[petsc-users] TAO: armijo condition not fulfilled

Andreas Mang andreas at ices.utexas.edu
Thu Jun 11 16:54:15 CDT 2015 

Hey Jason:

I’ve added the flag and it works like a charm (see output below). Yaaayyyy! :)

Thanks! /A

P.S: I still wonder why the successive evaluations of the objective kicked me out, though (i.e. why I did get monotonically *increasing* objective values; I also tried to switch the search direction using “tao_ls_armijo_nondescending” which did not help). Anyway...

Output:

Tao Object: 1 MPI processes
  type: nls
      Newton steps: 2
      BFGS steps: 0
      Scaled gradient steps: 0
      Gradient steps: 0
      nls ksp atol: 0
      nls ksp rtol: 2
      nls ksp ctol: 0
      nls ksp negc: 0
      nls ksp dtol: 0
      nls ksp iter: 0
      nls ksp othr: 0
  TaoLineSearch Object:   1 MPI processes
    type: armijo
  KSP Object:   1 MPI processes
    type: cg
  total KSP iterations: 31
  convergence tolerances: fatol=0,   frtol=0
  convergence tolerances: gatol=0,   steptol=0,   gttol=0.0001
  Residual in Function/Gradient:=2.69882e-06
  Objective value=0.370287
  total number of iterations=2,                          (max: 50)
  total number of function evaluations=2,                  max: 10000
  total number of gradient evaluations=2,                  max: 10000
  total number of function/gradient evaluations=1,      (max: 10000)
  total number of Hessian evaluations=2
  Solution converged:    ||g(X)||/||g(X0)|| <= gttol


> On Jun 11, 2015, at 4:13 PM, Jason Sarich <jason.sarich at gmail.com> wrote:
> 
> Hi Andreas, 
> 
> I'm pretty sure this is a bug on my side, directly related to the ls->reason
> 
> Can you try fixing src/tao/linesearch/impls/armijo/armijo.c so it sets this correctly? 
> 
> before (line 275):
>  /* Successful termination, update memory */
>   armP->lastReference = ref;
> 
>   /* Successful termination, update memory */
>   ls->reason = TAOLINESEARCH_SUCCESS;
>   armP->lastReference = ref;
> 
> On Thu, Jun 11, 2015 at 3:26 PM, Andreas Mang <andreas at ices.utexas.edu <mailto:andreas at ices.utexas.edu>> wrote:
> Hey Jason:
> 
> Thanks for looking into this. In the meantime I have checked against your elliptic tao example using an Armijo linesearch. It works (i.e. converges) as you suggested in an earlier email even though it returns the “wrong" flag. For my problem it does even choke if I set the regularization parameter to 1E6 (essentially solving a quadratic problem).
> 
> A final question before I continue the struggle by myself: It says “gradient steps: 1” instead of “gradient steps: 0” in the outputs (Armijo vs. More-Thuente / Unit). Does it start doing gradient evaluations? Maybe this helps me to further poke my code. 
> 
> I’ll continue to look into this. I’ll come back to you if I discover that the problem is on the PETSc side of things and I can reproduce the problem with a toy example.
> 
> Thanks for your time! /Andreas
> 
> 
>> On Jun 11, 2015, at 3:03 PM, Jason Sarich <jason.sarich at gmail.com <mailto:jason.sarich at gmail.com>> wrote:
>> 
>> Hi Andreas,
>> 
>> I don't see anything obviously wrong. If the function is very flat, you can try setting -tao_ls_armijo_sigma to a smaller number. If you continue to have problems, please let me know. It would definitely help if you have an example you could send me that reproduces this behavior.
>> 
>> Jason
>> 
>> 
>> 
>> 
>> On Thu, Jun 11, 2015 at 1:12 PM, Andreas Mang <andreas at ices.utexas.edu <mailto:andreas at ices.utexas.edu>> wrote:
>> Hey Jason:
>> 
>> The line search fails. If I use Armijo I get
>> 
>> TaoLineSearch Object:
>>   type: armijo
>>       maxf=30, ftol=1e-10, gtol=0.0001
>>       Armijo linesearch    : alpha=1 beta=0.5     sigma=0.0001     memsize=1
>>   maximum function evaluations=30
>>   tolerances: ftol=0.0001, rtol=1e-10, gtol=0.9
>>   total number of function evaluations=1
>>   total number of gradient evaluations=1
>>   total number of function/gradient evaluations=0
>>   Termination reason: 0
>> 
>> The parameters seem to be the default ones also suggested by Nocedal and Wright. So I did not change anything. The termination reason is equivalent to TAOLINESEARCH_CONTINUE_ITERATING. I am not checking the reason directly. I guess it starts reducing the step size after that. I can see that my objective function get’s evaluated (as expected); however, the objective values increase (from what I see when monitoring the evaluations of my objective). This leads to a failure in the line search and made (still makes) me believe there is a bug on my side (which I have not found yet). However, if I use a unit step it converges (relative change of the gradient e.g. to 1E-9; see bottom of this email).  If I use More & Thuente, same thing. No reduction in step size necessary.
>> 
>> If you suggest that I should do some further testing on simpler problems, I’m happy to do so. After looking at the code, I just felt like there obviously is something wrong in the line-search implementation.
>> 
>> Thanks for your help.
>> /Andreas
>> 
>> Here’s the output after the first iteration (where the Armijo line search fails):
>> 
>> TaoLineSearch Object:
>>   type: armijo
>>       maxf=30, ftol=1e-10, gtol=0.0001
>>       Armijo linesearch    : alpha=1 beta=0.5     sigma=0.0001     memsize=1
>>   maximum function evaluations=30
>>   tolerances: ftol=0.0001, rtol=1e-10, gtol=0.9
>>   total number of function evaluations=1
>>   total number of gradient evaluations=1
>>   total number of function/gradient evaluations=0
>>   Termination reason: 0
>> TaoLineSearch Object:
>>   type: armijo
>>       maxf=30, ftol=1e-10, gtol=0.0001
>>       Armijo linesearch    : alpha=1 beta=0.5     sigma=0.0001     memsize=1
>>   maximum function evaluations=30
>>   tolerances: ftol=0.0001, rtol=1e-10, gtol=0.9
>>   total number of function evaluations=30
>>   total number of gradient evaluations=0
>>   total number of function/gradient evaluations=0
>>   Termination reason: 4
>> 
>> With final output (end of optimization):
>> 
>> Tao Object: 1 MPI processes
>>   type: nls
>>       Newton steps: 1
>>       BFGS steps: 0
>>       Scaled gradient steps: 0
>>       Gradient steps: 1
>>       nls ksp atol: 0
>>       nls ksp rtol: 1
>>       nls ksp ctol: 0
>>       nls ksp negc: 0
>>       nls ksp dtol: 0
>>       nls ksp iter: 0
>>       nls ksp othr: 0
>>   TaoLineSearch Object:   1 MPI processes
>>     type: armijo
>>   KSP Object:   1 MPI processes
>>     type: cg
>>   total KSP iterations: 21
>>   convergence tolerances: fatol=0,   frtol=0
>>   convergence tolerances: gatol=0,   steptol=0,   gttol=0.0001
>>   Residual in Function/Gradient:=0.038741
>>   Objective value=0.639121
>>   total number of iterations=0,                          (max: 50)
>>   total number of function evaluations=31,                  max: 10000
>>   total number of gradient evaluations=1,                  max: 10000
>>   total number of function/gradient evaluations=1,      (max: 10000)
>>   total number of Hessian evaluations=1
>>   Solver terminated: -6   Line Search Failure
>> 
>> This is without line-search (unit step size):
>> 
>> Tao Object: 1 MPI processes
>>   type: nls
>>       Newton steps: 3
>>       BFGS steps: 0
>>       Scaled gradient steps: 0
>>       Gradient steps: 0
>>       nls ksp atol: 0
>>       nls ksp rtol: 3
>>       nls ksp ctol: 0
>>       nls ksp negc: 0
>>       nls ksp dtol: 0
>>       nls ksp iter: 0
>>       nls ksp othr: 0
>>   TaoLineSearch Object:   1 MPI processes
>>     type: unit
>>   KSP Object:   1 MPI processes
>>     type: cg
>>   total KSP iterations: 71
>>   convergence tolerances: fatol=0,   frtol=0
>>   convergence tolerances: gatol=0,   steptol=0,   gttol=0.0001
>>   Residual in Function/Gradient:=1.91135e-11
>>   Objective value=0.160914
>>   total number of iterations=3,                          (max: 50)
>>   total number of function/gradient evaluations=4,      (max: 10000)
>>   total number of Hessian evaluations=3
>>   Solution converged:    ||g(X)||/||g(X0)|| <= gttol
>> 
>>  
>> 
>>> On Jun 11, 2015, at 12:44 PM, Jason Sarich <jason.sarich at gmail.com <mailto:jason.sarich at gmail.com>> wrote:
>>> 
>>> Hi Andreas,
>>> 
>>> Yes it looks like a bug that the reason is never set, but the line should still terminate. Is the problem you are having with the line search itself, or is it failing because you are checking this ls->reason directly?
>>> 
>>> Jason Sarich
>>> 
>>> 
>>> On Thu, Jun 11, 2015 at 9:53 AM, Andreas Mang <andreas at ices.utexas.edu <mailto:andreas at ices.utexas.edu>> wrote:
>>> Hi guys:
>>> 
>>> I have a problem with the TAO Armijo line search (petsc-3.5.4). My algorithm works if I use the More & Thuente line search (default). I have numerically checked the gradient of my objective. It’s correct. I am happy to write a small snippet of code and do an easy test if you guys disagree, but from what I’ve seen in the line search code it seems obvious to me that there is a bug. Am I missing something or are you not setting
>>> 
>>> ls->reason
>>> 
>>> to
>>> 
>>> TAOLINESEARCH_SUCCESS
>>> 
>>> if the Armijo condition is fulfilled (TaoLineSearchApply_Armijo in armijo.c; line 118 - 302)?!
>>> 
>>> It seems to me that ls->reason is and will remain to be set to
>>> 
>>> TAOLINESEARCH_CONTINUE_ITERATING
>>> 
>>> if everything works (i.e. I don’t hit one of the exceptions). Does this make sense? If not I’ll invest the time and put together a simple test case and, if that works, continue to check my code.
>>> 
>>> /Andreas
>>> 
>>> 
>>> 
>> 
>> 
> 
> 

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