feat: add DistributionallyRobustSampler (ICML 2022)

[Rishabh-git10]

Contributor Agreements

Please read the contributor agreements and if you agree, please click the checkbox below.

• I agree to the contributor agreements.

Motivation

Resolves #75
Adds support for Bayesian Optimization with Distributionally Robust Chance Constraints (DRCC). Standard BO assumes known distributions for environmental variables. This sampler targets optimization in environments with uncertain/noisy variables where strict safety thresholds must be maintained, implementing the algorithm from "Bayesian Optimization for Distributionally Robust Chance-constrained Problem" (Imamura et al., ICML 2022).

Description of the changes

• Added DistributionallyRobustSampler under samplers/distributionally_robust_bo.
• Kept the package lightweight (no BoTorch dependency). The 1D RBF Gaussian Process uses numpy, and chance constraints are evaluated via scipy.optimize.linprog (Highs solver), directly mirroring the authors' original lpSolve methodology.
• Implemented the proposed Acquisition Function (AF_num 6) to penalize candidates failing the $P(g(x,w) > h) \ge \alpha$ constraint.
• Integrated exploration fallbacks and micro-jitter to prevent GP convergence collapse on identical candidates.

Empirical Validation:

Note for reviewer: Benchmark compares this against TPESampler on a noisy maximization problem subject to a safety threshold $h = -10$. TPE frequently violates the constraint due to environmental noise, whereas DRCC remains conservative and stabilizes safely above the threshold.

TODO List towards PR Merge

• Copy ./template/ to create your package
• Replace <COPYRIGHT HOLDER> in LICENSE of your package with your name
• Fill out README.md in your package
• Add import statements of your function or class names to be used in __init__.py
• (Optional) Add from __future__ import annotations at the head of any Python files that include typing to support older Python versions
• Apply the formatter based on the tips in README.md
• Check whether your module works as intended based on the tips in README.md