[WIP] POI + DiffOpt = S2

[joaquimg]

@andrewrosemberg motivated me.

I love how well layers can play with each other.

This will not be merged (as part of POI src) as it does not make sense to add DiffOpt as a dep for POI.

This should be either: 1 - An extension here (POI) 2 - A separate package 3 - An extension at DiffOpt

Semantically, option 3 makes lots of sense. But this uses too much of POI internals. Option 2 has a similar issue, we will have to pin a POI version. Currently, I like 1.

Still requires:

• [x] Reverse mode
• [x] More tests (objectives, vector affine, more constraints...)
• [ ] Deal with cached data (a reset_input_sensitivities in DiffOpt would be handy)
• [x] Deal with type stability (add barriers)
• [ ] Move it to the right place

cc @matbesancon, @blegat

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[andrewrosemberg]

I am implementing a test that I believe should work:

function test_diff_projection()
    num_A = 2
    ##### SecondOrderCone #####
    _x_hat = rand(num_A)
    μ = rand(num_A) * 10
    Σ_12 = rand(num_A, num_A)
    Σ = Σ_12 * Σ_12' + 0.1 * I
    γ = 1.0
    model = direct_model(POI.Optimizer(DiffOpt.diff_optimizer(SCS.Optimizer)))
    set_silent(model)
    @variable(model, x[1:num_A])
    @variable(model, x_hat[1:num_A] in MOI.Parameter.(_x_hat))
    @variable(model, norm_2)
    # (x - x_hat)^T Σ^-1 (x - x_hat) <= γ
    @constraint(
        model,
        (x - μ)' * inv(Σ) * (x - μ) <= γ,
    )
    # norm_2 >= ||x - x_hat||_2
    @constraint(model, [norm_2; x - x_hat] in SecondOrderCone())
    @objective(model, Min, norm_2)
    optimize!(model)
    MOI.set.(model, POI.ForwardParameter(), x_hat, ones(num_A))
    DiffOpt.forward_differentiate!(model) # ERROR
    #@test TBD
    return
end

But I am getting an error at the forward_differentiate step:

ERROR: MethodError: no method matching throw_set_error_fallback(::MathOptInterface.Bridges.LazyBridgeOptimizer{DiffOpt.ConicProgram.Model}, ::DiffOpt.ObjectiveFunctionAttribute{DiffOpt.ObjectiveDualStart, MathOptInterface.VariableIndex}, ::MathOptInterface.Bridges.Objective.FunctionConversionBridge{Float64, MathOptInterface.ScalarAffineFunction{Float64}, MathOptInterface.VariableIndex}, ::Float64)

stacktrace:

Stacktrace:
 [1] set(::MathOptInterface.Bridges.LazyBridgeOptimizer{DiffOpt.ConicProgram.Model}, ::DiffOpt.ObjectiveFunctionAttribute{DiffOpt.ObjectiveDualStart, MathOptInterface.VariableIndex}, ::MathOptInterface.Bridges.Objective.FunctionConversionBridge{Float64, MathOptInterface.ScalarAffineFunction{Float64}, MathOptInterface.VariableIndex}, ::Float64)
   @ MathOptInterface ~/.julia/packages/MathOptInterface/IiXiU/src/attributes.jl:550
 [2] set(b::MathOptInterface.Bridges.LazyBridgeOptimizer{DiffOpt.ConicProgram.Model}, attr::DiffOpt.ObjectiveFunctionAttribute{DiffOpt.ObjectiveDualStart, MathOptInterface.VariableIndex}, value::Float64)
   @ DiffOpt ~/.julia/packages/DiffOpt/6Xx9R/src/copy_dual.jl:90
 [3] set(b::MathOptInterface.Bridges.LazyBridgeOptimizer{DiffOpt.ConicProgram.Model}, attr::DiffOpt.ObjectiveDualStart, value::Float64)
   @ DiffOpt ~/.julia/packages/DiffOpt/6Xx9R/src/copy_dual.jl:114
 [4] _copy_dual(dest::MathOptInterface.Bridges.LazyBridgeOptimizer{DiffOpt.ConicProgram.Model}, src::MathOptInterface.Utilities.CachingOptimizer{MathOptInterface.Bridges.LazyBridgeOptimizer{MathOptInterface.Utilities.CachingOptimizer{SCS.Optimizer, MathOptInterface.Utilities.UniversalFallback{MathOptInterface.Utilities.Model{Float64}}}}, MathOptInterface.Utilities.UniversalFallback{MathOptInterface.Utilities.Model{Float64}}}, index_map::MathOptInterface.Utilities.IndexMap)
   @ DiffOpt ~/.julia/packages/DiffOpt/6Xx9R/src/copy_dual.jl:176
 [5] _diff(model::DiffOpt.Optimizer{MathOptInterface.Utilities.CachingOptimizer{MathOptInterface.Bridges.LazyBridgeOptimizer{MathOptInterface.Utilities.CachingOptimizer{SCS.Optimizer, MathOptInterface.Utilities.UniversalFallback{MathOptInterface.Utilities.Model{Float64}}}}, MathOptInterface.Utilities.UniversalFallback{MathOptInterface.Utilities.Model{Float64}}}})
   @ DiffOpt ~/.julia/packages/DiffOpt/6Xx9R/src/moi_wrapper.jl:600
 [6] forward_differentiate!(model::DiffOpt.Optimizer{MathOptInterface.Utilities.CachingOptimizer{MathOptInterface.Bridges.LazyBridgeOptimizer{MathOptInterface.Utilities.CachingOptimizer{SCS.Optimizer, MathOptInterface.Utilities.UniversalFallback{MathOptInterface.Utilities.Model{Float64}}}}, MathOptInterface.Utilities.UniversalFallback{MathOptInterface.Utilities.Model{Float64}}}})
   @ DiffOpt ~/.julia/packages/DiffOpt/6Xx9R/src/moi_wrapper.jl:525
 [7] forward_differentiate!(model::ParametricOptInterface.Optimizer{Float64, DiffOpt.Optimizer{MathOptInterface.Utilities.CachingOptimizer{MathOptInterface.Bridges.LazyBridgeOptimizer{MathOptInterface.Utilities.CachingOptimizer{SCS.Optimizer, MathOptInterface.Utilities.UniversalFallback{MathOptInterface.Utilities.Model{Float64}}}}, MathOptInterface.Utilities.UniversalFallback{MathOptInterface.Utilities.Model{Float64}}}}})
   @ ParametricOptInterface ~/Workspace/ParametricOptInterface.jl/src/diff.jl:222
 [8] forward_differentiate!(model::Model)
   @ DiffOpt ~/.julia/packages/DiffOpt/6Xx9R/src/jump_moi_overloads.jl:307
 [9] top-level scope
   @ REPL[48]:1

Edit: I imagine that this is a missing bridge right ?

[Giovanni3A]

I encountered an error while working with DiffOpt and POI. To demonstrate the problem, I created a minimal example:

This creates a simple problem using an explicitly indexed constraint (con[i=1:2]), then applies reverse_differentiate and it works:

using JuMP, DiffOpt, HiGHS
import ParametricOptInterface as POI

b = [1.0, 2.0]

m = Model(() -> POI.Optimizer(DiffOpt.diff_optimizer(HiGHS.Optimizer)))
@variable(m, x[1:2] >= 0)
@variable(m, c[1:2] in MOI.Parameter.(b))
@constraint(m, con[i=1:2], x[i] <= c[i])
@objective(m, Max, sum(x))
optimize!(m)

MOI.set(m, DiffOpt.ReverseVariablePrimal(), m[:x][1], 1.0)
DiffOpt.reverse_differentiate!(m)
MOI.get(m, POI.ReverseParameter(), m[:c][1])

>>> 1.0

but when I declare the constraint in a non-indexed fashion, like this: @constraint(m, con, x <= c)

I get an error when calling DiffOpt.reverse_differentiate!(m):

ERROR: ArgumentError: Bridge of type `ScalarizeBridge` does not support accessing the attribute `DiffOpt.ReverseConstraintFunction()`.

The error still happens if the constraint is not declared with a name (con in this case).