SQN: SQN guided optimizer
In stochQN: Stochastic Limited Memory Quasi-Newton Optimizers

Description Usage Arguments Value References See Also Examples

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

SQN(x0, grad_fun, hess_vec_fun = NULL, pred_fun = NULL,
  initial_step = 0.001, step_fun = function(iter) 1/sqrt((iter/10) +
  1), callback_iter = NULL, args_cb = NULL, verbose = TRUE,
  mem_size = 10, bfgs_upd_freq = 20, min_curvature = 1e-04,
  y_reg = NULL, use_grad_diff = FALSE, check_nan = TRUE,
  nthreads = -1)

`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.
`hess_vec_fun`	Function taking as unnamed arguments 'x_curr' (variable values), 'vec' (numeric vector), 'X' (covariates), 'y' (target variable), and 'w' (weights), plus additional arguments ('...'), and producing the expected value of the Hessian (with variable values at 'x_curr') when evalauted on that data, multiplied by the vector 'vec'. Not required when using 'use_grad_diff' = 'TRUE'.
`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.
`bfgs_upd_freq`	Number of iterations (batches) after which to generate a BFGS correction pair.
`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.
`use_grad_diff`	Whether to create the correction pairs using differences between gradients instead of Hessian-vector products. 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.

an 'SQN' 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'.

Byrd, R.H., Hansen, S.L., Nocedal, J. and Singer, Y., 2016. "A stochastic quasi-Newton method for large-scale optimization." SIAM Journal on Optimization, 26(2), pp.1008-1031.
Wright, S. and Nocedal, J., 1999. "Numerical optimization." (ch 7) Springer Science, 35(67-68), p.7.

partial_fit , predict.stochQN_guided , SQN_free

### Example logistic regression with randomly-generated data
library(stochQN)

### Will sample data y ~ Bernoulli(sigm(Ax))
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 <- 1 / (1 + exp(-as.numeric(X %*% true_coefs)))
  y <- as.numeric(y >= runif(n))
  return(list(X = X, y = y))
}

### Logistic regression likelihood/loss
eval_fun <- function(coefs, X, y, weights=NULL, lambda=1e-5) {
  pred    <- 1 / (1 + exp(-as.numeric(X %*% coefs)))
  logloss <- mean(-(y * log(pred) + (1 - y) * log(1 - pred)))
  reg     <- lambda * as.numeric(coefs %*% coefs)
  return(logloss + reg)
}

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

eval_Hess_vec <- function(coefs, vec, X, y, weights=NULL, lambda=1e-5) {
  pred <- 1 / (1 + exp(-as.numeric(X %*% coefs)))
  diag <- pred * (1 - pred)
  Hp   <- (t(X) * diag) %*% (X %*% vec)
  Hp   <- Hp / NROW(X) + 2 * lambda * vec
  return(as.numeric(Hp))
}

pred_fun <- function(X, coefs, ...) {
  return(1 / (1 + exp(-as.numeric(X %*% coefs))))
}


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

### Fit to 250 batches of data, 100 observations each
set.seed(1)
for (i in 1:250) {
  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 %3d - 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)