vgupta1 / ddus.jl Goto Github PK

Hi,

Thanks for your well-documented repository.
I failed to run the code using the Julia version 1. potentially because of the incompatibility of JuMPeR with these versions.
Earlier versions of Julia (version 0.) are also obsolete.
Do you have any suggestions on how I can reproduce your code?

Thanks,

I'm guessing because of something happening inside kappa(eps_k)?

Seems like Travis isn't turned on on the Travis website?

As discussed in the paper, it'd be nice to set up a general facility for using cross-validation (leveraging MLBase) to

• Build a set using a part of the data
• solve the optimization problem
• test solution on remainder of data
• amalgamate results
• repeat for a grid of epsilon/alpha/choices of set

@IainNZ I'd be interested in your thoughts on what the architecture might look like to do this....

In the meantime, it's on my todo list to write an explicit example to doing this in an adhoc way for a set.

Given an uncertainty set of form U = U_1 \cup U_2, a linear robust constraint over U can rewritten as

u^T x <= 0 for all u in U

as there exists x1, x2 such that

u^T x1 <= 0 for all u in U1
u^T x2 <= 0 for all u in U2
x1 + x2 = x

This suggests a way of decomposing complicated uncertainty sets into a portion for which there exists a nice reformulation and second portion for which we'd using cutting planes. In particular, for the sets in DDUS.jl we could handle additional constraints on the support intersected with the data-driven sets.

Ideally, I'm thinking something like:

#add some generic constraints, to be handled by general oracle
@defUnc(m, us[1:10] >=0)
addConstraint(m, sum(us) == 1)

#build a data-driven, or other complicated oracle
w = DDUS.UCSOracle( ... )

#add a robust constraint, designating the additional oracle
addConstraint(m, dot(us, xs) <= 0, w)

#solve... JuMP, or more likely the oracle itself, does the above decomposition on the back end to enforce both uncertainty sets.
solveRobust(m)

Thoughts @IainNZ ?

Right now using a pretty coarse approximation. Should replace with a better one.

The paper discusses optimizing the choice of epsilons when you have multiple constraints by

• solving the original robust problem for a initial choice of epsilons
• extracting the solution
• solving a small auxiliary LP
• updating the choice of epsilons with a gradient step

Again, it'd be nice to have a general facility for doing this. Thoughts @IainNZ ?