Constrained Bayesian Optimization (CBO)

Source code for the paper: Optimistic Constrained Bayesian Optimization

Implementation of multiple acquisition functions for Bayesian Optimization with unknown constraints.

Overview

This project implements and compares several constrained Bayesian optimization algorithms:

• UCBC (Upper Confidence Bound Constrained) - S⁻ set-based approach with adaptive/coupled query modes
• ObsoleteAwareUCB - Direct violation-based with obsolete constraint detection (recommended)
  • Paper: Optimistic Constrained Bayesian Optimization
• EIC (Expected Improvement with Constraints) - Classic constrained BO
• CMES-IBO (Max-value Entropy Search) - Information-theoretic approach

Installation

# Create virtual environment using uv
uv venv
source .venv/bin/activate  # On Windows: .venv\Scripts\activate

# Install dependencies
uv pip install -r requirements.txt

Requirements

• Python 3.7+
• PyTorch >= 1.9.0
• GPyTorch >= 1.6.0
• NumPy >= 1.19.0
• Matplotlib >= 3.3.0

Quick Start

# Run single experiment with ObsoleteAwareUCB (recommended)
python run-multi-constraint-bo.py \
  --num-rand 10 \
  --acqfunc obsolete_aware_ucb_mixed \
  experiment_config/branin_branin.json

# Run batch experiments
sh script_branin_branin.sh
sh script_gas_transmission.sh
sh script_welded_beam_design.sh

Acquisition Functions

Name	Description	Queries per Iteration	Notes
ucbc_decoupled	UCBC with adaptive queries	1 (target OR constraint)	S⁻ set-based
ucbc_coupled	UCBC querying all together	n+1 (all)	Conservative
obsolete_aware_ucb	Direct violation-based	1 (target OR constraint)	Simplified
obsolete_aware_ucb_mixed	With obsolete detection	1+	⭐ Recommended
eic	Expected Improvement	2 (target AND constraint)	Classic
cmes_ibo	Entropy-based	2 (target AND constraint)	Info-theoretic

Algorithm Comparison

UCBC vs ObsoleteAwareUCB:

• UCBC: Uses S⁻ set (points where both lower and upper bounds satisfy constraints) to decide queries
• ObsoleteAwareUCB: Directly compares violation magnitude with target uncertainty (simpler, more robust)
• Mixed mode: Detects under-explored constraints (std > 2.0 × target_std) and queries them to prevent GP errors

Experiment Configuration

Experiments are defined in JSON files under experiment_config/. Example:

{
  "target": {
    "module_name": "branin",
    "identifier": "original_2_1",
    "n_init_observations": 3,
    "noise_std": 0.01,
    "ard": true,
    "is_hyperparameter_trainable": true,
    "gp_prior": {
      "lengthscale": {"gamma": {"concentration": 0.25, "rate": 0.5}},
      "outputscale": {"gamma": {"concentration": 2.0, "rate": 0.15}},
      "noise_std": {"gaussian": {"loc": 0.0, "scale": 0.1}}
    }
  },
  "constraints": [
    {
      "module_name": "branin",
      "share_observation_with_constraint": -1,
      "identifier": "original_2_1",
      "inequality": "greater_than_equal_to",
      "threshold": 0.6,
      "fix_mean_at": 0.6,
      "n_init_observations": 3,
      "noise_std": 0.01,
      "ard": true,
      "is_hyperparameter_trainable": true
    }
  ],
  "xsize": 100,
  "zsize": 100,
  "n_bo_iterations": 101,
  "beta": 40.0,
  "n_training_iter_gp_hyper": 30,
  "update_gp_hyper_every_iter": 1
}

Key Configuration Parameters

Target/Constraint Settings:

• module_name: Function to optimize (e.g., branin, welded_beam_design_2_3_5_obj)
• identifier: Task variant (e.g., original_2_1)
• n_init_observations: Number of random initial observations
• noise_std: Observation noise standard deviation
• ard: Use Automatic Relevance Determination (different lengthscales per dimension)
• is_hyperparameter_trainable: Whether to optimize GP hyperparameters

Constraint-Specific:

• share_observation_with_constraint: Share observations with another constraint (-1 = no sharing)
• inequality: "greater_than_equal_to" or "less_than_equal_to"
• threshold: Constraint threshold value
• fix_mean_at: Fix GP mean at threshold to prevent empty feasible region estimation

Optimization Settings:

• xsize, zsize: Discrete domain grid size (total points = xsize × zsize)
• n_bo_iterations: Number of BO iterations
• beta: Exploration-exploitation trade-off (higher = more exploration)
• n_training_iter_gp_hyper: GP hyperparameter optimization iterations
• update_gp_hyper_every_iter: Update GP hyperparameters every N iterations

Benchmark Problems

Synthetic Functions (2D)

• Branin: Classic test function
• Goldstein-Price: Multi-modal function
• Six-Hump Camel: Multiple local optima
• Hartmann 3D/6D: Higher-dimensional test functions

Real-World Engineering Problems

• Welded Beam Design (4D, 5 constraints): Structural optimization
• Gas Transmission (5D, 1 constraint): Pipeline design
• CIFAR-10 CNN (10 constraints): Neural network hyperparameter tuning

Project Structure

cbo/
├── run-multi-constraint-bo.py      # Main runner for BO algorithms
├── multi_constraint_bo.py          # Core BO framework
├── ucbc.py                         # UCBC implementation (S⁻ set-based)
├── obsolete_aware_ucb.py           # ObsoleteAwareUCB (violation-based)
├── eic.py                          # Expected Improvement with Constraints
├── cmes_ibo.py                     # Max-value Entropy Search
├── gp.py                           # Gaussian Process wrapper (GPyTorch)
├── utils.py                        # Utility functions
├── function/                       # Benchmark function implementations
│   ├── branin.py
│   ├── welded_beam_design_2_3_5_*.py
│   ├── gas_transmission_2_3_15_*.py
│   └── ...
├── experiment_config/              # JSON experiment configurations
│   ├── branin_branin.json
│   ├── welded_beam_design_2_3_5.json
│   └── ...
├── script_*.sh                     # Batch execution scripts
├── out/                            # Results directory
└── log/                            # Execution logs

Output Files

Results are saved in out/ directory:

• {experiment}_{acqfunc}_regrets.pkl:

  • instantaneous: Regret at each iteration
  • cumulative: Cumulative regret over time

• {experiment}_{acqfunc}_bo_info.pkl:

  • query_types: History of what was queried (target/constraint)
  • target_xz, target_y: Target function observations
  • constraint_xz_dict, constraint_y_dict: Constraint observations
  • cidx_to_moidx: Constraint index to model index mapping

Usage Examples

Run Single Algorithm

python run-multi-constraint-bo.py \
  --num-rand 5 \
  --acqfunc obsolete_aware_ucb_mixed \
  experiment_config/branin_branin.json

Compare Multiple Algorithms

Edit shell scripts to uncomment desired algorithms:

# In script_branin_branin.sh, uncomment:
python run-multi-constraint-bo.py ... --acqfunc obsolete_aware_ucb_mixed ...
python run-multi-constraint-bo.py ... --acqfunc eic ...
python run-multi-constraint-bo.py ... --acqfunc cmes_ibo ...

Monitor Progress

# Watch log file
tail -f log/log_obsolete_aware_ucb_mixed_branin_branin.txt

# Check results
python -c "import pickle; print(pickle.load(open('out/branin_branin_obsolete_aware_ucb_mixed_regrets.pkl', 'rb')))"

Citation

If you use this code, please cite the relevant papers for the algorithms you use.