Integrate with POI to improve UX

[joaquimg]

Add multiple improvements to DiffOpt leading to a massive UX improvement.

• The ability to differentiate w.r.t. parameter (MOI.Parameters) activate through: with_parametric_opt_interface = true using Prepare integration with DiffOpt ParametricOptInterface.jl#161
• Selection of diff method with the keyword method (maybe switch to model_constructor)
• Function to cleanup sensitivities instead of having to set everything to zero/nothing empty_input_sensitivities! ( close Resetting differentiation input in-between differentiations #259)

About the integration with POI:

• with_parametric_opt_interface is false by default, for now. I want to make it true.
• when using POI, only (Forward/Reverse)ConstraintSet for MOI.Parameters is supported (ObjectiveFunction and ConstraintFunction are not supported)
• for now, ConstraintSet only woks for MOI.Parameters. We can add EqualTo etc in a future PR.
• the pure usage of sensitivities plays well with 🚀 Add NonLinearProgram Support to DiffOpt.jl #260

TODO:

• incorporate usage with Parameters in readme (done) and docs (to be done in Add a JuMP-like syntax to diff wrt parameters #271 )
• decide on set_forward_parameter, set_forward or only MOI. .... The first two make total sense for JuMP users, the MOI method will remain in the code for MOI users and extensions. I am strongly in favor of a JuMP-like method. now Add a JuMP-like syntax to diff wrt parameters #271
• wait for Prepare integration with DiffOpt ParametricOptInterface.jl#161
• reproduce and fix the errors from [WIP] POI + DiffOpt = S2 ParametricOptInterface.jl#143

[joaquimg]

Last commit is an attempt to solve the error raised by:

    using JuMP, DiffOpt, HiGHS

    b = [1.0, 2.0]

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

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

which is:

ERROR: ArgumentError: Bridge of type `ScalarizeBridge` does not support accessing the attribute `DiffOpt.ReverseConstraintFunction()`. If you encountered this error unexpectedly, it probably means your model has been reformulated using the bridge, and you are attempting to query an attribute that we haven't implemented yet for this bridge. Please open an issue at https://github.com/jump-dev/MathOptInterface.jl/issues/new and provide a reproducible example explaining what you were trying to do.
Stacktrace:
  [1] get(::MathOptInterface.Bridges.LazyBridgeOptimizer{…}, attr::DiffOpt.ReverseConstraintFunction, bridge::MathOptInterface.Bridges.Constraint.ScalarizeBridge{…})
    @ MathOptInterface.Bridges C:\JG\Julia\packages\MathOptInterface\gLl4d\src\Bridges\bridge.jl:149
  [2] (::MathOptInterface.Bridges.var"#3#4"{…})(bridge::MathOptInterface.Bridges.Constraint.ScalarizeBridge{…})
    @ MathOptInterface.Bridges C:\JG\Julia\packages\MathOptInterface\gLl4d\src\Bridges\bridge_optimizer.jl:324
  [3] (::MathOptInterface.Bridges.var"#1#2"{…})()
    @ MathOptInterface.Bridges C:\JG\Julia\packages\MathOptInterface\gLl4d\src\Bridges\bridge_optimizer.jl:309
  [4] call_in_context(map::MathOptInterface.Bridges.Variable.Map, bridge_index::Int64, f::MathOptInterface.Bridges.var"#1#2"{…})
    @ MathOptInterface.Bridges.Variable C:\JG\Julia\packages\MathOptInterface\gLl4d\src\Bridges\Variable\map.jl:620
  [5] call_in_context
    @ C:\JG\Julia\packages\MathOptInterface\gLl4d\src\Bridges\Variable\map.jl:651 [inlined]
  [6] call_in_context
    @ C:\JG\Julia\packages\MathOptInterface\gLl4d\src\Bridges\bridge_optimizer.jl:306 [inlined]
  [7] call_in_context
    @ C:\JG\Julia\packages\MathOptInterface\gLl4d\src\Bridges\bridge_optimizer.jl:321 [inlined]
  [8] get(b::MathOptInterface.Bridges.LazyBridgeOptimizer{…}, attr::DiffOpt.ReverseConstraintFunction, ci::MathOptInterface.ConstraintIndex{…})
    @ MathOptInterface.Bridges C:\JG\Julia\packages\MathOptInterface\gLl4d\src\Bridges\bridge_optimizer.jl:1497
  [9] get(model::DiffOpt.Optimizer{…}, attr::DiffOpt.ReverseConstraintFunction, ci::MathOptInterface.ConstraintIndex{…})
    @ DiffOpt C:\JG\Julia\dev\DiffOpt\src\moi_wrapper.jl:715
 [10] _constraint_get_reverse!(model::ParametricOptInterface.Optimizer{…}, vector_affine_constraint_cache_dict::MathOptInterface.Utilities.DoubleDicts.DoubleDictInner{…}, ::Type{…})
    @ DiffOpt C:\JG\Julia\dev\DiffOpt\src\parameters.jl:384
 [11] reverse_differentiate!(model::ParametricOptInterface.Optimizer{Float64, DiffOpt.Optimizer{…}})
    @ DiffOpt C:\JG\Julia\dev\DiffOpt\src\parameters.jl:533
 [12] reverse_differentiate!
    @ C:\JG\Julia\dev\DiffOpt\src\jump_moi_overloads.jl:333 [inlined]
 [13] reverse_differentiate!(model::MathOptInterface.Utilities.CachingOptimizer{…})
    @ DiffOpt C:\JG\Julia\dev\DiffOpt\src\jump_moi_overloads.jl:318
 [14] reverse_differentiate!(model::Model)
    @ DiffOpt C:\JG\Julia\dev\DiffOpt\src\jump_moi_overloads.jl:303

[joaquimg]

this still fails

using JuMP, DiffOpt, SCS, LinearAlgebra

    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(
        DiffOpt.diff_optimizer(
            SCS.Optimizer;
            with_parametric_opt_interface = true,
        ),
    )
    # 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))
    MOI.set.(model, DiffOpt.ForwardConstraintSet(), ParameterRef.(x_hat), 1)
    DiffOpt.forward_differentiate!(model) # ERROR

with:

ERROR: MethodError: no method matching throw_set_error_fallback(::MathOptInterface.Bridges.LazyBridgeOptimizer{…}, ::DiffOpt.ObjectiveFunctionAttribute{…}, ::MathOptInterface.Bridges.Objective.FunctionConversionBridge{…}, ::Float64)

Closest candidates are:
  throw_set_error_fallback(::MathOptInterface.ModelLike, ::Union{MathOptInterface.AbstractModelAttribute, MathOptInterface.AbstractOptimizerAttribute}, ::Any; error_if_supported)
   @ MathOptInterface C:\JG\Julia\packages\MathOptInterface\gLl4d\src\attributes.jl:580
  throw_set_error_fallback(::MathOptInterface.ModelLike, ::MathOptInterface.Bridges.Objective.SlackBridgePrimalDualStart, ::MathOptInterface.Bridges.Objective.AbstractBridge, ::Nothing)
   @ MathOptInterface C:\JG\Julia\packages\MathOptInterface\gLl4d\src\Bridges\Objective\bridges\slack.jl:202
  throw_set_error_fallback(::MathOptInterface.ModelLike, ::DiffOpt.ObjectiveSlackGapPrimalStart, ::Any)
   @ DiffOpt C:\JG\Julia\dev\DiffOpt\src\copy_dual.jl:45
  ...

Stacktrace:
 [1] set(::MathOptInterface.Bridges.LazyBridgeOptimizer{…}, ::DiffOpt.ObjectiveFunctionAttribute{…}, ::MathOptInterface.Bridges.Objective.FunctionConversionBridge{…}, ::Float64)
   @ MathOptInterface C:\JG\Julia\packages\MathOptInterface\gLl4d\src\attributes.jl:553
 [2] set(b::MathOptInterface.Bridges.LazyBridgeOptimizer{…}, attr::DiffOpt.ObjectiveFunctionAttribute{…}, value::Float64)
   @ DiffOpt C:\JG\Julia\dev\DiffOpt\src\copy_dual.jl:90
 [3] set(b::MathOptInterface.Bridges.LazyBridgeOptimizer{…}, attr::DiffOpt.ObjectiveDualStart, value::Float64)
   @ DiffOpt C:\JG\Julia\dev\DiffOpt\src\copy_dual.jl:114
 [4] _copy_dual(dest::MathOptInterface.Bridges.LazyBridgeOptimizer{…}, src::MathOptInterface.Utilities.CachingOptimizer{…}, index_map::MathOptInterface.Utilities.IndexMap)
   @ DiffOpt C:\JG\Julia\dev\DiffOpt\src\copy_dual.jl:176
 [5] _diff(model::DiffOpt.Optimizer{MathOptInterface.Utilities.CachingOptimizer{…}})
   @ DiffOpt C:\JG\Julia\dev\DiffOpt\src\moi_wrapper.jl:627
 [6] forward_differentiate!(model::DiffOpt.Optimizer{MathOptInterface.Utilities.CachingOptimizer{…}})
   @ DiffOpt C:\JG\Julia\dev\DiffOpt\src\moi_wrapper.jl:547
 [7] forward_differentiate!(model::ParametricOptInterface.Optimizer{Float64, DiffOpt.Optimizer{…}})
   @ DiffOpt C:\JG\Julia\dev\DiffOpt\src\parameters.jl:302
 [8] forward_differentiate!(model::Model)
   @ DiffOpt C:\JG\Julia\dev\DiffOpt\src\jump_moi_overloads.jl:307

if we switch to

 @objective(model, Min, 3*norm_2)

it works. so it looks like a VariableIndex typed objective.
but only happens if there is a SOC.

Found a MWE:

    model = Model(
        () -> DiffOpt.diff_optimizer(
            SCS.Optimizer;
            with_parametric_opt_interface = true,
        ),
    )
    MOI.set(model, DiffOpt.ModelConstructor(), DiffOpt.ConicProgram.Model)
    set_silent(model)
    @variable(model, x)
    @variable(model, p in Parameter(3.0))
    @constraint(model, cons, x >= 3 * p)

    @objective(model, Min, x)
    optimize!(model)
    DiffOpt.set_forward_parameter(model, p, 1)
    DiffOpt.forward_differentiate!(model)

the issue is conic backend + VariabelIndex objective
which leads to the full error:

julia> show(err)
1-element ExceptionStack:
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)

Closest candidates are:
  throw_set_error_fallback(::MathOptInterface.ModelLike, ::Union{MathOptInterface.AbstractModelAttribute, MathOptInterface.AbstractOptimizerAttribute}, ::Any; error_if_supported)
   @ MathOptInterface C:\JG\Julia\packages\MathOptInterface\gLl4d\src\attributes.jl:580
  throw_set_error_fallback(::MathOptInterface.ModelLike, ::MathOptInterface.Bridges.Objective.SlackBridgePrimalDualStart, ::MathOptInterface.Bridges.Objective.AbstractBridge, ::Nothing)
   @ MathOptInterface C:\JG\Julia\packages\MathOptInterface\gLl4d\src\Bridges\Objective\bridges\slack.jl:202
  throw_set_error_fallback(::MathOptInterface.ModelLike, ::DiffOpt.ObjectiveSlackGapPrimalStart, ::Any)
   @ DiffOpt C:\JG\Julia\dev\DiffOpt\src\copy_dual.jl:45
  ...

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 C:\JG\Julia\packages\MathOptInterface\gLl4d\src\attributes.jl:553
  [2] set(b::MathOptInterface.Bridges.LazyBridgeOptimizer{DiffOpt.ConicProgram.Model}, attr::DiffOpt.ObjectiveFunctionAttribute{DiffOpt.ObjectiveDualStart, MathOptInterface.VariableIndex}, value::Float64)
    @ DiffOpt C:\JG\Julia\dev\DiffOpt\src\copy_dual.jl:90
  [3] set(b::MathOptInterface.Bridges.LazyBridgeOptimizer{DiffOpt.ConicProgram.Model}, attr::DiffOpt.ObjectiveDualStart,
 value::Float64)
    @ DiffOpt C:\JG\Julia\dev\DiffOpt\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 C:\JG\Julia\dev\DiffOpt\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 C:\JG\Julia\dev\DiffOpt\src\moi_wrapper.jl:627
  [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 C:\JG\Julia\dev\DiffOpt\src\moi_wrapper.jl:547
  [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}}}}})
    @ DiffOpt C:\JG\Julia\dev\DiffOpt\src\parameters.jl:302
  [8] forward_differentiate!
    @ C:\JG\Julia\dev\DiffOpt\src\jump_moi_overloads.jl:337 [inlined]
  [9] forward_differentiate!(model::MathOptInterface.Utilities.CachingOptimizer{MathOptInterface.Bridges.LazyBridgeOptimizer{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}}}}}}, MathOptInterface.Utilities.UniversalFallback{MathOptInterface.Utilities.Model{Float64}}})
    @ DiffOpt C:\JG\Julia\dev\DiffOpt\src\jump_moi_overloads.jl:322
 [10] forward_differentiate!(model::Model)
    @ DiffOpt C:\JG\Julia\dev\DiffOpt\src\jump_moi_overloads.jl:307
 [11] top-level scope
    @ REPL[226]:1

[joaquimg]

@blegat,
in the above,

Looking at MathOptInterface.Bridges.Objective.FunctionConversionBridge{Float64, MathOptInterface.ScalarAffineFunction{Float64}, MathOptInterface.VariableIndex}
it seems the bridge is converting VI to SAF, which is not a comment conversion in the docs of such a bridge.

So the error might be where the bridge is being triggered?

if I add:

function MOI.set(
    model::MOI.ModelLike,
    ::ObjectiveFunctionAttribute{ObjectiveDualStart},
    b::MOI.Bridges.Objective.FunctionConversionBridge,
    value,
)
    return
end

function MOI.set(
    model::MOI.ModelLike,
    ::ObjectiveFunctionAttribute{ObjectiveSlackGapPrimalStart},
    b::MOI.Bridges.Objective.FunctionConversionBridge,
    value,
)
    return
end

the error goes away, but I am not sure if this is correct.

[blegat]

Maybe we need to start reviving #253 otherwise we'll spend time on a fix that will need to be updated once we merge it

[joaquimg]

Agreed!

[blegat]

Let me know if rebasing on master fixed the error

[joaquimg]

bridging errors were fixed by #253

[codecov]

Codecov Report

Attention: Patch coverage is 88.28829% with 39 lines in your changes missing coverage. Please review.

Project coverage is 86.77%. Comparing base (07478f8) to head (35cd234).
Report is 4 commits behind head on master.

Files with missing lines	Patch %	Lines
src/parameters.jl	94.48%	16 Missing ⚠️
src/jump_moi_overloads.jl	50.00%	9 Missing ⚠️
src/utils.jl	0.00%	9 Missing ⚠️
src/bridges.jl	0.00%	5 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #262      +/-   ##
==========================================
+ Coverage   85.38%   86.77%   +1.39%     
==========================================
  Files          12       13       +1     
  Lines        1156     1474     +318     
==========================================
+ Hits          987     1279     +292     
- Misses        169      195      +26     

☔ View full report in Codecov by Sentry.
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[joaquimg]

Not a WIP anymore, this is ready for review.

[blegat]

I'd say set_forward_parameter is more explicit than set_forward. We wouldn't need the _parameter if the fact that the variable is a parameter is part of the signature of the method but here the type of the variable is VariableRef and the fact that it's a parameter is only due to the state of the optimizer so set_forward_parameter seems appropriate. On the other hand, it's not like we support it for something else than parameters so why do we have to be so explicit, set_forward is maybe enough.