Uncomputable Oracle Optimizer

Video Demonstration

Overview

The Uncomputable Oracle Optimizer is a groundbreaking framework that addresses a fundamental challenge in optimization: what happens when computation itself is uncertain? Traditional optimization assumes that evaluating f(x) always returns a value, but in reality, some computations might take too long to complete, never finish, or have varying computation times.

This project combines concepts from computability theory, Bayesian optimization, and risk-aware decision making to create an intelligent optimizer that can navigate the delicate balance between seeking valuable insights and avoiding computational dead-ends.

Key Features

• Risk-Aware Bayesian Optimization: Combines traditional Bayesian optimization with computational risk assessment
• Gaussian Process Models: Uses probabilistic models to learn both the objective function and computation success probability
• Visualization Tools: Rich visualization of the optimization process and model beliefs
• Educational Focus: Designed to be both practical and educational, with detailed documentation and examples

Technical Details

Phase 1: Simulating Computational Uncertainty

• Creating an oracle that may or may not return values
• Modeling halting probability
• Handling timeouts and penalties

Phase 2: Building Probabilistic Surrogate Models

• Gaussian Process Regression for objective function
• Gaussian Process Classification for halting probability
• Uncertainty quantification

Phase 3: Making Risk-Aware Decisions

• Expected Improvement with halting probability
• Balancing exploration and exploitation
• Risk-aware acquisition functions

Phase 4: The Optimization Loop

• Iterative optimization process
• Visualization and analysis
• Real-world applications