Constrained Hyperparameter Optimization via Bayesian Entropy Search
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Solution Overview
Problem
Optimizing hyperparameters for machine learning models, especially large neural networks, is challenging due to the need to minimize validation error while meeting execution latency constraints, as existing methods are costly and inefficient in handling constraints and black-box functions.
Innovation Solution
The implementation of Constrained Maximum Value Entropy Search (cMES) for Bayesian optimization, which uses probabilistic models and acquisition functions to automatically determine optimal hyperparameters by balancing exploration and exploitation, and handling both real-valued and binary constraints through independent Gaussian process priors and expectation propagation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional hyperparameter optimization methods are used, then the validation error can be minimized, but the number of costly evaluations increases and execution latency constraints cannot be effectively met
Solution Approach 1:
The patent introduces probabilistic models (Gaussian processes) as intermediaries to approximate the black-box validation error function and constraint functions. These probabilistic models serve as mediators between the hyperparameter space and the costly validation evaluations, enabling the optimizer to predict performance and constraints without repeatedly invoking expensive training validations. This intermediary layer reduces the number of actual evaluations needed while maintaining optimization accuracy.
Solution Approach 2:
The patent replaces the mechanical trial-and-error evaluation process with a probabilistic inference system. Instead of mechanically testing each hyperparameter configuration through costly training validations, the system uses probabilistic models to infer the likely performance and constraint satisfaction, substituting the mechanical evaluation system with a computational inference system that is much faster and more efficient.
2Measurement precision
If black-box validation error functions are used, then model accuracy can be optimized, but the optimization process becomes intractable under execution latency constraints
Solution Approach 1:
The patent transforms the intractable black-box optimization problem into a tractable probabilistic inference problem by changing the representation parameters. Instead of directly optimizing the black-box validation error function, the system parameterizes the problem using probabilistic models with specific distribution assumptions (Gaussian processes), which enable analytical solutions and efficient computation even under constraints. This parameter transformation makes the optimization process tractable while preserving the ability to measure validation error accurately.
3Ease of operation
If conventional optimization methods are used, then hyperparameter tuning can be performed, but they fail to efficiently handle both real-valued and binary constraints simultaneously
Solution Approach 1:
The patent creates a universal constrained optimization framework that can handle both real-valued constraints (e.g., execution latency) and binary constraints (e.g., feasibility indicators) through the same probabilistic model structure. The Gaussian process framework provides multi-functionality by accommodating different constraint types within a unified mathematical formulation, enabling the optimizer to simultaneously consider multiple constraint types without requiring separate specialized methods for each constraint category.
Data Source
AI summary
Hyperparameters for tuning a machine learning system may be optimized using Bayesian optimization with constraints. The hyperparameter optimization may be performed for a received training set and received constraints. Respective probabilistic models for the machine learning system and constraint functions may be initialized, then hyperparameter optimization may include iteratively identifying respective values for hyperparameters using analysis of the respective models performed using an acquisition function implementing entropy search on the respective models, training the machine learning system using the identified values to determine measures of accuracy and constraint metrics, and updating the respective models using the determined measures.