# ============================================================================
# T09 — Comparing Bayesian optimization vs grid search vs random search for
# hyperparameter tuning of random forests on UCI benchmark datasets
# ----------------------------------------------------------------------------
# Unlike paper_replication's P01-P07, the "synthesis" here frames a research
# QUESTION rather than a known paper's method. The model must design the
# experiment (conditions, metrics, datasets) — we only commit to what a
# competent study of this topic would include and what the rubric expects.
# ============================================================================

id: ML09
title: "Bayesian optimization vs grid vs random search for random-forest tuning"
arxiv_id: null
venue: "ARC-Bench 2026"
paper_asset: null

# The "synthesis" plays the role of the upstream briefing: research question,
# background, why the question matters, what "a reasonable experiment" looks
# like. It deliberately does NOT pre-specify a single method to reproduce.
synthesis: |
  Hyperparameter tuning often dominates practical AutoML performance, yet in
  CPU-limited settings the search strategy itself can matter as much as the
  model family. For random forests, common tunables (number of trees,
  max_depth, min_samples_split, min_samples_leaf, max_features) define a mixed
  discrete-continuous space where exhaustive grids can be wasteful,
  random search can be surprisingly strong, and Bayesian optimization can use
  surrogate modeling to focus evaluations on promising regions.

  A concise benchmark can test this tradeoff by fixing a single model class
  (RandomForestClassifier), fixed CV protocol, and comparable evaluation budget
  across search methods. Grid search should use a compact but principled grid;
  random search should sample from the same parameter ranges; Bayesian
  optimization can be implemented with sklearn's Gaussian-process based
  optimizer (e.g., BayesSearchCV if available is not allowed here, so a custom
  lightweight GP + acquisition loop or scipy/sklearn surrogate approach is
  expected). The key is fairness: equal or near-equal numbers of objective
  evaluations and identical data splits.

  Since this benchmark must run in under 15 minutes on one CPU core,
  datasets should be small-to-medium sklearn/UCI-style classification tasks
  already available in sklearn (e.g., wine, breast_cancer, digits). The
  analysis should report best cross-validation score, held-out test accuracy,
  and search efficiency (score gain per evaluation or wall-clock).
  Multi-seed repeats are desirable to reduce noise, but can be kept modest to
  remain within runtime limits.

  The experiment should answer whether Bayesian optimization delivers better
  best-found configurations under tight evaluation budgets, or whether simpler
  baselines (especially random search) are effectively equivalent for these
  tabular tasks. Interpretation should explicitly separate optimization quality
  from compute cost.

  *Under a fixed small evaluation budget, does Bayesian optimization find better random-forest hyperparameters than grid and random search on sklearn UCI-style classification benchmarks?*

hypotheses:
  - id: H1
    statement: "With an equal budget of 20 hyperparameter evaluations per dataset, Bayesian optimization achieves higher mean best_cv_score than random search on at least 2 of 3 datasets."
    measurable: true
  - id: H2
    statement: "Random search matches or exceeds grid search in best_cv_score on at least 2 of 3 datasets under the same maximum number of evaluated configurations."
    measurable: true
  - id: H3
    statement: "The mean held-out test accuracy of the best Bayesian-tuned model is at least 0.5 percentage points higher than the best grid-tuned model on at least 1 of 3 datasets."
    measurable: true

experiment_design:
  research_question: "Under a fixed evaluation budget, which tuning strategy (Bayesian optimization, grid search, random search) yields the best random-forest cross-validation and test performance on sklearn UCI-style datasets?"
  conditions:
    - name: "grid_search_budget20"
      description: "Grid search over a compact predefined grid for RandomForestClassifier, capped at 20 evaluated configurations per dataset."
    - name: "random_search_budget20"
      description: "Random search over matched hyperparameter ranges with 20 sampled configurations per dataset."
    - name: "bayes_opt_budget20"
      description: "Bayesian optimization using a Gaussian-process surrogate and acquisition-guided proposals for 20 total evaluations per dataset."
    - name: "default_rf"
      description: "Untuned RandomForestClassifier with sklearn default hyperparameters as a reference baseline."
  baselines:
    - "default_rf as no-tuning baseline"
    - "grid_search_budget20 as classical tuning baseline"
  metrics:
    - name: "best_cv_score"
      direction: "maximize"
      description: "Best mean 3-fold cross-validation accuracy discovered by each search method."
    - name: "test_accuracy"
      direction: "maximize"
      description: "Accuracy on a held-out test split using the best hyperparameters found by each method."
    - name: "search_time_sec"
      direction: "minimize"
      description: "Wall-clock time spent in hyperparameter search per method and dataset."
  datasets:
    - name: "wine"
      source: "sklearn.datasets.load_wine"
    - name: "breast_cancer"
      source: "sklearn.datasets.load_breast_cancer"
    - name: "digits"
      source: "sklearn.datasets.load_digits"
  compute_requirements:
    gpu_required: false
    estimated_wall_clock_sec: 780

rubric_path: "experiments/arc_bench/config/ml/rubrics/ML09.json"