L2ODLL.jl

L2ODLL.jl implements the Dual Lagrangian Learning (DLL) method of Tanneau and Hentenryck (2024) using JuMP.

Installation

import Pkg
Pkg.add(; url="https://github.com/LearningToOptimize/L2ODLL.jl")

Usage

This package simplifies the implementation of DLL by taking as input a primal JuMP model, then automatically generating the dual projection and completion functions which can be used in the training and inference of DLL models. The basic usage is as follows:

Define your (primal) model using JuMP

For the purposes of this example, we'll use a portfolio optimization problem.

using JuMP, LinearAlgebra

model = Model()

# define constant problem data
Σ = [166 34 58; 34 64 4; 58 4 100] / 100^2
N = size(Σ, 1)

# define variables
@variable(model, x[1:N])
set_lower_bound.(x, 0)  # we explicitly set upper and lower bounds
set_upper_bound.(x, 1)  #   in order to use the BoundDecomposition

# define parameteric problem data
μ0 = randn(N)
γ0 = rand()
@variable(model, μ[1:N] in MOI.Parameter.(μ0))
@variable(model, γ in MOI.Parameter(γ0))

# define constraints
@constraint(model, simplex, sum(x) == 1)
@constraint(model, risk, [γ; cholesky(Σ).L * x] in SecondOrderCone())

# define objective
@objective(model, Max, dot(μ,x))

Decompose and build the functions

Since all the variables have finite bounds, L2ODLL will automatically pick the BoundDecomposition.

using L2ODLL

L2ODLL.decompose!(model)

Now, L2ODLL has automatically generated the dual projection and completion layer. To compute the dual objective value and gradient with respect to the prediction, use:

param_value = ... # some values for μ and γ
y_predicted = nn(param_value) # e.g. neural network inference

dobj = L2ODLL.dual_objective(model, y_predicted, param_value)
dobj_wrt_y = L2ODLL.dual_objective_gradient(model, y_predicted, param_value)

This also works with batches, using broadcasting:

dobj = L2ODLL.dual_objective.(model, y_predicted_batch, param_value_batch)
dobj_wrt_y = L2ODLL.dual_objective_gradient.(model, y_predicted_batch, param_value_batch)