[WIP] Wrappers for OT barycenter solvers

[cedricvincentcuaz]

Types of changes

• creation of the class ot.utils.BaryResult extending OTResult

first draft for OT barycenter solvers with samples and predefined metric ot.solvers.bary_sample built on top of ot.solvers.solve_sample extending significantly available OT losses for the barycenter problem.

• 1-a) learn_X=True and learn_b=False equivalent to free support POT solvers using BCD with closed form. Only metrics in ('sqeuclidean', 'euclidean') are support for now. The solver calls an hidden function _bary_sample_bcd.
• 1-b) [TO DO] extend metrics
• 1-c) handle variations in masses across OT problems only for unbalanced problems - keeping masses unchanged for exact and inexact sinkhorn like solvers - via parameter update_masses in ot.solvers._bary_sample_bcd.
• 1-d) Handle given initialization of transport plans & potentials + warmstart strategies : added parameter warmstart to bary_sample, and based on the requested inner solver, we pick the adequate strategy warmstart_plan or warmstart_potentials passed to _bary_sample_bcd .
• 1-e) Options for stopping criterion between losses and barycenter variations: added parameter stopping_criterion in ('loss', 'bary') passed to _bary_sample_bcd.
• 2. [TO DO] see how to best handle learn_X=True and learn_b=True
• 3. [TO DO] learn_X=False and learn_b=True should be solved via future ot.solvers.bary after computing built-in cost matrices.
• 4. [TO DO] Extension to support lazy tensors as in ot.solve_sample
• 5. [TO DO] Complete documentation

Motivation and context / Related issue

• 1. test.test_solvers.assert_allclose_bary_sol method to compare solutions as BaryResult objects. test_bary_sample grid across all available barycenter solvers depending on those available in ot.solvers.solve_sample.

How has this been tested (if it applies)

PR checklist

• I have read the CONTRIBUTING document.
• The documentation is up-to-date with the changes I made (check build artifacts).
• All tests passed, and additional code has been covered with new tests.
• I have added the PR and Issue fix to the RELEASES.md file.

[codecov]

Codecov Report

Attention: Patch coverage is 83.64486% with 35 lines in your changes missing coverage. Please review.

Project coverage is 85.27%. Comparing base (8aed2d7) to head (671788d).

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HEAD has 25 uploads less than BASE

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Additional details and impacted files

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- Coverage   97.09%   85.27%   -11.82%     
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- Hits        19839    17605     -2234     
- Misses        593     3039     +2446     

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