Probabilistic Inverse Optimization for Noisy Time-Varying Decisions

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Solution Overview

Problem

Existing inverse optimization techniques struggle to handle time-varying optimization problems and recover both objectives and constraints in an online manner, particularly in complex decision-making scenarios like nurse scheduling, where data quality and agent decisions are noisy and time-dependent.

Innovation Solution

An online probabilistic inverse optimization system that infers objectives and constraints using machine learning techniques, treating the problem as a maximum likelihood estimation, allowing for flexible adaptation to changing data and agent decisions.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Adaptability or versatility

If standard inverse optimization techniques are used to recover objectives from agent decisions, then the objectives can be obtained, but the techniques cannot handle time-varying optimization problems where data and parameters change over time

Engineering Contradiction:

Improveability to handle time-varying problemsVSAvoidaccuracy of objective recovery

Core Design Contradiction:

Adaptability or versatilityVSReliability

Solution Approach 1:

The patent transforms the static inverse optimization problem into a dynamic online learning framework where objectives are continuously updated as new data arrives. The system adapts to time-varying problems by processing sequential observations and updating objective estimates in real-time, making the recovery process dynamic rather than static.

Inventive Principle:

Principle #15Dynamics

Solution Approach 2:

The patent incorporates feedback mechanisms where the system continuously observes agent decisions and problem data changes, then uses this feedback to refine and update the recovered objectives. This iterative feedback loop enables the system to adapt to changing conditions while maintaining accuracy in objective recovery.

Inventive Principle:

Principle #23Feedback

2Adaptability or versatility

If online learning is used to adapt to changing data, then the system can handle time-varying problems, but the presence of noisy data and suboptimal agent decisions reduces measurement precision

Engineering Contradiction:

Improveonline adaptation capabilityVSAvoidaccuracy of objective estimation

Core Design Contradiction:

Adaptability or versatilityVSMeasurement precision

Solution Approach 1:

The patent employs probabilistic models that treat individual observations as temporary, low-cost data points that contribute to the overall estimation without requiring perfect accuracy. Each noisy observation is processed probabilistically, allowing the system to tolerate suboptimal decisions and noisy data while still converging to accurate objective estimates through aggregation of many such observations.

Inventive Principle:

Principle #27Cheap short-living objects (Disposable)

Solution Approach 2:

The patent uses probabilistic parameter estimation where the objectives are represented as probability distributions rather than fixed values. This allows the system to incorporate uncertainty from noisy data and suboptimal decisions, gradually refining the parameter estimates as more data becomes available, thus maintaining measurement precision despite online adaptation requirements.

Inventive Principle:

Principle #35Parameter changes

3Adaptability or versatility

If multiple objectives and constraints are recovered simultaneously, then the system can capture complex agent behavior, but the device complexity and computational requirements increase

Engineering Contradiction:

Improvecapability to recover multiple objectives and constraintsVSAvoidsystem complexity

Core Design Contradiction:

Adaptability or versatilityVSDevice complexity

Solution Approach 1:

The patent segments the complex task of recovering multiple objectives and constraints into separate, manageable components. The system processes different types of information (objectives, constraints, parameters) through distinct but coordinated learning mechanisms, reducing the overall system complexity while maintaining the capability to recover all elements simultaneously.

Inventive Principle:

Principle #1Segmentation

Solution Approach 2:

The patent employs a unified probabilistic learning framework that serves multiple functions: it recovers objectives, constraints, and parameters simultaneously using the same underlying mathematical structure. This universal approach reduces device complexity by avoiding the need for separate specialized systems for each recovery task.

Inventive Principle:

Principle #6Universality (Multi-functionality)

Data Source

PatentUS12524682B2Online probabilistic inverse optimization system for decision making, online probabilistic inverse optimization method for decision making, and online probabilistic inverse optimization program for decision making

Publication Date: 2026.01.13 NEC CORP

AI summary

An online probabilistic inverse optimization system 10 is proposed for inferring objectives and constraints in an online fashion from changing problem data and corresponding agent decisions. The online probabilistic inverse optimization system 10 includes: a computing unit 11 which computes optimal solutions or decisions based on the forward optimization problem using the problem data that may include objectives, constraints and parameters; and a solving unit 12 which solves the inverse optimization problem using the agent decisions.