Cross-entropy optimization
Algorithms AIMech:CrossEntropyOptimization DRAFT
Aliases: Cross-entropy method for optimization
A stochastic optimization method that iteratively samples a parameterized search distribution, selects high-performing samples using an adaptive threshold, and refits the distribution by maximum likelihood on those selected samples.
Identity Notes & Concept Scope
This is the optimization branch of the cross-entropy method, represented by Algorithm2.3 in the inspected 2005 tutorial. It is distinct from the rare-event probability estimator, the cross-entropy loss used to train a classifier, NES natural-gradient steps, and CMA-ES evolution-path covariance adaptation. The sampling family and its fit define concrete instances; the generic algorithm is not limited to independent Bernoulli variables or a Gaussian implementation. No normalized identity match was found across all 442 pinned AIO labels/scoped synonyms and 285 preceding native IDs/names/aliases. Full-checkout fixed-string searches included ignored and hidden files in worktree and main, returning 15 and 15 lines respectively. Every text hit was a prior candidate lead. Nine exact AIO CLASS nodes with scoped synonyms/comments and outgoing edges and seven native neighboring mechanisms were inspected. Absence is bounded to this snapshot and semantic neighborhood.
Claims & Grounded Evidence
1 Claim
Mechanism
#method
Specify a sampling family f(x;v), initial parameter, sample size N, elite parameter rho and stopping rule. For maximization, draw candidates from the current distribution, evaluate their scores and choose the empirical (1−rho) quantile as threshold gamma. Fit new parameters by maximizing the sum of log f(x;v) over sampled candidates with score at least gamma. The optimization formulation uses unit weights: it redefines the associated stochastic problem at each iteration, so the rare-event algorithm’s nominal-to-current likelihood ratio is absent. Optionally smooth the fitted parameter toward the old one via v_new=alpha*v_fit+(1−alpha)*v_old. For independent Bernoulli coordinates, the unsmoothed fit is the coordinatewise fraction of ones among selected samples. Iterate until the chosen stopping condition; the displayed Algorithm2.3 uses an unchanged threshold over several iterations. The source’s cross-entropy derivation minimizes KL from the ideal selected-event distribution to the parameterized sampling distribution, not the reverse direction.
⚠️ Curated Limitations & Negative Results
- A score>=threshold rule need not select exactly rho*N candidates: order-statistic indexing and tied scores can increase the elite count. Implementations must state their quantile, tie and optimization-direction conventions; minimization requires the corresponding lower-score criterion or an equivalent score transformation.
- Unsmoothed finite-sample fitting can produce Bernoulli probabilities 0 or 1 and remove future exploration. Interior initialization and 0<alpha<1 prevent exact endpoints after a single convex smoothing step in exact arithmetic; smoothing alone does not guarantee exploration forever or a global optimum, and finite precision can still collapse support.
- The choice of sampling family, initial support, sample size, elite fraction, fit constraints and stopping rule matters. A stabilized threshold is not an optimality certificate; the source explicitly permits getting trapped at a local minimum and limits its asymptotic discussion.
- Maximum-likelihood fitting of selected candidates is a sampling-distribution update, not an unbiased gradient of raw expected fitness. It does not require derivatives of the black-box objective; solving the distribution fit may still require numerical optimization. No universal performance or convergence-rate claim is curated.
Artificial Intelligence Ontology (AIO) Grounding
Explicit AIO Snapshot Assessment: No Match
Rationale: No suitable mapping was found for this general optimization method in the inspected pin. Learning tasks, evolutionary language models, predictive forests, bias concepts and a generic stochastic-process representation do not establish the defining identity. This is a bounded local assessment, not a claim of absence from other ontologies.
Search Scope: All 442 pinned AIO CLASS identities/scoped synonyms, all 285 preceding maintained identities, ignored/hidden full-checkout text, and semantic inspection of nine exact AIO targets and seven native neighbors.
| Examined AIO Candidate | Rejection Reason |
|---|---|
AIO:EvolutionaryLLM
|
This exact CLASS is a large language model using evolutionary computation. Its related synonym evolutionary algorithms does not denote every stochastic optimizer or establish model equivalence. |
AIO:TrainingStrategy
|
The definition concerns preprocessing/training machine-learning models. Optional neural-network or policy optimization applications do not define the full general optimization method. |
AIO:MachineLearningTask
|
General objective optimization is not necessarily a task of learning from data as in this target. |
AIO:MetaLearning
|
Updating optimizer state or a search distribution is not necessarily learning from metadata about machine-learning experiments. |
AIO:ActiveLearning
|
Objective evaluation does not require querying labels for data points. |
AIO:ReinforcementLearning
|
These general optimizers do not inherently specify a policy/environment learning task; a possible use in policy search is insufficient. |
AIO:RandomForest
|
Neither particle memory nor an adaptive sampling distribution is a predictive decision-tree ensemble. |
AIO:EvaluationBias
|
This class describes evaluation population/metric bias rather than an optimization algorithm. |
AIO:MarkovChain
|
A possible augmented-state Markov representation is too generic to identify this optimizer. The inspected defining operation is particle motion or elite-distribution refitting, not construction of a target-invariant Markov sampler; the pinned network/model is not an equivalent or necessary semantic parent. |
Evidence Sources & Primary Literature
1 Source| Source ID | Publication / Document | Type / Access | Reference & Checksum |
|---|---|---|---|
method-source
|
Pieter-Tjerk de Boer, Dirk P. Kroese, Shie Mannor, Reuven Y. Rubinstein
|
primary paper
full_text
|
ID: https://people.smp.uq.edu.au/DirkKroese/ps/aortut.pdf
sha256:f68c734c2789…
|
Curation Provenance
Curator: Codex
Method: ai_assisted
Model: GPT-6
Created: 2026-10-11T13:05:37Z
Updated: 2026-10-11T13:05:37Z
Source File:
data/curated/CrossEntropyOptimization.yaml