Bayesian Optimization for High-Dimensional Resource Allocation
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Solution Overview
Problem
Existing optimization techniques struggle with high-dimensional resource allocation problems, often resulting in sub-optimal solutions due to local optima and the lack of explicit objective functions.
Innovation Solution
The implementation of Bayesian optimization with tailored local modeling, which evaluates initial candidates using an objective function and constraint functions, generates local models, and iteratively updates them to identify optimal resource allocations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional optimization techniques are used for high-dimensional resource allocation, then the problem can be solved with simple methods, but the solutions are sub-optimal due to local optima
Solution Approach 1:
The patent divides the high-dimensional search space into multiple low-dimensional subspaces by selecting different combinations of variables. Each subspace is optimized separately using Bayesian optimization, and the results are aggregated to find the global optimum. This segmentation allows the system to avoid local optima in the full high-dimensional space while maintaining computational feasibility.
Solution Approach 2:
The patent transforms the high-dimensional optimization problem into multiple low-dimensional problems by projecting the search space onto different subspaces. Each subspace optimization operates in a lower dimension, making the problem tractable while the aggregation of results across multiple subspaces recovers the global optimization objective.
2Ease of manufacture
If explicit objective functions are used, then optimization can be performed efficiently, but they are impossible to generate for complex resource allocation problems
Solution Approach 1:
The patent introduces an intermediary component (the objective function evaluator) that bridges the gap between complex resource allocation configurations and their performance metrics. This evaluator computes the objective function value by simulating the resource allocation scenario and measuring the outcome, allowing the optimization algorithm to work with implicit objectives without requiring explicit analytical formulations.
Solution Approach 2:
The system uses the resource allocation system itself to evaluate the objective function by actually performing the allocation and measuring the result. This self-service approach eliminates the need for separate explicit objective function definitions, as the system's own operation provides the evaluation metric needed for optimization.
3Reliability
If local models are updated iteratively, then optimal solutions can be found in high-dimensional spaces, but the computational cost increases
Solution Approach 1:
The patent segments the high-dimensional search space into multiple low-dimensional subspaces, each with its own local model. This segmentation reduces the computational burden of updating local models, as each model operates in a lower dimension. The system updates only the relevant local models for the current subspace being explored, rather than maintaining and updating a single model for the entire high-dimensional space.
Solution Approach 2:
The patent performs partial optimization by focusing on low-dimensional subspaces rather than attempting to optimize the entire high-dimensional space at once. This partial action approach finds sufficiently good solutions by exploring representative subspaces, trading off some global optimality for reduced computational cost and faster convergence.
Data Source
AI summary
A system optimizes an objective function by iteratively refining the objective function. The system evaluates an initial set of results for a set of initial candidates according to an objective function. The system generates a local model. The system identifies a plurality of new candidates. The system determines, for each new candidate, a prediction of whether the candidate violates a constraint. The system selects a new candidate based on the prediction for each of the candidates and updates the local model using the new candidate. The system identifies a potential optimal solution from the updated local model. The system distributes resources of a computing system according to the potential optimal solution.