Test DICG with Probability Simplex and MOI LMO.

examples/optimal_experiment_design.jl

@@ -4,6 +4,10 @@ using Random
 using Distributions
 using LinearAlgebra
 using Statistics
+using SCIP
+using MathOptInterface
+const MOI = MathOptInterface
+using SparseArrays
 using Test
 
 # The Optimal Experiment Design Problem consists of choosing a subset of experiments
@@ -43,6 +47,29 @@ function build_data(m)
     return A 
 end
 
+"""
+Build MOI version of the lmo.
+"""
+function build_moi_lmo(m)
+    o = SCIP.Optimizer()
+    MOI.empty!(o)
+    MOI.set(o, MOI.Silent(), true)
+
+    x = MOI.add_variables(o, m)
+
+    for xi in x 
+        # each var has to be non-negative
+        MOI.add_constraint(o, xi, MOI.GreaterThan(0.0))
+    end
+
+    # sum of all variables has to be less than 1.0
+    MOI.add_constraint(o, sum(x, init=0.0), MOI.LessThan(1.0))
+
+    lmo = FrankWolfe.MathOptLMO(o)
+
+    return lmo
+end
+
 """
 Check if given point is in the domain of f, i.e. X = transpose(A) * diagm(x) * A 
 positive definite.
@@ -87,12 +114,11 @@ function build_start_point(A)
     V = Vector{Float64}[]
 
     for i in S
-        v = zeros(m)
-        v[i] = 1.0
+        v = FrankWolfe.ScaledHotVector(1.0, i, m)
         push!(V, v)
     end
 
-    x = sum(V .* 1/n)
+    x = SparseArrays.SparseVector(sum(V .* 1/n))
     active_set= FrankWolfe.ActiveSet(fill(1/n, n), V, x)
 
     return x, active_set, S
@@ -232,10 +258,20 @@ m = 300
         f, grad! = build_a_criterion(A, build_safe=false)
         x0, active_set = build_start_point(A)
         domain_oracle = build_domain_oracle(A)
-        x, _, primal, dual_gap, traj_data = decomposition_invariant_conditional_gradient(f, grad!, lmo, x0, verbose=true,line_search=FrankWolfe.Secant(domain_oracle=domain_oracle), trajectory=true)
+        x_d, _, primal, dual_gap, traj_data_d = FrankWolfe.decomposition_invariant_conditional_gradient(f, grad!, lmo, x0, verbose=true,line_search=FrankWolfe.Secant(domain_oracle=domain_oracle), trajectory=true)
+
+        lmo = build_moi_lmo(m)
+        f, grad! = build_a_criterion(A, build_safe=false)
+        x0, active_set = build_start_point(A)
+        domain_oracle = build_domain_oracle(A)
+        x_d_m, _, primal, dual_gap, traj_data_d_m = FrankWolfe.decomposition_invariant_conditional_gradient(f, grad!, lmo, x0, verbose=true,line_search=FrankWolfe.Secant(domain_oracle=domain_oracle), trajectory=true)
 
         @test traj_data_s[end][1] < traj_data[end][1]
+        @test traj_data_d[end][1] <= traj_data_s[end][1]
+        @test traj_data_d_m[end][1] <= traj_data_s[end][1]
         @test isapprox(f(x_s), f(x))
+        @test isapprox(f(x_s), f(x_d))
+        @test isapprox(f(x_s), f(x_d_m))
     end
 
     @testset "D-Optimal Design" begin
@@ -256,10 +292,20 @@ m = 300
         f, grad! = build_d_criterion(A, build_safe=false)
         x0, active_set = build_start_point(A)
         domain_oracle = build_domain_oracle(A)
-        x, _, primal, dual_gap, traj_data = decomposition_invariant_conditional_gradient(f, grad!, lmo, x0, verbose=true,line_search=FrankWolfe.Secant(domain_oracle=domain_oracle), trajectory=true)
+        x_d, _, primal, dual_gap, traj_data_d = FrankWolfe.decomposition_invariant_conditional_gradient(f, grad!, lmo, x0, verbose=true,line_search=FrankWolfe.Secant(domain_oracle=domain_oracle), trajectory=true)
+
+        lmo = build_moi_lmo(m)
+        f, grad! = build_d_criterion(A, build_safe=false)
+        x0, active_set = build_start_point(A)
+        domain_oracle = build_domain_oracle(A)
+        x_d_m, _, primal, dual_gap, traj_data_d_m = FrankWolfe.decomposition_invariant_conditional_gradient(f, grad!, lmo, x0, verbose=true,line_search=FrankWolfe.Secant(domain_oracle=domain_oracle), trajectory=true)
 
         @test traj_data_s[end][1] < traj_data[end][1]
+        @test traj_data_d[end][1] <= traj_data_s[end][1]
+        @test traj_data_d_m[end][1] <= traj_data_s[end][1]
         @test isapprox(f(x_s), f(x))
+        @test isapprox(f(x_s), f(x_d))
+        @test isapprox(f(x_s), f(x_d_m))
     end
 end