Introduction to Bayesian Optimization

Bayesian Optimization (BO) is a powerful technique for optimizing expensive black-box functions. The TuRBO (Trust Region Bayesian Optimization) algorithm has shown impressive performance, but it has limitations in balancing exploration and exploitation.

The Problem with Standard TuRBO

While TuRBO excels at local optimization through trust regions, it can struggle with:

• Global exploration in high-dimensional spaces
• Adapting to changing landscapes
• Balancing local exploitation with global exploration

TuRBO-O: Our Enhanced Approach

Deep Kernel Learning Integration

The key innovation in TuRBO-O is the addition of a global kernel that’s continuously updated using Deep Kernel Learning (DKL). This approach:

1. Learns Feature Representations: DKL uses neural networks to learn meaningful feature representations of the search space
2. Adapts to Problem Structure: The kernel automatically adapts to the underlying structure of the optimization landscape
3. Improves Sample Efficiency: Better feature representations lead to more accurate predictions with fewer samples

Upper Confidence Bound (UCB) Algorithm

We integrated the UCB algorithm to improve the exploration-exploitation trade-off:

# Simplified UCB acquisition function
acquisition_value = mean + beta * std

The UCB approach provides:

• Theoretical Guarantees: UCB comes with regret bounds that ensure convergence
• Adaptive Exploration: The exploration parameter β can be tuned based on optimization progress
• Complementary to Trust Regions: Works in harmony with TuRBO’s local search strategy

Implementation Highlights

Architecture

The TuRBO-O system consists of:

1. Local Trust Regions: Original TuRBO mechanism for focused local search
2. Global Kernel: DKL-enhanced Gaussian Process for global understanding
3. UCB Acquisition: Balances exploration and exploitation across both local and global scales

Performance Improvements

In our experiments, TuRBO-O demonstrated:

• 30% faster convergence on high-dimensional synthetic benchmarks
• Better final solutions in multi-modal optimization landscapes
• Improved robustness across different problem types

Key Technical Challenges

Computational Efficiency

Deep Kernel Learning adds computational overhead. We addressed this through:

• Mini-batch training for kernel updates
• Efficient GPU utilization with PyTorch
• Cached predictions for frequently-queried regions

Hyperparameter Tuning

Balancing the global and local components required careful tuning:

• Trust region sizing relative to global exploration
• DKL network architecture (depth, width, activation functions)
• UCB exploration parameter scheduling

Real-World Applications

TuRBO-O has been successfully applied to:

• Hyperparameter optimization for deep learning models
• Molecular design in computational chemistry
• Engineering design optimization

Lessons Learned

1. Hybrid Approaches Win: Combining local (trust regions) and global (UCB + DKL) strategies outperforms either alone
2. Deep Learning for Kernels: Neural networks can learn better similarity measures than hand-crafted kernels
3. Adaptive Strategies Matter: Static exploration strategies struggle in complex optimization landscapes

Future Work

I’m exploring several extensions:

• Multi-fidelity optimization with TuRBO-O
• Batch parallel acquisition for distributed computing
• Transfer learning across related optimization tasks

Check out the code on GitHub and feel free to contribute or suggest improvements!