Bayesian Optimization Using Risk-Averse Acquisition Functions
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Solution Overview
Problem
Existing Bayesian optimization methods, such as Gaussian process optimization, often focus on expected value, which may not adequately capture robustness or risk characteristics, leading to inefficient search processes when optimizing risk aversion indices like Conditional Value-at-Risk (CVaR).
Innovation Solution
The proposed solution involves an information processing device that estimates risk aversion indices using a kernel function and observation history, calculates an acquisition function, and searches for a target point based on this function to improve search efficiency, employing kernel mean embedding to model probability distributions and optimize CVaR.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If expected value optimization is used in Bayesian optimization, then the optimization process is simple and straightforward, but it fails to capture robustness or risk characteristics adequately
Solution Approach 1:
The patent transforms the optimization objective from expected value to risk aversion index (CVaR) by changing the parameter being optimized. This allows the system to capture risk characteristics while maintaining the Bayesian optimization framework, resolving the contradiction between simplicity and reliability.
Solution Approach 2:
The patent introduces an acquisition function as an intermediary between the observed values and the optimization decision. This acquisition function incorporates risk aversion indices to guide the selection of next observation points, enabling robust optimization without fundamentally changing the Bayesian optimization process.
2Reliability
If risk aversion index optimization is implemented, then robustness and risk characteristics are captured accurately, but the search process becomes less efficient
Solution Approach 1:
The patent implements feedback by using the risk aversion index to update the acquisition function, which in turn guides the selection of next observation points. This feedback mechanism ensures that the optimization process efficiently explores regions of the search space that are relevant to risk characteristics, improving search efficiency while maintaining reliability.
3Ease of operation
If traditional acquisition functions are used, then the selection of next observation points is straightforward, but points that balance expected value and uncertainty are not effectively selected
Solution Approach 1:
The patent creates a composite acquisition function that combines multiple components: expected value, uncertainty (variance), and risk aversion index. This composite function effectively balances exploration and exploitation, selecting observation points that optimize both expected value and uncertainty while maintaining ease of operation within the Bayesian optimization framework.
Data Source
AI summary
A non-transitory computer-readable recording medium stores a program for causing a computer to execute a process, the process includes obtaining an estimated value of a risk aversion index for each of a plurality of candidate points in a search space based on a kernel function and an observation history including one or a plurality of observation points and an observed value of a random variable for each of the one or the plurality of observation points, obtaining a value of an acquisition function for each of the plurality of candidate points based on the estimated value of the risk aversion index, searching for a target point corresponding to a predetermined value of the acquisition function from among the plurality of candidate points based on the value of the acquisition function, and outputting a search result including the target point.