AI Agent Risk-Sensitive Decisions Using Sigma-Algebra Probability Spaces
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Solution Overview
Problem
Traditional decision-making models, particularly those based on expected utility theory, fail to explicitly incorporate risk attitude, leading to suboptimal decisions in uncertain and risky situations.
Innovation Solution
A machine learning system that employs risk-sensitive utility functions and a specification of the probability space, using a sigma algebra to account for risk preferences, allowing AI agents to make more informed decisions by balancing utility values and risk parameters.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If traditional expected utility theory is used for decision-making, then the model is simple and computationally efficient, but it fails to explicitly incorporate risk attitude leading to suboptimal decisions
Solution Approach 1:
The patent introduces a risk parameter θ that modifies the utility function to explicitly incorporate risk attitude. The transformed utility function U_θ(x) = θ * u(x) + (1-θ) * v(x) combines the original utility function u(x) with a risk-adjusted version v(x), allowing the system to adapt to different risk preferences while maintaining the overall decision-making framework
Solution Approach 2:
The patent makes the utility function dynamic by allowing the risk parameter θ to vary based on the decision context, state, and available information. This enables the AI agent to adjust its risk sensitivity dynamically rather than using a fixed risk attitude, thereby improving decision reliability across different scenarios
2Ease of operation
If risk factors are eliminated through iterated expectations, then the optimization problem becomes simpler, but the model cannot capture risk-averse or risk-seeking behavior
Solution Approach 1:
The patent extracts the risk attitude component from the general decision-making process by introducing a separate risk parameter θ that can be independently adjusted. This allows the system to maintain simple optimization while separately modeling risk preferences through the transformed utility function that incorporates both expected utility and risk-adjusted utility
3Measurement precision
If the probability space is fully specified using sigma algebra, then the model accurately represents uncertainty, but the computational complexity increases
Solution Approach 1:
The patent applies partial action by specifying the probability space only for the relevant events and outcomes that affect the decision, rather than fully enumerating all possible events in the sigma algebra. The system calculates expected utility and risk-adjusted utility for the specific outcomes of interest, avoiding the computational burden of processing the entire probability space
Data Source
AI summary
In an example, a method for decision-making by an Artificial Intelligence (AI) agent based on risk attitude includes processing an explored state space of an environment to identify one or more potential outcomes for each of a plurality of potential decisions; assigning, based on a utility function, a utility value to each of the one or more potential outcomes for each of the plurality of potential decisions, wherein the utility function depends on a risk parameter indicative of a specified risk preference of the AI agent; determining, based on a predefined sigma algebra defining a set of events that may occur in the environment, a probability of each of the one or more potential outcomes occurring for each of the plurality of potential decisions; selecting a decision from the plurality of potential decisions based on the utility values and the probabilities; and outputting an indication of the decision.