RFC: more generic convergence assessment (#530)

* more generic convergence assessment

* fix initial convergence

* added tests for gradient_convergence_assessment and initial_convergence

src/multivariate/optimize/optimize.jl

@@ -13,6 +13,12 @@ update_h!(d, state, method::SecondOrderOptimizer) = hessian!(d, state.x)
 
 after_while!(d, state, method, options) = nothing
 
+function initial_convergence(d, state, method::AbstractOptimizer, initial_x, options) 
+    gradient!(d, initial_x)
+    vecnorm(gradient(d), Inf) < options.g_tol
+end 
+initial_convergence(d, state, method::ZerothOrderOptimizer, initial_x, options) = false
+
 function optimize(d::D, initial_x::AbstractArray{Tx, N}, method::M,
                   options::Options = Options(;default_options(method)...),
                   state = initial_state(method, options, d, complex_to_real(d, initial_x))) where {D<:AbstractObjective, M<:AbstractOptimizer, Tx, N}
@@ -31,16 +37,7 @@ function optimize(d::D, initial_x::AbstractArray{Tx, N}, method::M,
     f_limit_reached, g_limit_reached, h_limit_reached = false, false, false
     x_converged, f_converged, f_increased = false, false, false
 
-    g_converged = if typeof(method) <: NelderMead
-        nmobjective(state.f_simplex, state.m, n) < options.g_tol
-    elseif  typeof(method) <: ParticleSwarm || typeof(method) <: SimulatedAnnealing
-        # TODO: remove KrylovTrustRegion when TwiceDifferentiableHV is in NLSolversBase
-        false
-    else
-        gradient!(d, initial_x)
-        vecnorm(gradient(d), Inf) < options.g_tol
-    end
-
+    g_converged = initial_convergence(d, state, method, initial_x, options)
     converged = g_converged
 
     # prepare iteration counter (used to make "initial state" trace entry)

src/multivariate/solvers/zeroth_order/nelder_mead.jl

@@ -281,6 +281,10 @@ function assess_convergence(state::NelderMeadState, d, options)
     return false, false, g_converged, g_converged, false
 end
 
+function initial_convergence(d, state::NelderMeadState, method::NelderMead, initial_x, options)
+    nmobjective(state.f_simplex, state.m, length(initial_x)) < options.g_tol
+end 
+
 function trace!(tr, d, state, iteration, method::NelderMead, options)
     dt = Dict()
     if options.extended_trace

src/utilities/assess_convergence.jl

@@ -63,11 +63,13 @@ function default_convergence_assessment(state::AbstractOptimizerState, d, option
         f_increased = true
     end
 
-    if g_residual(gradient(d)) ≤ options.g_tol
-        g_converged = true
-    end
-
+    g_converged = gradient_convergence_assessment(state,d,options)
+
     converged = x_converged || f_converged || g_converged
 
     return x_converged, f_converged, g_converged, converged, f_increased
 end
+
+gradient_convergence_assessment(state::AbstractOptimizerState, d, options) = g_residual(gradient(d)) ≤ options.g_tol
+gradient_convergence_assessment(state::ZerothOrderState, d, options) = false
+

test/general/convergence.jl

@@ -1,4 +1,12 @@
-mutable struct DummyState
+mutable struct DummyState <: Optim.AbstractOptimizerState
+    x
+    x_previous
+    f_x
+    f_x_previous
+    g
+end
+
+mutable struct DummyStateZeroth <: Optim.ZerothOrderState
     x
     x_previous
     f_x
@@ -12,7 +20,13 @@ mutable struct DummyOptions
     g_tol
 end
 
-@testset "assess_convergence" begin
+mutable struct DummyMethod <: Optim.AbstractOptimizer end
+mutable struct DummyMethodZeroth <: Optim.ZerothOrderOptimizer end
+
+@testset "Convergence assessment" begin
+
+    ## assess_convergence
+
     # should converge
     x0, x1 = [1.], [1.0 - 1e-7]
     f0, f1 = 1.0, 1.0 - 1e-7
@@ -28,8 +42,6 @@ end
     f_tol = 1e-12
     @test Optim.assess_convergence(x1, x0, f1, f0, g, x_tol, f_tol, g_tol) == (true, false, true, true, true)
 
-    ds = DummyState(x1, x0, f1, f0, g)
-    dOpt = DummyOptions(x_tol, f_tol, g_tol)
     @test Optim.assess_convergence(x1, x0, f1, f0, g, x_tol, f_tol, g_tol) == (true, false, true, true, true)
 
     f_tol = 1e-6 # rel tol
@@ -40,5 +52,30 @@ end
     dOpt = DummyOptions(x_tol, f_tol, g_tol)
     @test Optim.assess_convergence(x1, x0, f1, f0, g, x_tol, f_tol, g_tol) == (true, true, true, true, false)
 
+    ## initial_convergence and gradient_convergence_assessment
+
+    ds = DummyState(x1, x0, f1, f0, g)
+    dOpt = DummyOptions(x_tol, f_tol, g_tol)
+    dm = DummyMethod()
+
+    # >= First Order
+    d = Optim.OnceDifferentiable(x->sum(abs2.(x)),zeros(2))
+
+    Optim.gradient!(d,ones(2))
+    @test Optim.gradient_convergence_assessment(ds,d,dOpt) == false
+    Optim.gradient!(d,zeros(2))
+    @test Optim.gradient_convergence_assessment(ds,d,dOpt) == true
+
+    @test Optim.initial_convergence(d, ds, dm, ones(2), dOpt) == false     
+    @test Optim.initial_convergence(d, ds, dm, zeros(2), dOpt) == true 
+
+    # Zeroth order methods have no gradient -> returns false by default
+    ds = DummyStateZeroth(x1, x0, f1, f0, g)
+    dm = DummyMethodZeroth()
+
+    @test Optim.gradient_convergence_assessment(ds,d,dOpt) == false
+    @test Optim.initial_convergence(d, ds, dm, ones(2), dOpt) == false 
+
     # should check all other methods as well
+
 end