diff --git a/src/linesearch.jl b/src/linesearch.jl
index 70c4788ea..cc52f175e 100644
--- a/src/linesearch.jl
+++ b/src/linesearch.jl
@@ -26,15 +26,15 @@ build_linesearch_workspace(::LineSearchMethod, x, gradient) = nothing
 """
 Computes step size: `l/(l + t)` at iteration `t`, given `l > 0`.
 
-See:
+Using `l ≥ 4` is advised only for strongly convex sets, see:
 > Acceleration of Frank-Wolfe Algorithms with Open-Loop Step-Sizes, Wirth, Kerdreux, Pokutta, 2023.
-
 """
 struct Agnostic{T<:Real} <: LineSearchMethod
     l::Int
 end
 
 Agnostic() = Agnostic{Float64}(2)
+Agnostic(l::Int) = Agnostic{Float64}(l)
 
 Agnostic{T}() where {T} = Agnostic{T}(2)
 
diff --git a/test/trajectory_tests/open_loop_parametric.jl b/test/trajectory_tests/open_loop_parametric.jl
new file mode 100644
index 000000000..83c209e21
--- /dev/null
+++ b/test/trajectory_tests/open_loop_parametric.jl
@@ -0,0 +1,91 @@
+using FrankWolfe
+
+using Test
+using LinearAlgebra
+
+@testset "Open-loop FW on polytope" begin
+    n = Int(1e2)
+    k = Int(1e4)
+
+    xp = ones(n)
+    f(x) = norm(x - xp)^2
+    function grad!(storage, x)
+        @. storage = 2 * (x - xp)
+    end
+
+    lmo = FrankWolfe.KSparseLMO(40, 1.0)
+
+    x0 = FrankWolfe.compute_extreme_point(lmo, zeros(n))
+
+    res_2 = FrankWolfe.frank_wolfe(
+        f,
+        grad!,
+        lmo,
+        copy(x0),
+        max_iteration=k,
+        line_search=FrankWolfe.Agnostic(2),
+        print_iter=k / 10,
+        epsilon=1e-5,
+        verbose=true,
+        trajectory=true,
+    )
+
+    res_10 = FrankWolfe.frank_wolfe(
+        f,
+        grad!,
+        lmo,
+        copy(x0),
+        max_iteration=k,
+        line_search=FrankWolfe.Agnostic(10),
+        print_iter=k / 10,
+        epsilon=1e-5,
+        verbose=true,
+        trajectory=true,
+    )
+
+    @test res_2[4] ≤  0.004799839951985518
+    @test res_10[4] ≤ 0.02399919272834694
+
+    # strongly convex set
+    xp2 = 10 * ones(n)
+    diag_term = 100 * rand(n)
+    covariance_matrix = LinearAlgebra.Diagonal(diag_term)
+    lmo2 = FrankWolfe.EllipsoidLMO(covariance_matrix)
+
+    f2(x) = norm(x - xp2)^2
+    function grad2!(storage, x)
+        @. storage = 2 * (x - xp2)
+    end
+
+    x0 = FrankWolfe.compute_extreme_point(lmo2, randn(n))
+
+    res_2 = FrankWolfe.frank_wolfe(
+        f2,
+        grad2!,
+        lmo2,
+        copy(x0),
+        max_iteration=k,
+        line_search=FrankWolfe.Agnostic(2),
+        print_iter=k / 10,
+        epsilon=1e-5,
+        verbose=true,
+        trajectory=true,
+    )
+
+    res_10 = FrankWolfe.frank_wolfe(
+        f2,
+        grad2!,
+        lmo2,
+        copy(x0),
+        max_iteration=k,
+        line_search=FrankWolfe.Agnostic(10),
+        print_iter=k / 10,
+        epsilon=1e-5,
+        verbose=true,
+        trajectory=true,
+    )
+
+    @test length(res_10[end]) <= 8
+    @test length(res_2[end]) <= 71
+
+end