cmaes — separable CMA-ES (sampler)

Role: optimization · kind: n4m_sampler_kind_t = N4M_SAMPLER_CMAES · since: ABI 2.1 (F4)

Covariance Matrix Adaptation Evolution Strategy, separable (diagonal) variant (Ros & Hansen 2008), over the unit hypercube. A generation of λ = 4 + ⌊3·ln P⌋ candidates is sampled from N(m, σ²·diag(C)) and clamped to [0,1); once resolved, the best completed and scored members (up to μ = λ/2) update the mean m, diagonal covariance C, global step-size σ, and two evolution paths. The diagonal covariance drops the eigendecomposition of full CMA-ES, so the sampler stays cheap for modest numeric dimensionality.

CMA-ES adapts every numeric axis (int, float, log_int, log_float) in unit space; stepped and integer proposals are snapped during decoding. Categorical and ordinal axes are drawn independently from the native RNG and do not update the CMA distribution. A sorted_tuple axis is likewise generated independently and is not modelled. This is a native mixed-space behavior, not an external-library compatibility guarantee; for heavily categorical spaces prefer tpe or ga.

Synchronous update (F4): the distribution advances only once its whole generation is terminal (liar = none), so ask_batch returns a partial batch at a generation boundary, and warm-start (n4m_optimizer_enqueue) is unsupported (N4M_ERR_UNSUPPORTED). The distribution updates from completed, scored members only — pruned and failed trials never enter the mean/covariance. Any non-none liar value is rejected at optimizer creation with N4M_ERR_NOT_IMPLEMENTED.

Conditional activation is honored by the decode. Search spaces containing hard mutex_group, requires or exclude constraints are rejected by n4m_optimizer_create with N4M_ERR_UNSUPPORTED; CMA-ES never treats an infeasible configuration as a host-supplied poor fitness. Hard constraints that reference a sorted_tuple root are rejected for every sampler.

Usage (C ABI)

n4m_optimizer_options_t opts;
n4m_optimizer_options_init(&opts);
opts.sampler = N4M_SAMPLER_CMAES;
opts.seed = 42;

Parity

  • Tier B-state target: the distribution state after ranked tells is deterministic for a fixed seed, ask/tell order and score tape. Track-Q currently commits the native cmaes_sphere2 proposal trace; it has no state-level pycma fixture and does not cover every pruner or mixed-space combination. Convergence on a smooth objective is verified in the C++ tests.

References

  • Hansen & Ostermeier, Completely Derandomized Self-Adaptation in Evolution Strategies, Evol. Comput. 9 (2001), 159–195; Ros & Hansen, A Simple Modification in CMA-ES Achieving Linear Time and Space Complexity, PPSN (2008); Hansen, The CMA Evolution Strategy: A Tutorial (2016). See _finetuning_bibliography.bib.