oLBFGS {stochQN}

oLBFGS guided optimizer

Description

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

Usage

oLBFGS(x0, grad_fun, pred_fun = NULL, initial_step = 0.01,
  step_fun = function(iter) 1/sqrt((iter/10) + 1),
  callback_iter = NULL, args_cb = NULL, verbose = TRUE,
  mem_size = 10, hess_init = NULL, min_curvature = 1e-04,
  y_reg = NULL, check_nan = TRUE, nthreads = -1)

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.

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.

hess_init

Value to which to initialize the diagonal of H0. If passing 'NULL', will use the same initializion as for SQN ((s_last * y_last) / (y_last * y_last)).

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.

check_nan

Whether to check for variables becoming NA 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.

Value

an 'oLBFGS' 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

• Schraudolph, N.N., Yu, J. and Guenter, S., 2007, March. "A stochastic quasi-Newton method for online convex optimization." In Artificial Intelligence and Statistics (pp. 436-443).

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

See Also

partial_fit , predict.stochQN_guided , oLBFGS_free

Examples

### 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  <- 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 <- oLBFGS(x0, grad_fun=eval_grad,
  pred_fun=pred_fun, initial_step=1e-1)
val_data <- generate_data_batch(true_coefs, n=100)

### Fit to 50 batches of data, 100 observations each
set.seed(1)
for (i in 1:50) {
  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)