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Introduce the approximate Hessian as a default in trust regions. #237

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14 changes: 14 additions & 0 deletions Changelog.md
Original file line number Diff line number Diff line change
Expand Up @@ -5,6 +5,20 @@ All notable Changes to the Julia package `Manopt.jl` will be documented in this
The format is based on [Keep a Changelog](https://keepachangelog.com/en/1.0.0/),
and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0.html).

## [0.4.15] - 13/04/2023

### Changed

* `trust_regions(M, f, grad_f, hess_f, p)` now has the Hessian `hess_f` as well as
the start point `p0` as an optional parameter and approximate it otherwise.
* `trust_regions!(M, f, grad_f, hess_f, p)` has the Hessian as an optional parameter
and approximate it otherwise.

### Removed

* support for `ManifoldsBase.jl` 0.13.x, since with the definition of `copy(M,p::Number)`,
in 0.14.4, we now use that instead of defining it ourselves.

## [0.4.14] - 06/04/2023

### Changed
Expand Down
6 changes: 3 additions & 3 deletions Project.toml
Original file line number Diff line number Diff line change
@@ -1,7 +1,7 @@
name = "Manopt"
uuid = "0fc0a36d-df90-57f3-8f93-d78a9fc72bb5"
authors = ["Ronny Bergmann <[email protected]>"]
version = "0.4.14"
version = "0.4.15"

[deps]
ColorSchemes = "35d6a980-a343-548e-a6ea-1d62b119f2f4"
Expand All @@ -27,8 +27,8 @@ ColorTypes = "0.9.1, 0.10, 0.11"
Colors = "0.11.2, 0.12"
DataStructures = "0.17, 0.18"
ManifoldDiff = "0.2, 0.3"
Manifolds = "0.8.43"
ManifoldsBase = "0.13.30, 0.14"
Manifolds = "0.8.57"
ManifoldsBase = "0.14.4"
Requires = "0.5, 1"
StaticArrays = "0.12, 1.0"
julia = "1.6"
Expand Down
22 changes: 16 additions & 6 deletions src/plans/hessian_plan.jl
Original file line number Diff line number Diff line change
Expand Up @@ -151,7 +151,14 @@ update_hessian!(M, f, p, p_proposal, X) = f
update_hessian_basis!(M, f, p) = f

@doc raw"""
ApproxHessianFiniteDifference{E, P, T, G, RTR,, VTR, R <: Real}
AbstractApproxHessian <: Function

An abstract supertypes for approximate hessian functions, declares them also to be functions.
"""
abstract type AbstractApproxHessian <: Function end

@doc raw"""
ApproxHessianFiniteDifference{E, P, T, G, RTR,, VTR, R <: Real} <: AbstractApproxHessian

A functor to approximate the Hessian by a finite difference of gradient evaluation.

Expand Down Expand Up @@ -191,7 +198,8 @@ Then we approximate the Hessian by the finite difference of the gradients, where
* `retraction_method` – (`default_retraction_method(M, typeof(p))`) a `retraction(M, p, X)` to use in the approximation.
* `vector_transport_method` - (`default_vector_transport_method(M, typeof(p))`) a vector transport to use
"""
mutable struct ApproxHessianFiniteDifference{E,P,T,G,RTR,VTR,R<:Real}
mutable struct ApproxHessianFiniteDifference{E,P,T,G,RTR,VTR,R<:Real} <:
AbstractApproxHessian
p_dir::P
gradient!!::G
grad_tmp::T
Expand Down Expand Up @@ -251,7 +259,8 @@ function (f::ApproxHessianFiniteDifference{InplaceEvaluation})(M, Y, p, X)
end

@doc raw"""
ApproxHessianSymmetricRankOne{E, P, G, T, B<:AbstractBasis{ℝ}, VTR, R<:Real}
ApproxHessianSymmetricRankOne{E, P, G, T, B<:AbstractBasis{ℝ}, VTR, R<:Real} <: AbstractApproxHessian

A functor to approximate the Hessian by the symmetric rank one update.
# Fields
* `gradient!!` the gradient function (either allocating or mutating, see `evaluation` parameter).
Expand All @@ -271,7 +280,8 @@ A functor to approximate the Hessian by the symmetric rank one update.
* `evaluation` ([`AllocatingEvaluation`](@ref)) whether the gradient is given as an allocation function or an in-place ([`InplaceEvaluation`](@ref)).
* `vector_transport_method` (`ParallelTransport()`) vector transport ``\mathcal T_{\cdot\gets\cdot}`` to use.
"""
mutable struct ApproxHessianSymmetricRankOne{E,P,G,T,B<:AbstractBasis{ℝ},VTR,R<:Real}
mutable struct ApproxHessianSymmetricRankOne{E,P,G,T,B<:AbstractBasis{ℝ},VTR,R<:Real} <:
AbstractApproxHessian
p_tmp::P
gradient!!::G
grad_tmp::T
Expand Down Expand Up @@ -384,7 +394,7 @@ function update_hessian_basis!(M, f::ApproxHessianSymmetricRankOne{InplaceEvalua
end

@doc raw"""
ApproxHessianBFGS{E, P, G, T, B<:AbstractBasis{ℝ}, VTR, R<:Real}
ApproxHessianBFGS{E, P, G, T, B<:AbstractBasis{ℝ}, VTR, R<:Real} <: AbstractApproxHessian
A functor to approximate the Hessian by the BFGS update.
# Fields
* `gradient!!` the gradient function (either allocating or mutating, see `evaluation` parameter).
Expand All @@ -406,7 +416,7 @@ A functor to approximate the Hessian by the BFGS update.
"""
mutable struct ApproxHessianBFGS{
E,P,G,T,B<:AbstractBasis{ℝ},VTR<:AbstractVectorTransportMethod
}
} <: AbstractApproxHessian
p_tmp::P
gradient!!::G
grad_tmp::T
Expand Down
2 changes: 0 additions & 2 deletions src/plans/nonmutating_manifolds_plans.jl
Original file line number Diff line number Diff line change
Expand Up @@ -88,5 +88,3 @@ function step_solver!(
s.p = retract(get_manifold(p), s.p, -step * s.X, s.retraction_method)
return s
end
#Hack for now?
copy(::NONMUTATINGMANIFOLDS, p) = p
62 changes: 55 additions & 7 deletions src/solvers/trust_regions.jl
Original file line number Diff line number Diff line change
Expand Up @@ -258,24 +258,50 @@ the obtained (approximate) minimizer ``p^*``, see [`get_solver_return`](@ref) fo
[`truncated_conjugate_gradient_descent`](@ref)
"""
function trust_regions(
M::AbstractManifold, f::TF, grad_f::TdF, Hess_f::TH, p; kwargs...
) where {TF,TdF,TH}
M::AbstractManifold, f::TF, grad_f::TdF, Hess_f::TH, p=rand(M); kwargs...
) where {TF,TdF,TH<:Function}
q = copy(M, p)
return trust_regions!(M, f, grad_f, Hess_f, q; kwargs...)
end

function trust_regions(
M::AbstractManifold,
f::TF,
grad_f::TdF,
p=rand(M);
evaluation=AllocatingEvaluation(),
retraction_method::AbstractRetractionMethod=default_retraction_method(M, typeof(p)),
kwargs...,
) where {TF,TdF}
hess_f = ApproxHessianFiniteDifference(
M, copy(M, p), grad_f; evaluation=evaluation, retraction_method=retraction_method
)
return trust_regions(
M,
f,
grad_f,
hess_f,
p;
evaluation=evaluation,
retraction_method=retraction_method,
kwargs...,
)
end
@doc raw"""
trust_regions!(M, f, grad_f, Hess_f, x; kwargs...)
trust_regions!(M, f, grad_f, Hess_f, p; kwargs...)
trust_regions!(M, f, grad_f, p; kwargs...)

evaluate the Riemannian trust-regions solver for optimization on manifolds in place of `x`.
evaluate the Riemannian trust-regions solver for optimization on manifolds in place of `p`.

# Input
* `M` – a manifold ``\mathcal M``
* `f` – a cost function ``F: \mathcal M → ℝ`` to minimize
* `grad_f`- the gradient ``\operatorname{grad}F: \mathcal M → T \mathcal M`` of ``F``
* `Hess_f` – the hessian ``H( \mathcal M, x, ξ)`` of ``F``
* `Hess_f` – (optional) the hessian ``H( \mathcal M, x, ξ)`` of ``F``
* `x` – an initial value ``x ∈ \mathcal M``

For the case that no hessian is provided, the Hessian is computed using finite difference, see
[`ApproxHessianFiniteDifference`](@ref).

for more details and all options, see [`trust_regions`](@ref)
"""
function trust_regions!(
Expand Down Expand Up @@ -349,7 +375,29 @@ function trust_regions!(
trs = decorate_state!(trs; kwargs...)
return get_solver_return(solve!(mp, trs))
end

function trust_regions!(
M::AbstractManifold,
f::TF,
grad_f::TdF,
p;
evaluation=AllocatingEvaluation(),
retraction_method::AbstractRetractionMethod=default_retraction_method(M, typeof(p)),
kwargs...,
) where {TF,TdF}
hess_f = ApproxHessianFiniteDifference(
M, copy(M, p), grad_f; evaluation=evaluation, retraction_method=retraction_method
)
return trust_regions!(
M,
f,
grad_f,
hess_f,
p;
evaluation=evaluation,
retraction_method=retraction_method,
kwargs...,
)
end
function initialize_solver!(mp::AbstractManoptProblem, trs::TrustRegionsState)
M = get_manifold(mp)
get_gradient!(mp, trs.X, trs.p)
Expand Down
14 changes: 0 additions & 14 deletions test/solvers/test_trust_regions.jl
Original file line number Diff line number Diff line change
Expand Up @@ -45,13 +45,6 @@ include("trust_region_model.jl")
M,
cost,
rgrad,
ApproxHessianFiniteDifference(
M,
p,
rgrad;
steplength=2^(-9),
vector_transport_method=ProjectionTransport(),
),
p;
max_trust_region_radius=8.0,
stopping_criterion=StopAfterIteration(2000) | StopWhenGradientNormLess(1e-6),
Expand All @@ -61,13 +54,6 @@ include("trust_region_model.jl")
M,
cost,
rgrad,
ApproxHessianFiniteDifference(
M,
p,
rgrad;
steplength=2^(-9),
vector_transport_method=ProjectionTransport(),
),
q2;
stopping_criterion=StopAfterIteration(2000) | StopWhenGradientNormLess(1e-6),
max_trust_region_radius=8.0,
Expand Down