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/***********************************************************************/
/* */
/* svm_loqo.c */
/* */
/* Interface to the PR_LOQO optimization package for SVM. */
/* */
/* Author: Thorsten Joachims */
/* Date: 19.07.99 */
/* */
/* Copyright (c) 1999 Universitaet Dortmund - All rights reserved */
/* */
/* This software is available for non-commercial use only. It must */
/* not be modified and distributed without prior permission of the */
/* author. The author is not responsible for implications from the */
/* use of this software. */
/* */
/***********************************************************************/
# include <math.h>
# include "pr_loqo/pr_loqo.h"
# include "svm_common.h"
/* Common Block Declarations */
long verbosity;
/* /////////////////////////////////////////////////////////////// */
# define DEF_PRECISION_LINEAR 1E-8
# define DEF_PRECISION_NONLINEAR 1E-14
double *optimize_qp();
double *primal=0,*dual=0;
double init_margin=0.15;
long init_iter=500,precision_violations=0;
double model_b;
double opt_precision=DEF_PRECISION_LINEAR;
/* /////////////////////////////////////////////////////////////// */
void *my_malloc();
double *optimize_qp(qp,epsilon_crit,nx,threshold,learn_parm)
QP *qp;
double *epsilon_crit;
long nx; /* Maximum number of variables in QP */
double *threshold;
LEARN_PARM *learn_parm;
/* start the optimizer and return the optimal values */
{
register long i,j,result;
double margin,obj_before,obj_after;
double sigdig,dist,epsilon_loqo;
int iter;
if(!primal) { /* allocate memory at first call */
primal=(double *)my_malloc(sizeof(double)*nx*3);
dual=(double *)my_malloc(sizeof(double)*(nx*2+1));
}
if(verbosity>=4) { /* really verbose */
printf("\n\n");
for(i=0;i<qp->opt_n;i++) {
printf("%f: ",qp->opt_g0[i]);
for(j=0;j<qp->opt_n;j++) {
printf("%f ",qp->opt_g[i*qp->opt_n+j]);
}
printf(": a%ld=%.10f < %f",i,qp->opt_xinit[i],qp->opt_up[i]);
printf(": y=%f\n",qp->opt_ce[i]);
}
for(j=0;j<qp->opt_m;j++) {
printf("EQ-%ld: %f*a0",j,qp->opt_ce[j]);
for(i=1;i<qp->opt_n;i++) {
printf(" + %f*a%ld",qp->opt_ce[i],i);
}
printf(" = %f\n\n",-qp->opt_ce0[0]);
}
}
obj_before=0; /* calculate objective before optimization */
for(i=0;i<qp->opt_n;i++) {
obj_before+=(qp->opt_g0[i]*qp->opt_xinit[i]);
obj_before+=(0.5*qp->opt_xinit[i]*qp->opt_xinit[i]*qp->opt_g[i*qp->opt_n+i]);
for(j=0;j<i;j++) {
obj_before+=(qp->opt_xinit[j]*qp->opt_xinit[i]*qp->opt_g[j*qp->opt_n+i]);
}
}
result=STILL_RUNNING;
qp->opt_ce0[0]*=(-1.0);
/* Run pr_loqo. If a run fails, try again with parameters which lead */
/* to a slower, but more robust setting. */
for(margin=init_margin,iter=init_iter;
(margin<=0.9999999) && (result!=OPTIMAL_SOLUTION);) {
sigdig=-log10(opt_precision);
result=pr_loqo((int)qp->opt_n,(int)qp->opt_m,
(double *)qp->opt_g0,(double *)qp->opt_g,
(double *)qp->opt_ce,(double *)qp->opt_ce0,
(double *)qp->opt_low,(double *)qp->opt_up,
(double *)primal,(double *)dual,
(int)(verbosity-2),
(double)sigdig,(int)iter,
(double)margin,(double)(qp->opt_up[0])/4.0,(int)0);
if(isnan(dual[0])) { /* check for choldc problem */
if(verbosity>=2) {
printf("NOTICE: Restarting PR_LOQO with more conservative parameters.\n");
}
if(init_margin<0.80) { /* become more conservative in general */
init_margin=(4.0*margin+1.0)/5.0;
}
margin=(margin+1.0)/2.0;
(opt_precision)*=10.0; /* reduce precision */
if(verbosity>=2) {
printf("NOTICE: Reducing precision of PR_LOQO.\n");
}
}
else if(result!=OPTIMAL_SOLUTION) {
iter+=2000;
init_iter+=10;
(opt_precision)*=10.0; /* reduce precision */
if(verbosity>=2) {
printf("NOTICE: Reducing precision of PR_LOQO due to (%ld).\n",result);
}
}
}
if(qp->opt_m) /* Thanks to Alex Smola for this hint */
model_b=dual[0];
else
model_b=0;
/* Check the precision of the alphas. If results of current optimization */
/* violate KT-Conditions, relax the epsilon on the bounds on alphas. */
epsilon_loqo=1E-10;
for(i=0;i<qp->opt_n;i++) {
dist=-model_b*qp->opt_ce[i];
dist+=(qp->opt_g0[i]+1.0);
for(j=0;j<i;j++) {
dist+=(primal[j]*qp->opt_g[j*qp->opt_n+i]);
}
for(j=i;j<qp->opt_n;j++) {
dist+=(primal[j]*qp->opt_g[i*qp->opt_n+j]);
}
/* printf("LOQO: a[%d]=%f, dist=%f, b=%f\n",i,primal[i],dist,dual[0]); */
if((primal[i]<(qp->opt_up[i]-epsilon_loqo)) && (dist < (1.0-(*epsilon_crit)))) {
epsilon_loqo=(qp->opt_up[i]-primal[i])*2.0;
}
else if((primal[i]>(0+epsilon_loqo)) && (dist > (1.0+(*epsilon_crit)))) {
epsilon_loqo=primal[i]*2.0;
}
}
for(i=0;i<qp->opt_n;i++) { /* clip alphas to bounds */
if(primal[i]<=(0+epsilon_loqo)) {
primal[i]=0;
}
else if(primal[i]>=(qp->opt_up[i]-epsilon_loqo)) {
primal[i]=qp->opt_up[i];
}
}
obj_after=0; /* calculate objective after optimization */
for(i=0;i<qp->opt_n;i++) {
obj_after+=(qp->opt_g0[i]*primal[i]);
obj_after+=(0.5*primal[i]*primal[i]*qp->opt_g[i*qp->opt_n+i]);
for(j=0;j<i;j++) {
obj_after+=(primal[j]*primal[i]*qp->opt_g[j*qp->opt_n+i]);
}
}
/* if optimizer returned NAN values, reset and retry with smaller */
/* working set. */
if(isnan(obj_after) || isnan(model_b)) {
for(i=0;i<qp->opt_n;i++) {
primal[i]=qp->opt_xinit[i];
}
model_b=0;
if(learn_parm->svm_maxqpsize>2) {
learn_parm->svm_maxqpsize--; /* decrease size of qp-subproblems */
}
}
if(obj_after >= obj_before) { /* check whether there was progress */
(opt_precision)/=100.0;
precision_violations++;
if(verbosity>=2) {
printf("NOTICE: Increasing Precision of PR_LOQO.\n");
}
}
if(precision_violations > 500) {
(*epsilon_crit)*=10.0;
precision_violations=0;
if(verbosity>=1) {
printf("\nWARNING: Relaxing epsilon on KT-Conditions.\n");
}
}
(*threshold)=model_b;
if(result!=OPTIMAL_SOLUTION) {
printf("\nERROR: PR_LOQO did not converge. \n");
return(qp->opt_xinit);
}
else {
return(primal);
}
}