Remove default non-negativity constraint on least core subsidy

[AnesBenmerzoug]

Description

This PR closes #294

Changes

• Add non_negative_subsidy flag to least core methods with a default value of False.
• Remove empty subset from lower bound constraints, if found, because it is the same as using the constraint $e >= 0$ if $u(\emptyset) = 0$ (which is true in almost all cases) (i.e. setting non_negative_subsidy=True)
• Remove total utility from lower bound constraints, if found, because it is the same as using the constraint $e >= 0$ (i.e. setting non_negative_subsidy=True)
• Rename options to solver_options.
• Pass solver_options as dictionary instead of as kwargs.
• Shows a deprecation warnings when passing solver options as kwargs.
• Change default solver from ECOS to SCS.
• Set default solver max iterations to 10000.
• Update least core notebook.
• Update core and least core docs' constraints to use proper non-empty subsets.

Checklist

• Wrote Unit tests (if necessary)
• Updated Documentation (if necessary)
• Updated Changelog
• If notebooks were added/changed, added boilerplate cells are tagged with "nbsphinx":"hidden"

[mdbenito]

(without looking at the PR) Note that the constraint for the empty set only implies e > 0 if u(S)=0

[mdbenito]

And, since you update the docs, would it be possible to keep the notation consistent with the rest of the docs? i.e. identify points $x_i$ with their indices $i$ and use $v_i$ instead of $v_u(x_i)$

[AnesBenmerzoug]

@mdbenito I actually used the same notation as in the rest of the data valuation documentation.

Do you mean only in the docstring? If not, then I would suggest we leave that as a separate issue and discuss it tomorrow.

[mdbenito]

@mdbenito I actually used the same notation as in the rest of the data valuation documentation.

My bad, it's the rest of the doc that's quite inconsistent.

Do you mean only in the docstring? If not, then I would suggest we leave that as a separate issue and discuss it tomorrow.

See #308

[mdbenito]

Just had a couple of questions. Otherwise this looks good. We should repeat the experiments, btw...