Inner approximations

[bfpc]

An initial version of inner approximations for Value functions. Currently, supports only LinearPolicyGraphs, and no belief/objective states.

[codecov]

Codecov Report

Attention: Patch coverage is 86.10272% with 46 lines in your changes missing coverage. Please review.

Project coverage is 95.52%. Comparing base (90bab46) to head (edc065c).
Report is 7 commits behind head on master.

Files with missing lines	Patch %	Lines
src/Inner.jl	86.10%	46 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #830      +/-   ##
==========================================
- Coverage   96.38%   95.52%   -0.87%     
==========================================
  Files          26       27       +1     
  Lines        3624     3955     +331     
==========================================
+ Hits         3493     3778     +285     
- Misses        131      177      +46     

☔ View full report in Codecov by Sentry.
📢 Have feedback on the report? Share it here.

🚀 New features to boost your workflow:

• ❄️ Test Analytics: Detect flaky tests, report on failures, and find test suite problems.
• 📦 JS Bundle Analysis: Save yourself from yourself by tracking and limiting bundle sizes in JS merges.

[odow]

Suggested change

	using JuMP
	import JuMP

Our suggested best practice is to use import Package within any other package. This forces you to prefix Package. on all calls, which is more explicit, and it avoids future breakage if JuMP starts exporting a new symbol. For example, if JuMP starts exporting delete, did we mean Base.delete or JuMP.delete?

[bfpc]

I guess I have now "converged" to a more reasonable PR. I guess the next steps are:

• "duplicate" a graph, in order to build the "inner" policy graph from the "outer" one;
• Implement multi-vertices; do we (a) keep the notation MULTI_CUT (b) add new constants SINGLE_VERTEX & MULTI_VERTEX (c) replace by something like NODEWISE & BRANCHWISE (which could work for both and at the same time is not very common)
• Test for cyclic graphs / Markovian graphs / ...

but feel free to suggest other directions ;-)

[odow]

I think the next step is to add more tests.

See https://app.codecov.io/gh/odow/SDDP.jl/pull/830/blob/src/Inner.jl?dropdown=coverage

We should add a test for every red uncovered line.

There really a few that are unreachable, because there's an error("Not implemented") followed by some code. We should delete that code for now, and add a case that tests the error is hit.

[odow]

There's also a bunch of stuff for the risk-set and multi-cuts. Do you use any of that? I don't think so at the moment. So delete.

I don't know if we need multi-vertex support?

[bfpc]

Hi Oscar,

So, my idea would be that in the (near-ish) future we could provide something like this to evaluate the gap:

model = ...
SDDP.train(model)
SDDP.build_inner_bound(model)

Naturally, this would need a function to "copy" a PolicyGraph into a blank one, then perform a backward inner pass (or other strategy, but let's start with that). As far as I see it, the next "low-hanging fruits" should be multi-cuts and (non-cyclic) Markovian Policy Graphs.

My idea is to create a "tracking issue" for those two (which seem independent to me), and maybe also add other features of SDDP.jl on a "wish-list". My not-so-low next candidate would be Unicyclic policy graphs (because they are useful) but the backward inner pass should be modified to perform at least some loops in order to sufficiently approximate the inner functions.

[odow]

Suggested change

	# The goal is # to operate one hydro-dam and two thermal plants over time
	# The goal is to operate one hydro-dam and two thermal plants over time

[odow]

You can see the preview here: https://sddp.dev/previews/PR830/examples/inner_hydro_1d/

[odow]

Let's give this a better name

[odow]

Could we add something like

!!! warning
    The code in this example is experimental and the API may change in any future release.