Online Probabilistic Inverse Optimization for 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 fashion, particularly in complex scenarios like employee scheduling, where data and parameters change over time, and existing methods are limited by linear assumptions and lack flexibility in handling noisy data and suboptimal solutions.
Innovation Solution
An online probabilistic inverse optimization system that employs machine learning techniques to infer objectives and constraints in a probabilistic framework, treating the inverse optimization problem as a maximum likelihood problem, allowing for flexible adaptation to changing data and decisions, and using KKT and dualization concepts to refine the learning process.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If standard inverse optimization techniques are used, then objectives can be recovered from agent decisions, but the techniques cannot handle time-varying optimization problems where data and parameters change over time
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 processes streaming data sequentially and adapts the recovered objectives in real-time, making the technique capable of handling time-varying optimization problems while maintaining reliability through probabilistic modeling.
Solution Approach 2:
The patent changes the parameter representation from fixed linear weights to probabilistic distributions that evolve over time. By modeling objective parameters as random variables with time-varying distributions, the system can capture the dynamic nature of optimization problems while providing statistically sound objective recovery.
2Ease of manufacture
If linear objective assumptions are made, then the inverse optimization problem becomes computationally tractable, but the approach lacks flexibility in handling noisy data and suboptimal solutions
Solution Approach 1:
The patent replaces the deterministic mechanical optimization framework with a probabilistic learning framework. Instead of directly solving for linear weights through algebraic methods, the system uses probabilistic inference and statistical learning techniques that naturally handle noise and uncertainty while remaining computationally tractable through efficient algorithms.
Solution Approach 2:
The patent introduces probabilistic models as an intermediary layer between the observed decisions and the underlying objectives. This intermediary probabilistic framework allows the system to handle noisy and suboptimal data by modeling the uncertainty in the decision-making process, while still enabling efficient computation through probabilistic inference algorithms.
3Productivity
If existing inverse optimization methods are applied, then single-objective problems can be solved, but simultaneous learning of multiple objectives and constraints is not achieved
Solution Approach 1:
The patent merges the learning of multiple objectives and constraints into a unified probabilistic framework. By combining multiple objective functions and constraint conditions into a single probabilistic model that processes all information simultaneously, the system achieves efficient simultaneous learning without requiring separate processing for each objective or constraint.
Solution Approach 2:
The patent creates a universal probabilistic learning framework that can handle multiple objectives, constraints, and time-varying conditions through a single integrated system. This multi-functional approach allows the same framework to recover various types of optimization parameters (objectives, constraints, weights) simultaneously, improving productivity while managing complexity through unified modeling.
Data Source
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.