Optim: InexactError: Int64(0.01) 使用 IPNewton 时

Question

我有这段代码可以使用IPNewton方法（ error.jl ）优化 function：

import Optim

"""
Generate a matrix of constants used in computation
"""
function get_const(x::Vector{Float64}, sigma::Vector{Float64})::Array{Float64, 2}
    exp.(-x'.^2 ./ (2 .* sigma.^2)) ./ (sigma .* sqrt(2 * π))
end

# Log likelihood for mixture model
log_likelihood(p, C::Array{Float64, 2}) = sum(log.(p' * C))

"""
Constraint: all probabilities (ps) must sum to 1
"""
function constraint!(c, ps)::typeof(c)
    c[1] = sum(ps)
    c
end

N = 100
x = range(-1, 1, length=1000) |> collect
sigma = range(0.001, 2, length=N) |> collect

C = get_const(x, sigma)

constraints = Optim.TwiceDifferentiableConstraints(
    constraint!,
    fill(0, N), fill(1, N), # 0 <= (each probability) <= 1
    fill(1, N), fill(1, N)  # 1 <= constraint(p) <= 1 (probabilities sum to 1)
)
p0 = fill(1, N) / N # initial guess == equal probabilities

res = Optim.optimize(
    ps -> -log_likelihood(ps, C), # want to MAXIMIZE, so negate
    constraints, p0,
    Optim.IPNewton()
)

Project.toml ：

[deps]
Optim = "429524aa-4258-5aef-a3af-852621145aeb"

Julia 版本：

forcebru@thing ~/test> julia --version
julia version 1.5.3

错误信息：

forcebru@thing ~/test> julia error.jl
ERROR: LoadError: InexactError: Int64(0.01)
Stacktrace:
 [1] Int64 at ./float.jl:710 [inlined]
 [2] convert at ./number.jl:7 [inlined]
 [3] setindex! at ./array.jl:847 [inlined]
 [4] _unsafe_copyto!(::Array{Int64,1}, ::Int64, ::Array{Float64,1}, ::Int64, ::Int64) at ./array.jl:257
 [5] unsafe_copyto! at ./array.jl:311 [inlined]
 [6] _copyto_impl! at ./array.jl:335 [inlined]
 [7] copyto! at ./array.jl:321 [inlined]
 [8] copyto! at ./array.jl:347 [inlined]
 [9] finite_difference_jacobian!(::Array{Float64,2}, ::typeof(constraint!), ::Array{Float64,1}, ::FiniteDiff.JacobianCache{Array{Int64,1},Array{Int64,1},Array{Int64,1},UnitRange{Int64},Nothing,Val{:central}(),Int64}, ::Nothing; relstep::Float64, absstep::Float64, colorvec::UnitRange{Int64}, sparsity::Nothing, dir::Bool) at /Users/forcebru/.julia/packages/FiniteDiff/jLwWI/src/jacobians.jl:338
 [10] finite_difference_jacobian!(::Array{Float64,2}, ::Function, ::Array{Float64,1}, ::FiniteDiff.JacobianCache{Array{Int64,1},Array{Int64,1},Array{Int64,1},UnitRange{Int64},Nothing,Val{:central}(),Int64}, ::Nothing) at /Users/forcebru/.julia/packages/FiniteDiff/jLwWI/src/jacobians.jl:334 (repeats 2 times)
 [11] jac! at /Users/forcebru/.julia/packages/NLSolversBase/QPnui/src/objective_types/constraints.jl:298 [inlined]
 [12] initial_state(::Optim.IPNewton{typeof(Optim.backtrack_constrained_grad),Symbol}, ::Optim.Options{Float64,Nothing}, ::NLSolversBase.TwiceDifferentiable{Float64,Array{Float64,1},Array{Float64,2},Array{Float64,1}}, ::NLSolversBase.TwiceDifferentiableConstraints{typeof(constraint!),NLSolversBase.var"#jac!#126"{typeof(constraint!),FiniteDiff.JacobianCache{Array{Int64,1},Array{Int64,1},Array{Int64,1},UnitRange{Int64},Nothing,Val{:central}(),Int64}},NLSolversBase.var"#con_hess!#130"{Int64,Array{Int64,2},Array{Int64,3},NLSolversBase.var"#jac_vec!#129"{Int64,Int64},FiniteDiff.JacobianCache{Array{Int64,1},Array{Int64,1},Array{Int64,1},UnitRange{Int64},Nothing,Val{:central}(),Int64}},Int64}, ::Array{Float64,1}) at /Users/forcebru/.julia/packages/Optim/D7azp/src/multivariate/solvers/constrained/ipnewton/ipnewton.jl:135
 [13] optimize(::NLSolversBase.TwiceDifferentiable{Float64,Array{Float64,1},Array{Float64,2},Array{Float64,1}}, ::NLSolversBase.TwiceDifferentiableConstraints{typeof(constraint!),NLSolversBase.var"#jac!#126"{typeof(constraint!),FiniteDiff.JacobianCache{Array{Int64,1},Array{Int64,1},Array{Int64,1},UnitRange{Int64},Nothing,Val{:central}(),Int64}},NLSolversBase.var"#con_hess!#130"{Int64,Array{Int64,2},Array{Int64,3},NLSolversBase.var"#jac_vec!#129"{Int64,Int64},FiniteDiff.JacobianCache{Array{Int64,1},Array{Int64,1},Array{Int64,1},UnitRange{Int64},Nothing,Val{:central}(),Int64}},Int64}, ::Array{Float64,1}, ::Optim.IPNewton{typeof(Optim.backtrack_constrained_grad),Symbol}, ::Optim.Options{Float64,Nothing}) at /Users/forcebru/.julia/packages/Optim/D7azp/src/multivariate/solvers/constrained/ipnewton/interior.jl:228
 [14] optimize(::Function, ::NLSolversBase.TwiceDifferentiableConstraints{typeof(constraint!),NLSolversBase.var"#jac!#126"{typeof(constraint!),FiniteDiff.JacobianCache{Array{Int64,1},Array{Int64,1},Array{Int64,1},UnitRange{Int64},Nothing,Val{:central}(),Int64}},NLSolversBase.var"#con_hess!#130"{Int64,Array{Int64,2},Array{Int64,3},NLSolversBase.var"#jac_vec!#129"{Int64,Int64},FiniteDiff.JacobianCache{Array{Int64,1},Array{Int64,1},Array{Int64,1},UnitRange{Int64},Nothing,Val{:central}(),Int64}},Int64}, ::Array{Float64,1}, ::Optim.IPNewton{typeof(Optim.backtrack_constrained_grad),Symbol}, ::Optim.Options{Float64,Nothing}; inplace::Bool, autodiff::Symbol) at /Users/forcebru/.julia/packages/Optim/D7azp/src/multivariate/optimize/interface.jl:148
 [15] optimize(::Function, ::NLSolversBase.TwiceDifferentiableConstraints{typeof(constraint!),NLSolversBase.var"#jac!#126"{typeof(constraint!),FiniteDiff.JacobianCache{Array{Int64,1},Array{Int64,1},Array{Int64,1},UnitRange{Int64},Nothing,Val{:central}(),Int64}},NLSolversBase.var"#con_hess!#130"{Int64,Array{Int64,2},Array{Int64,3},NLSolversBase.var"#jac_vec!#129"{Int64,Int64},FiniteDiff.JacobianCache{Array{Int64,1},Array{Int64,1},Array{Int64,1},UnitRange{Int64},Nothing,Val{:central}(),Int64}},Int64}, ::Array{Float64,1}, ::Optim.IPNewton{typeof(Optim.backtrack_constrained_grad),Symbol}, ::Optim.Options{Float64,Nothing}) at /Users/forcebru/.julia/packages/Optim/D7azp/src/multivariate/optimize/interface.jl:147 (repeats 2 times)
 [16] top-level scope at /Users/forcebru/test/error.jl:27
 [17] include(::Function, ::Module, ::String) at ./Base.jl:380
 [18] include(::Module, ::String) at ./Base.jl:368
 [19] exec_options(::Base.JLOptions) at ./client.jl:296
 [20] _start() at ./client.jl:506
in expression starting at /Users/forcebru/test/error.jl:27
forcebru@thing ~/test [1]> 

所以... InexactError: Int64(0.01) ？ 它似乎也起源于Optim内部？

我知道这里的InexactError意味着 Julia 无法将0.01转换为 integer，这是有道理的。 但我不知道0.01是从哪里来的！ 如何查出产地？ 这段代码有什么问题，可以做些什么来解决这个问题？

---

编辑：我注意到0.01必须是p0 = fill(1, N) / N的一个元素，因为如果我设置N = 50 ，则错误变为InexactError: Int64(0.02) ，其中0.02 == 1/N 。 但为什么它试图将其转换为 integer？

Answer 1

在仔细查看错误消息的这些部分之后：

 [8] copyto! at ./array.jl:347 [inlined]
 [9] finite_difference_jacobian!(::Array{Float64,2}, ::typeof(constraint!), ::Array{Float64,1}, ::FiniteDiff.JacobianCache{Array{Int64,1},Array{Int64,1},Array{Int64,1},UnitRange{Int64},Nothing,Val{:central}(),Int64}, ::Nothing; relstep::Float64, absstep::Float64, colorvec::UnitRange{Int64}, sparsity::Nothing, dir::Bool) at /Users/forcebru/.julia/packages/FiniteDiff/jLwWI/src/jacobians.jl:338
 ...
 [15] optimize(::Function, ::NLSolversBase.TwiceDifferentiableConstraints{typeof(constraint!),NLSolversBase.var"#jac!#126"{typeof(constraint!),FiniteDiff.JacobianCache{Array{Int64,1},Array{Int64,1},Array{Int64,1},UnitRange{Int64},Nothing,Val{:central}(),Int64}},NLSolversBase.var"#con_hess!#130"{Int64,Array{Int64,2},Array{Int64,3},NLSolversBase.var"#jac_vec!#129"{Int64,Int64},FiniteDiff.JacobianCache{Array{Int64,1},Array{Int64,1},Array{Int64,1},UnitRange{Int64},Nothing,Val{:central}(),Int64}},Int64}, ::Array{Float64,1}, ::Optim.IPNewton{typeof(Optim.backtrack_constrained_grad),Symbol}, ::Optim.Options{Float64,Nothing}) at /Users/forcebru/.julia/packages/Optim/D7azp/src/multivariate/optimize/interface.jl:147 (repeats 2 times)
 [16] top-level scope at /Users/forcebru/test/error.jl:27

...我看到约束的FiniteDiff.JacobianCache被推断为在Int64上进行参数化：

FiniteDiff.JacobianCache{
    Array{Int64,1},
    Array{Int64,1},
    Array{Int64,1},
    UnitRange{Int64},
    Nothing,
    Val{:central}(),
    Int64
}

...这很奇怪，因为我显然想优化实数。

事实证明，在这部分代码中：

constraints = Optim.TwiceDifferentiableConstraints(
    constraint!,
    fill(0, N), fill(1, N), # 0 <= (each probability) <= 1
    fill(1, N), fill(1, N)  # 1 <= constraint(p) <= 1 (probabilities sum to 1)
)

fill(0, N)和朋友都是整数，因为0是 integer。 看起来这导致尝试从浮点转换为 integer。

我将此代码更改为：

constraints = Optim.TwiceDifferentiableConstraints(
    constraint!,
    fill(0., N), fill(1., N), # 0 <= (each probability) <= 1
    fill(1., N), fill(1., N)  # 1 <= constraint(p) <= 1 (probabilities sum to 1)
)

...现在没有错误（虽然算法不收敛，但这是一个不同的问题）。