My (current) objective function has about 30 parameters, so N^2 complexity isn't a problem (storage-wise or matrix multiplication time wise). Also, for my current work, the objective function is much slower than the optimization routine itself, so the overhead of a full inverse Hessian is relatively small.
In Optim.jl, L-BFGS seems to use the same line search routine as BFGS. Is there a reason to think it should take substantively different search path? -thom On Wednesday, August 20, 2014 9:18:29 AM UTC-5, John Myles White wrote: > > I don’t think I’m going to have time to look into this soon, but why do > you use BFGS? In my experience L-BFGS is almost always better. > > Of course, we want our BFGS code to be better. But I use BFGS only quite > rarely because of its O(N^2) complexity. > > — John > > On Aug 20, 2014, at 7:16 AM, Thomas Covert <[email protected] > <javascript:>> wrote: > > Ok after reading the paper which the hz_linesearch! routine is based on, I > can see that I'm wrong about this. Still puzzled, but definitely wrong! > > On Tuesday, August 19, 2014 1:51:37 PM UTC-5, Thomas Covert wrote: >> >> I'm seeing this same error (ERROR: assertion failed: lsr.slope[ib] < 0) >> again, and this time my gradients (evaluated at "reasonable" input values) >> match the finite difference output generated by Calculus.jl's "gradient" >> function. The function I am trying to minize is globally convex (its a >> multinomial logit log-likelihood). >> >> I encounter this assertion error after a few successful iterations of >> BFGS and it is caused by NAN's in the gradient of the test point. BFGS >> gets to this >> test point because the step size it passes to hz_linesearch eventually >> gets to be large, and a big enough step can cause floating point errors in >> the calculation of the the derivatives. For example, on a recent >> minimization attempt, the assertion error happens when "c" (the step size >> passed by bfgs to hz_linesearch) appears to be about 380. >> >> I think this is happening because hz_linesearch (a) expands the step size >> by a factor of 5 (see line 280 in hz_linesearch) until it encounters upward >> movement and (b) passes this new value (or a moving average of it) back to >> the caller (i.e., bfgs). So, the next time bfgs calls hz_linesearch, it >> starts out with a potentially large value for the first step. >> >> I don't really know much about line search routines, but is this way >> things ought to be? I would have thought that for each new call to a line >> search routine, the step size should reset to a default value. >> >> By the way, is it possible to enable display of the internal values of >> "c" in the line search routines? It looks like there is some debugging >> code in there but I'm not sure how to turn it on. >> >> -thom >> >> >> On Wednesday, July 30, 2014 6:24:26 PM UTC-5, John Myles White wrote: >>> >>> I’ve never seen our line search methods produce an error that wasn’t >>> caused by errors in the gradient. The line search methods generally only >>> work with function values and gradients, so they’re either buggy (which >>> they haven’t proven to be) or they’re brittle to errors in function >>> definitions/gradient definitions. >>> >>> Producing better error message would be great. I once started to do >>> that, but realized that I needed to come back to fully understanding the >>> line search code before I could insert useful errors. Would love to see >>> improvements there. >>> >>> — John >>> >>> On Jul 30, 2014, at 3:17 PM, Thomas Covert <[email protected]> wrote: >>> >>> I've done some more sleuthing and have concluded that the problem was on >>> my end (a bug in the gradient calculation, as you predicted). >>> >>> Is an inaccurate gradient the only way someone should encounter this >>> assertion error? I don't know enough about line search methods to have an >>> intuition about that, but if it is the case, maybe the line search routine >>> should throw a more informative error? >>> >>> -Thom >>> >>> On Wednesday, July 30, 2014 3:44:51 PM UTC-5, John Myles White wrote: >>>> >>>> Would be useful to understand exactly what goes wrong if we want to fix >>>> this problem. I’m mostly used to errors caused by inaccurate gradients, so >>>> I don’t have an intuition for the cause of this problem. >>>> >>>> — John >>>> >>>> On Jul 30, 2014, at 10:45 AM, Thomas Covert <[email protected]> wrote: >>>> >>>> No, I haven't tried that yet - might someday, but I like the idea of >>>> running julia native code all the way... >>>> >>>> However, I did find that manually switching the line search routine to >>>> "backtracking_linesearch!" did the trick, so at least we know the problem >>>> isn't in Optim.jl's implementation of BFGS itself! >>>> >>>> -thom >>>> >>>> On Wednesday, July 30, 2014 12:43:16 PM UTC-5, jbeginner wrote: >>>>> >>>>> This is not really a solution for this problem but have you tried the >>>>> NLopt library? From my experience it produces much more stable results >>>>> and >>>>> because of problems like the one you describe I have switched to it. I >>>>> think there is an L-BFGS option also. Although I did not get AD to work >>>>> with it. The description for all algorithms can be seen here: >>>>> >>>>> http://ab-initio.mit.edu/wiki/index.php/NLopt_Algorithms >>>>> >>>>> >>>>> >>>>> On Wednesday, July 30, 2014 12:27:36 PM UTC-4, Thomas Covert wrote: >>>>>> >>>>>> Recently I've encountered line search errors when using Optim.jl with >>>>>> BFGS. Here is an example error message >>>>>> >>>>>> *ERROR: assertion failed: lsr.slope[ib] < 0* >>>>>> >>>>>> * in bisect! at >>>>>> /pathtojulia/.julia/v0.3/Optim/src/linesearch/hz_linesearch.jl:577* >>>>>> >>>>>> * in hz_linesearch! at /**pathtojulia* >>>>>> */.julia/v0.3/Optim/src/linesearch/hz_linesearch.jl:273* >>>>>> >>>>>> * in hz_linesearch! at /**pathtojulia* >>>>>> */.julia/v0.3/Optim/src/linesearch/hz_linesearch.jl:201* >>>>>> >>>>>> * in bfgs at /**pathtojulia**/.julia/v0.3/Optim/src/bfgs.jl:121* >>>>>> >>>>>> * in optimize at /**pathtojulia* >>>>>> */.julia/v0.3/Optim/src/optimize.jl:113* >>>>>> >>>>>> *while loading /pathtocode/code.jl, in expression starting on line >>>>>> 229* >>>>>> >>>>>> >>>>>> I've seen this error message before, and its usually because I have a >>>>>> bug in my code that erroneously generates function values or gradients >>>>>> which are very large (i.e., 1e100). However, in this case I can confirm >>>>>> that the "x" I've passed to the optimizer is totally reasonable (abs >>>>>> value >>>>>> of all points less than 100), the function value at that x is reasonable >>>>>> (on the order of 1e6), the gradients are reasonable (between -100 and >>>>>> +100), and the entries in the approximate inverse Hessian are also >>>>>> reasonable (smallest abs value is about 1e-9, largest is about 7). >>>>>> >>>>>> >>>>>> This isn't a failure on the first or second iteration of BFGS - it >>>>>> happens on the 34th iteration. >>>>>> >>>>>> >>>>>> Unfortunately its pretty hard for me to share my code or data at the >>>>>> moment, so I understand that it might be challenging to solve this >>>>>> problem >>>>>> but any advice you guys can offer is appreciated! >>>>>> >>>>>> >>>>>> -Thom >>>>>> >>>>> >>>> >>> >
