REBayes Error in KWDual MKS_RES_TERM_STALL - r

Question

I am trying to run the following simulation below. Note that this does require Mosek and RMosek to be installed!
I keep getting the error
Error in KWDual(A, d, w, ...) :
Mosek error: MSK_RES_TRM_STALL: The optimizer is terminated due to slow progress.
How can I resolve the MSK_RES_TRM_STALL error?
Further Research
When looking up the documentation for this I found this:
The optimizer is terminated due to slow progress.
Stalling means that numerical problems prevent the optimizer from making reasonable progress and that it makes no sense to continue. In many cases this happens if the problem is badly scaled or otherwise ill-conditioned. There is no guarantee that the solution will be feasible or optimal. However, often stalling happens near the optimum, and the returned solution may be of good quality. Therefore, it is recommended to check the status of the solution. If the solution status is optimal the solution is most likely good enough for most practical purposes.
Please note that if a linear optimization problem is solved using the interior-point optimizer with basis identification turned on, the returned basic solution likely to have high accuracy, even though the optimizer stalled.
Some common causes of stalling are a) badly scaled models, b) near feasible or near infeasible problems.
So I checked the final value A, but nothing was in it. I found that if I change the simulations from 1000 to 30 I do get values (A <- sim1(30, 30, setting = 1)), but this is suboptimal.
Reproducible Script
KFE <- function(y, T = 300, lambda = 1/3){
# Kernel Fourier Estimator: Stefanski and Carroll (Statistics, 1990)
ks <- function(s,x) exp(s^2/2) * cos(s * x)
K <- function(t, y, lambda = 1/3){
k <- y
for(i in 1:length(y)){
k[i] <- integrate(ks, 0, 1/lambda, x = (y[i] - t))$value/pi
}
mean(k)
}
eps <- 1e-04
if(length(T) == 1) T <- seq(min(y)-eps, max(y)+eps, length = T)
g <- T
for(j in 1:length(T))
g[j] <- K(T[j], y, lambda = lambda)
list(x = T, y = g)
}
BDE <- function(y, T = 300, df = 5, c0 = 1){
# Bayesian Deconvolution Estimator: Efron (B'ka, 2016)
require(splines)
eps <- 1e-04
if(length(T) == 1) T <- seq(min(y)-eps, max(y)+eps, length = T)
X <- ns(T, df = df)
a0 <- rep(0, ncol(X))
A <- dnorm(outer(y,T,"-"))
qmle <- function(a, X, A, c0){
g <- exp(X %*% a)
g <- g/sum(g)
f <- A %*% g
-sum(log(f)) + c0 * sum(a^2)^.5
}
ahat <- nlm(qmle, a0, X=X, A=A, c0 = c0)$estimate
g <- exp(X %*% ahat)
g <- g/integrate(approxfun(T,g),min(T),max(T))$value
list(x = T,y = g)
}
W <- function(G, h, interp = FALSE, eps = 0.001){
#Wasserstein distance: ||G-H||_W
H <- cumsum(h$y)
H <- H/H[length(H)]
W <- integrate(approxfun(h$x, abs(G(h$x) - H)),min(h$x),max(h$x))$value
list(W=W, H=H)
}
biweight <- function(x0, x, bw){
t <- (x - x0)/bw
(1-t^2)^2*((t> -1 & t<1)-0) *15/16
}
Wasser <- function(G, h, interp = FALSE, eps = 0.001, bw = 0.7){
#Wasserstein distance: ||G-H||_W
if(interp == "biweight"){
yk = h$x
for (j in 1:length(yk))
yk[j] = sum(biweight(h$x[j], h$x, bw = bw)*h$y/sum(h$y))
H <- cumsum(yk)
H <- H/H[length(H)]
}
else {
H <- cumsum(h$y)
H <- H/H[length(H)]
}
W <- integrate(approxfun(h$x, abs(G(h$x) - H)),min(h$x),max(h$x),
rel.tol = 0.001, subdivisions = 500)$value
list(W=W, H=H)
}
sim1 <- function(n, R = 10, setting = 0){
A <- matrix(0, 4, R)
if(setting == 0){
G0 <- function(t) punif(t,0,6)/8 + 7 * pnorm(t, 0, 0.5)/8
rf0 <- function(n){
s <- sample(0:1, n, replace = TRUE, prob = c(1,7)/8)
rnorm(n) + (1-s) * runif(n,0,6) + s * rnorm(n,0,0.5)
}
}
else{
G0 <- function(t) 0 + 7 * (t > 0)/8 + (t > 2)/8
rf0 <- function(n){
s <- sample(0:1, n, replace = TRUE, prob = c(1,7)/8)
rnorm(n) + (1-s) * 2 + s * 0
}
}
for(i in 1:R){
y <- rf0(n)
g <- BDE(y)
Wg <- Wasser(G0, g)
h <- GLmix(y)
Wh <- Wasser(G0, h)
Whs <- Wasser(G0, h, interp = "biweight")
k <- KFE(y)
Wk <- Wasser(G0, k)
A[,i] <- c(Wg$W, Wk$W, Wh$W, Whs$W)
}
A
}
require(REBayes)
set.seed(12)
A <- sim1(1000, 1000, setting = 1)

Answer 1

I ran the code and indeed it stalls at the end, but the solution is not any worse than in the preceding cases that solve without stall:
17 1.7e-07 3.1e-10 6.8e-12 1.00e+00 5.345949918e+00 5.345949582e+00 2.4e-10 0.40
18 2.6e-08 3.8e-11 2.9e-13 1.00e+00 5.345949389e+00 5.345949348e+00 2.9e-11 0.41
19 2.6e-08 3.8e-11 2.9e-13 1.00e+00 5.345949389e+00 5.345949348e+00 2.9e-11 0.48
20 2.6e-08 3.8e-11 2.9e-13 1.00e+00 5.345949389e+00 5.345949348e+00 2.9e-11 0.54
Optimizer terminated. Time: 0.62
Interior-point solution summary
Problem status : PRIMAL_AND_DUAL_FEASIBLE
Solution status : OPTIMAL
Primal. obj: 5.3459493890e+00 nrm: 6e+00 Viol. con: 2e-08 var: 0e+00 cones: 4e-09
Dual. obj: 5.3459493482e+00 nrm: 7e-01 Viol. con: 1e-11 var: 4e-11 cones: 0e+00
A quick hack for now that worked for me is to relax the termination tolerances a little bit in the call to GLmix:
control <- list()
control$dparam <- list(INTPNT_CO_TOL_REL_GAP=1e-7,INTPNT_CO_TOL_PFEAS=1e-7,INTPNT_CO_TOL_DFEAS=1e-7)
h <- GLmix(y,control=control,verb=5)
A better solution as I indicated in the comments is not to treat the stall termination code as an error by the REBayes package but use solution status/quality instead.

Answer 2

I have modified the return from KWDual to avoid such messages provided that
the status sol$itr$solsta from Mosek is "Optimal" in REBayes v2.2 now on CRAN.