Implements ExpressionCost

[RussTedrake]

Most importantly, now AddCost(Expression) will succeed, even if it is passed in an Expression that is non-Polynomial.

Resolves #17897.

+@jwnimmer-tri for feature review, please?

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This change is 

[jwnimmer-tri]

See RussTedrake/drake@expression_cost...jwnimmer-tri:drake:expression_cost for a suggested change. (No need to copy-paste the implementation.)

Reviewed 2 of 6 files at r1, all commit messages.
Reviewable status: 2 unresolved discussions, LGTM missing from assignee jwnimmer-tri(platform), needs at least two assigned reviewers (waiting on @RussTedrake)

a discussion (no related file):
The docs for this function on mathematical_program.h are out of date now:

  /**
   * Adds a cost in the symbolic form.
   * Note that the constant part of the cost is ignored. So if you set
   * `e = x + 2`, then only the cost on `x` is added, the constant term 2 is
   * ignored.
   * @param e The linear or quadratic expression of the cost.
   * @pre `e` is linear or `e` is quadratic. Otherwise throws a runtime error.
   * @return The newly created cost, together with the bound variables.
   *
   * @exclude_from_pydrake_mkdoc{Not bound in pydrake.}
   */
  Binding<Cost> AddCost(const symbolic::Expression& e);

Both in terms of the preconditions, and the ignoring of the constant factor.

When resolving it, having the constant factor be sometimes-ignored and sometimes-obeyed seems too confusing on first impression, so we will need to figure out how to do it all one way or the other, and the test cases should reflect whichever contract we choose.

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solvers/BUILD.bazel line 210 at r1 (raw file):

    ],
    deps = [
        "//common/symbolic:polynomial",

nit Unused new deps symbolic:polynomial?

[jwnimmer-tri]

Oops, I pasted the wrong URL. I meant to link to RussTedrake#49.

[RussTedrake]

i considered doing it this way, but didn't think we would want cost to depend on constraint at the root implementation level (plus it was only a few lines).

Reviewable status: 1 unresolved discussion, LGTM missing from assignee jwnimmer-tri(platform), needs at least two assigned reviewers, commits need curation (https://drake.mit.edu/reviewable.html#curated-commits) (waiting on @jwnimmer-tri and @RussTedrake)

a discussion (no related file):

Previously, jwnimmer-tri (Jeremy Nimmer) wrote…

The docs for this function on mathematical_program.h are out of date now:

  /**
   * Adds a cost in the symbolic form.
   * Note that the constant part of the cost is ignored. So if you set
   * `e = x + 2`, then only the cost on `x` is added, the constant term 2 is
   * ignored.
   * @param e The linear or quadratic expression of the cost.
   * @pre `e` is linear or `e` is quadratic. Otherwise throws a runtime error.
   * @return The newly created cost, together with the bound variables.
   *
   * @exclude_from_pydrake_mkdoc{Not bound in pydrake.}
   */
  Binding<Cost> AddCost(const symbolic::Expression& e);

Both in terms of the preconditions, and the ignoring of the constant factor.

When resolving it, having the constant factor be sometimes-ignored and sometimes-obeyed seems too confusing on first impression, so we will need to figure out how to do it all one way or the other, and the test cases should reflect whichever contract we choose.

Done. Good catch. It turns out the the AddQuadraticCost docstring was a lie, too. (The existing tests proved it, but I've added a narrower test to confirm). And the python binding was bizarre, but is now fixed.

I don't see any other places where it claims that the constant is dropped.

fyi @hongkai-dai

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solvers/BUILD.bazel line 210 at r1 (raw file):

Previously, jwnimmer-tri (Jeremy Nimmer) wrote…

nit Unused new deps symbolic:polynomial?

Done. (it was providing the decompose.h, but that was also not needed anymore)

[jwnimmer-tri]

I should have also clarified -- my main motivation in de-duplication was to avoiding duplicating the non-threadsafe environment_ member field into a second place.

feature.

+@xuchenhan-tri for platform review per schedule, please. (I'm on-call today.)

Reviewed 1 of 6 files at r1, 6 of 6 files at r2, all commit messages.
Reviewable status: 2 unresolved discussions, LGTM missing from assignee xuchenhan-tri(platform) (waiting on @xuchenhan-tri)

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solvers/cost.h line 8 at r2 (raw file):

#include <optional>
#include <string>
#include <unordered_map>

nit Unused <unordered_map>. (I thought I'd removed this line in my PR but maybe I forgot to push that edit to github.)

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solvers/test/cost_test.cc line 772 at r2 (raw file):

  std::ostringstream os;
  cost.Display(os, x_e);
  EXPECT_EQ(fmt::format("{}", os.str()), "ExpressionCost (x * sin(y))");

nit No need for format, as best I can tell.

Suggestion:

  EXPECT_EQ(os.str(), "ExpressionCost (x * sin(y))");

[RussTedrake]

Reviewable status: LGTM missing from assignee xuchenhan-tri(platform) (waiting on @xuchenhan-tri)

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solvers/cost.h line 8 at r2 (raw file):

Previously, jwnimmer-tri (Jeremy Nimmer) wrote…

nit Unused <unordered_map>. (I thought I'd removed this line in my PR but maybe I forgot to push that edit to github.)

Done. (I thought I'd put it back in to satisfy clang-format, but 🤷‍♂️ )

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solvers/test/cost_test.cc line 772 at r2 (raw file):

Previously, jwnimmer-tri (Jeremy Nimmer) wrote…

nit No need for format, as best I can tell.

Done.

[jwnimmer-tri]

Reviewed 2 of 2 files at r3, all commit messages.
Reviewable status: LGTM missing from assignee xuchenhan-tri(platform) (waiting on @xuchenhan-tri)

[xuchenhan-tri]

Platform

Reviewed 1 of 6 files at r1, 5 of 6 files at r2, 2 of 2 files at r3, all commit messages.
Reviewable status: complete! all discussions resolved, LGTM from assignees jwnimmer-tri(platform),xuchenhan-tri(platform)

[jwnimmer-tri]

Oops. I meant to remove the issue number from the commit message on merge. I should have left a nit to remind us. Oh well.

Maybe at some point we should configure reviewable to help us remember.