The first sample-efficient algorithm in heuropt. Bayesian optimization
maintains a Gaussian-process surrogate of the objective and at each
step picks the next decision by maximizing an acquisition function on
that surrogate, so the evaluation budget is used surgically.
Implementation:
- **Kernel**: anisotropic RBF (squared-exponential) with per-axis
length scales, signal variance, and a small noise/jitter floor.
Hyperparameters are exposed in the config; a future version can add
marginal-likelihood maximization.
- **Posterior**: standard formulation. Cholesky factorizes K (using
the new internal helper); mean and variance predictions follow.
- **Acquisition**: Expected Improvement against the best observed
feasible point. Optimized by best-of-N random sampling — simple,
predictable cost, no inner-optimizer footgun.
- **Initial design**: `initial_samples` uniform-random points in
bounds before the BO loop starts.
- **Constraints**: feasibility-aware EI — best observed value uses
only feasible points; infeasible candidates are penalized.
Vec<f64> decisions, single-objective only. Targets the regime no
existing heuropt algorithm covers: 50–500 evaluations on an
expensive black-box function (CFD sim, ML training run, real-world
measurement).
Tests cover convergence on the 1-D sphere within a tight evaluation
budget (~30 evals get to f < 1e-6 — vs population-based methods
needing thousands), deterministic reruns, and panic on
multi-objective + dim mismatches.
Hand-rolled `A = L · L^T` factorization plus forward/backward triangular
solves, used by the upcoming Bayesian Optimization implementation for
the GP posterior. Same f64 row-major Vec<Vec<f64>> interface as the
existing Jacobi eigen helper so we don't pull in nalgebra for one
algorithm.
Returns Err on non-positive-definite input (a small jitter is the
typical caller-side fix). Tested against the standard 2x2 case, the
3x3 known-result case, A·x = b round-trip, and the SPD-failure case.
Hansen & Ostermeier 2001 CMA-ES, the canonical real-valued
single-objective stochastic optimizer. Implements the full (μ/μ_w, λ)
update with rank-μ + rank-1 covariance updates and cumulative step-size
adaptation:
- Sample λ offspring from N(mean, σ² · C)
- Select the μ best, weight them, recompute mean
- Update evolution paths p_σ (step size) and p_c (covariance)
- Rank-1 update of C from p_c, plus rank-μ update from selected offspring
- Adapt σ via |p_σ| / E‖N(0,I)‖
Eigendecomposition (used to convert C into its B·D form for sampling
N(0, σ²·C)) goes through the new internal Jacobi helper, recomputed
every `eigen_decomposition_period` generations to amortize cost.
Vec<f64> decisions only. Bounds taken from a `RealBounds` field; mean
and offspring are clamped per dimension. Single-objective only.
Hyperparameters use the standard CMA-ES defaults (μ=λ/2, weights from
Hansen's tutorial, c_σ, c_c, c_1, c_μ, d_σ all formulae from §7.1).
Tests cover: convergence on Sphere1D and 5-D Rosenbrock, deterministic
reruns, panic on multi-objective, panic on `population_size < 4`.
Hand-rolled symmetric-matrix eigendecomposition via the cyclic Jacobi
rotation method. Returns sorted (eigenvalue, eigenvector) pairs in
descending order. Pure f64 row-major `Vec<Vec<f64>>` interface so we
don't pull in nalgebra for one algorithm.
Lives in `src/internal/eigen.rs` (new module). Used by the upcoming
CMA-ES implementation to maintain the covariance matrix's
eigendecomposition each generation. Tested against the standard
2x2 case, the diagonal case, and a known 3x3 result.
swaits