Continuous relaxation with fallback for inequality-constrained ordinal dims (#3261)

[ItsMrLin]

Summary:

_setup_continuous_relaxation in optimize_mixed.py blanket-excludes all
constrained discrete dimensions from continuous relaxation, forcing them into
discrete local search even when they have high cardinality. This is overly
conservative for inequality constraints and causes severe performance
degradation.

Problem: When ordinal parameters (e.g., integers 0-50) participate in
linear inequality constraints (e.g., x1 + x2 + x3 <= 100), they are kept
as discrete dims regardless of cardinality. In mixed search spaces, this
inflates the discrete combination count (e.g., 51^4 x 20 = 135M), forces
optimize_acqf_mixed_alternating, and with default optimizer budgets
(raw_samples=1024, maxiter_init=100, maxiter_alternating=64) across
many sequential candidates, produces ~900K+ acquisition function evaluations
-- taking hours instead of minutes.

Fix: Try continuous relaxation first for inequality-constrained dims, with
automatic fallback to keeping them discrete if infeasible candidates result.

Specifically, optimize_acqf_mixed_alternating now:

1. Fast path: Calls _setup_continuous_relaxation with
   inequality_constraints=None, allowing inequality-constrained dims to be
   relaxed and optimized continuously.
2. Feasibility check: After optimization, checks if the candidates satisfy
   all constraints via evaluate_feasibility.
3. Fallback: If any candidates are infeasible (e.g., due to rounding
   violations with non-contiguous discrete choices or tight constraints),
   re-runs with inequality-constrained dims kept discrete.

_setup_continuous_relaxation itself retains the D94963154 behavior of
excluding all constrained dims passed to it — the caller controls which
constraints are relevant by choosing what to pass.

The optimization body is extracted into _run_alternating_optimization to
enable the fallback without code duplication.

Differential Revision: D99304800

[meta-codesync]

@ItsMrLin has exported this pull request. If you are a Meta employee, you can view the originating Diff in D99304800.

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 99.98%. Comparing base (b16b28f) to head (8ced576).

Additional details and impacted files

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  Coverage   99.98%   99.98%           
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  Files         221      221           
  Lines       21902    21926   +24     
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+ Hits        21898    21922   +24     
  Misses          4        4           

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