value of the gradient when evalauted on that data.

obj_fun

Function taking as unnamed arguments `x_curr` (variable values), `X` (covariates), `y` (target variable), and `w` (weights), plus additional arguments (`...`), and producing the expected value of the objective function when evalauted on that data. Only required when using `max_incr`.

pred_fun

Function taking an unnamed argument as data, another unnamed argument as the variable values, and optional extra arguments (`...`). Will be called when using `predict` on the object returned by this function.

initial_step

Initial step size.

step_fun

Function accepting the iteration number as an unnamed parameter, which will output the number by which `initial_step` will be multiplied at each iteration to get the step size for that iteration.

callback_iter

Callback function which will be called at the end of each iteration. Will pass three unnamed arguments: the current variable values, the current iteration number, and `args_cb`. Pass `NULL` if there is no need to call a callback function.

args_cb

Extra argument to pass to the callback function.

verbose

Whether to print information about iteration statuses when something goes wrong.

mem_size

Number of correction pairs to store for approximation of Hessian-vector products.

fisher_size

Number of gradients to store for calculation of the empirical Fisher product with gradients. If passing `NULL`, will force `use_grad_diff` to `TRUE`.

bfgs_upd_freq

Number of iterations (batches) after which to generate a BFGS correction pair.

max_incr

Maximum ratio of function values in the validation set under the average values of `x` during current epoch vs. previous epoch. If the ratio is above this threshold, the BFGS and Fisher memories will be reset, and `x` values reverted to their previous average. If not using a validation set, will take a longer batch for function evaluations (same as used for gradients when using `use_grad_diff` = `TRUE`). Pass `NULL` for no function-increase checking.

min_curvature

Minimum value of (s * y) / (s * s) in order to accept a correction pair. Pass `NULL` for no minimum.

y_reg

Regularizer for 'y' vector (gets added y_reg * s). Pass `NULL` for no regularization.

scal_reg

Regularization parameter to use in the denominator for AdaGrad and RMSProp scaling.

rmsprop_weight

If not `NULL`, will use RMSProp formula instead of AdaGrad for approximated inverse-Hessian initialization.

use_grad_diff

Whether to create the correction pairs using differences between gradients instead of empirical Fisher matrix. These gradients are calculated on a larger batch than the regular ones (given by batch_size * bfgs_upd_freq).

check_nan

Whether to check for variables becoming NaN after each iteration, and reverting the step if they do (will also reset BFGS memory).

nthreads

Number of parallel threads to use. If set to -1, will determine the number of available threads and use all of them. Note however that not all the computations can be parallelized, and the BLAS backend might use a different number of threads.

X_val

Covariates to use as validation set (only used when passing `max_incr`). If not passed, will use a larger batch of stored data, in the same way as for Hessian-vector products in SQN.

y_val

Target variable for the covariates to use as validation set (only used when passing `max_incr`). If not passed, will use a larger batch of stored data, in the same way as for Hessian-vector products in SQN.

w_val

Sample weights for the covariates to use as validation set (only used when passing `max_incr`). If not passed, will use a larger batch of stored data, in the same way as for Hessian-vector products in SQN.

Value

an `adaQN` object with the user-supplied functions, which can be fit to batches of data through function `partial_fit`, and can produce predictions on new data through function `predict`.

References

• Keskar, N.S. and Berahas, A.S., 2016, September. "adaQN: An Adaptive Quasi-Newton Algorithm for Training RNNs." In Joint European Conference on Machine Learning and Knowledge Discovery in Databases (pp. 1-16). Springer, Cham.

• Wright, S. and Nocedal, J., 1999. "Numerical optimization." (ch 7) Springer Science, 35(67-68), p.7.

See Also

partial_fit , predict.stochQN_guided , adaQN_free

Examples

# NOT RUN {
### Example regression with randomly-generated data
library(stochQN)

### Will sample data y ~ Ax + epsilon
true_coefs <- c(1.12, 5.34, -6.123)

generate_data_batch <- function(true_coefs, n = 100) {
  X <- matrix(
    rnorm(length(true_coefs) * n),
    nrow=n, ncol=length(true_coefs))
  y <- X %*% true_coefs + rnorm(n)
  return(list(X = X, y = y))
}

### Regular regression function that minimizes RMSE
eval_fun <- function(coefs, X, y, weights=NULL, lambda=1e-5) {
  pred <- as.numeric(X %*% coefs)
  RMSE <- sqrt(mean((pred - y)^2))
  reg  <- 2 * lambda * as.numeric(coefs %*% coefs)
  return(RMSE + reg)
}

eval_grad <- function(coefs, X, y, weights=NULL, lambda=1e-5) {
  pred <- X %*% coefs
  grad <- colMeans(X * as.numeric(pred - y))
  grad <- grad + 2 * lambda * as.numeric(coefs^2)
  return(grad)
}

pred_fun <- function(X, coefs, ...) {
  return(as.numeric(X %*% coefs))
}

### Initialize optimizer form arbitrary values
x0 <- c(1, 1, 1)
optimizer <- adaQN(x0, grad_fun=eval_grad,
  pred_fun=pred_fun, obj_fun=eval_fun, initial_step=1e-0)
val_data <- generate_data_batch(true_coefs, n=100)

### Fit to 50 batches of data, 100 observations each
for (i in 1:50) {
  set.seed(i)
  new_batch <- generate_data_batch(true_coefs, n=100)
  partial_fit(
    optimizer,
    new_batch$X, new_batch$y,
    lambda=1e-5)
  x_curr <- get_curr_x(optimizer)
  i_curr <- get_iteration_number(optimizer)
  if ((i_curr %% 10)  == 0) {
    cat(sprintf(
      "Iteration %d - E[f(x)]: %f - values of x: [%f, %f, %f]\n",
      i_curr,
      eval_fun(x_curr, val_data$X, val_data$y, lambda=1e-5),
      x_curr[1], x_curr[2], x_curr[3]))
  }
}

### Predict for new data
new_batch <- generate_data_batch(true_coefs, n=10)
yhat <- predict(optimizer, new_batch$X)
# }