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Added another overload of poly_min_extrap() and also improved the speed of 

backtracking_line_search() by making it use 3rd degree polynomial interpolation
after the first step.  Also made it more robust to alpha inputs with improper
signs.
This commit is contained in:
Davis King 2013-09-23 22:53:08 -04:00
parent 53c908e72c
commit 8199ae1a48
2 changed files with 100 additions and 7 deletions
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83
dlib/optimization/optimization_line_search.h
View File

@ -183,6 +183,57 @@ namespace dlib
return put_in_range(0,1,alpha);
}
// ----------------------------------------------------------------------------------------
inline double poly_min_extrap (
double f0,
double d0,
double x1,
double f_x1,
double x2,
double f_x2
)
{
DLIB_ASSERT(0 < x1 && x1 < x2,"Invalid inputs were given to this function");
// The contents of this function follow the equations described on page 58 of the
// book Numerical Optimization by Nocedal and Wright, second edition.
matrix<double,2,2> m;
matrix<double,2,1> v;
const double aa2 = x2*x2;
const double aa1 = x1*x1;
m = aa2, -aa1,
-aa2*x2, aa1*x1;
v = f_x1 - f0 - d0*x1,
f_x2 - f0 - d0*x2;
double temp = aa2*aa1*(x1-x2);
// just take a guess if this happens
if (temp == 0)
{
return x1/2.0;
}
matrix<double,2,1> temp2;
temp2 = m*v/temp;
const double a = temp2(0);
const double b = temp2(1);
temp = b*b - 3*a*d0;
if (temp < 0 || a == 0)
{
// This is probably a line so just pick the lowest point
if (f0 < f_x2)
return 0;
else
return x2;
}
temp = (-b + std::sqrt(temp))/(3*a);
return put_in_range(0, x2, temp);
}
// ----------------------------------------------------------------------------------------
inline double lagrange_poly_min_extrap (
@ -447,11 +498,17 @@ namespace dlib
<< "\n\t max_iter: " << max_iter
);
// If the gradient is telling us we need to search backwards then that is what we
// will do.
if (d0 > 0 && alpha > 0)
// make sure alpha is going in the right direction. That is, it should be opposite
// the direction of the gradient.
if ((d0 > 0 && alpha > 0) ||
(d0 < 0 && alpha < 0))
{
alpha *= -1;
}
bool have_prev_alpha = false;
double prev_alpha = 0;
double prev_val = 0;
unsigned long iter = 0;
while (true)
{
@ -466,12 +523,26 @@ namespace dlib
// Interpolate a new alpha. We also make sure the step by which we
// reduce alpha is not super small.
double step;
if (!have_prev_alpha)
{
if (d0 < 0)
step = put_in_range(0.1,0.9, poly_min_extrap(f0, d0, val));
step = alpha*put_in_range(0.1,0.9, poly_min_extrap(f0, d0, val));
else
step = put_in_range(0.1,0.9, poly_min_extrap(f0, -d0, val));
step = alpha*put_in_range(0.1,0.9, poly_min_extrap(f0, -d0, val));
have_prev_alpha = true;
}
else
{
if (d0 < 0)
step = put_in_range(0.1*alpha,0.9*alpha, poly_min_extrap(f0, d0, alpha, val, prev_alpha, prev_val));
else
step = put_in_range(0.1*alpha,0.9*alpha, -poly_min_extrap(f0, -d0, -alpha, val, -prev_alpha, prev_val));
}
alpha *= step;
prev_alpha = alpha;
prev_val = val;
alpha = step;
}
}
}

22
dlib/optimization/optimization_line_search_abstract.h
View File

@ -119,6 +119,28 @@ namespace dlib
- returns the point in the range [0,1] that minimizes the polynomial c(x)
!*/
// ----------------------------------------------------------------------------------------
inline double poly_min_extrap (
double f0,
double d0,
double x1,
double f_x1,
double x2,
double f_x2
)
/*!
requires
- 0 < x1 < x2
ensures
- let f(x) be a 3rd degree polynomial such that:
- f(0) == f0
- derivative of f(x) at x==0 is d0
- f(x1) == f_x1
- f(x2) == f_x2
- returns the point in the range [0,x2] that minimizes the polynomial f(x)
!*/
// ----------------------------------------------------------------------------------------
inline double lagrange_poly_min_extrap (