# ============================================================================
# T16 — Comparing stochastic and adversarial bandit algorithms under drift
# ----------------------------------------------------------------------------
# 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: ML16
title: "Bandit algorithm robustness under stationary and drifting reward regimes"
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: |
  Multi-armed bandit algorithms encode different assumptions about reward
  generation and non-stationarity. Epsilon-greedy is simple and adaptable with
  persistent exploration; UCB1 is optimism-driven and often strong in
  stationary stochastic settings; Thompson sampling can be highly sample
  efficient when model assumptions are matched; Exp3 is designed for
  adversarial settings and may trade off stochastic efficiency for robustness.
  In small CPU-constrained studies, these differences are often discussed
  qualitatively but not tested with matched synthetic environments.

  A meaningful benchmark should evaluate both Bernoulli and Gaussian reward
  arms, because posterior/model assumptions and noise scale can materially
  change outcomes. It should also include stationary and drifting regimes:
  methods tuned for fixed means can degrade when the best arm changes over
  time. Regret, not just final reward, is the right primary metric because it
  captures online learning efficiency throughout the horizon.

  A credible experiment here implements the four algorithms with consistent
  action/reward interfaces, runs repeated simulations over multiple seeds, and
  reports cumulative regret trajectories and endpoint statistics. To keep the
  study CPU-friendly, horizons and arm counts should be modest (e.g., 5-10 arms,
  500-2000 steps), with vectorized numpy updates where possible.

  The key analytical value is comparative: identify where UCB1/Thompson excel
  in stationary stochastic settings, and whether epsilon-greedy or Exp3 is more
  resilient under drift. The objective is not reproducing a single paper, but
  testing algorithm-environment fit under controlled synthetic shifts.

  *How do epsilon-greedy, UCB1, Thompson sampling, and Exp3 trade off cumulative regret across Bernoulli vs Gaussian arms and stationary vs drifting reward regimes?*

hypotheses:
  - id: H1
    statement: "In stationary Bernoulli environments, either UCB1 or Thompson sampling achieves at least 10% lower mean cumulative regret than epsilon-greedy at horizon T on at least 2 of 3 datasets (averaged over >=20 seeds)."
    measurable: true
  - id: H2
    statement: "In drifting environments, epsilon-greedy or Exp3 achieves lower mean cumulative regret than UCB1 on at least 2 of 3 datasets at horizon T (averaged over >=20 seeds)."
    measurable: true
  - id: H3
    statement: "Across all evaluated datasets, no single algorithm is best (lowest mean cumulative regret) on every dataset, indicating environment-dependent performance."
    measurable: true

experiment_design:
  research_question: "How do epsilon-greedy, UCB1, Thompson sampling, and Exp3 compare in cumulative regret across stationary versus drifting synthetic bandit tasks with Bernoulli and Gaussian rewards?"
  conditions:
    - name: "epsilon_greedy_eps0.1"
      description: "Epsilon-greedy with constant epsilon=0.1 and sample-mean value estimates."
    - name: "ucb1"
      description: "UCB1 with exploration bonus sqrt(2 log t / n_a)."
    - name: "thompson_sampling"
      description: "Thompson sampling using Beta-Bernoulli updates for Bernoulli arms and Gaussian posterior sampling (known variance assumption) for Gaussian arms."
    - name: "exp3_gamma0.07"
      description: "Exp3 with gamma=0.07 and importance-weighted reward estimates."
  baselines:
    - "epsilon_greedy_eps0.1 as simple stochastic baseline"
    - "ucb1 as canonical optimism baseline"
  metrics:
    - name: "cumulative_regret"
      direction: "minimize"
      description: "Mean cumulative regret at final horizon T relative to oracle best arm per round, averaged over seeds."
    - name: "instantaneous_regret_auc"
      direction: "minimize"
      description: "Area under per-round regret curve over time (lower is better)."
    - name: "best_arm_selection_rate"
      direction: "maximize"
      description: "Fraction of rounds selecting the current optimal arm (for drift: time-varying optimum)."
  datasets:
    - name: "bernoulli_stationary_k10"
      source: "synthetic: 10 Bernoulli arms with fixed means sampled in [0.05, 0.95] and sorted gap >=0.05"
    - name: "bernoulli_drift_k10"
      source: "synthetic: 10 Bernoulli arms with piecewise-constant means; best arm switches at predefined changepoints"
    - name: "gaussian_drift_k8"
      source: "synthetic: 8 Gaussian arms (sigma=1) with linearly drifting means and periodic rank reversals"
  compute_requirements:
    gpu_required: false
    estimated_wall_clock_sec: 420

rubric_path: "experiments/arc_bench/config/ml/rubrics/ML16.json"