Inverse Reinforcement Learning for Combinatorial Optimization
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Solution Overview
Problem
Inverse Reinforcement Learning struggles to be applied effectively to combinatorial optimization problems due to difficulties in setting up probability distributions and calculating reward sums, especially in discrete value scenarios like routing and scheduling problems.
Innovation Solution
A learning device and method that uses a reward function with features satisfying the Lipschitz continuity condition, estimating a trajectory that minimizes the Wasserstein distance between expert and optimized trajectories, and updates parameters to maximize this distance using the non-expansive mapping gradient method.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If probability distributions are used to define differences between expert and optimized trajectories in Inverse Reinforcement Learning, then the reward function can be learned through gradient methods, but it becomes difficult to apply to combinatorial optimization problems with discrete values
Solution Approach 1:
The patent changes the distance metric parameter from probabilistic distances (KL divergence, JS divergence) to Wasserstein distance, which operates on value functions rather than probability distributions. This parameter change enables application to combinatorial optimization problems with discrete values while maintaining the ability to learn reward functions through gradient-based optimization.
2Productivity
If the reward function parameters are updated using gradient methods, then the learning process can be optimized, but it becomes difficult to handle combinatorial optimization problems where probability distributions cannot be easily set up
Solution Approach 1:
The patent introduces the value function as an intermediary between the reward function and the trajectory evaluation. Instead of directly comparing probability distributions, the Wasserstein distance operates on value functions, which can be computed for combinatorial optimization problems. This intermediary enables gradient-based learning while accommodating discrete value scenarios.
3Measurement precision
If KL divergence or JS divergence is used to measure trajectory differences, then the reward function can be learned through standard gradient methods, but the method cannot be applied to problems with discrete values like routing and scheduling
Solution Approach 1:
The patent changes the measurement parameter from probabilistic distances (which require continuous probability distributions) to Wasserstein distance (which operates on value functions). This parameter change maintains measurement precision while extending versatility to include combinatorial optimization problems with discrete values such as routing and scheduling problems.
Data Source
AI summary
A function input means 91 accepts input of a reward function whose features are set to satisfy a Lipschitz continuity condition. An estimation means 92 estimates a trajectory that minimizes Wasserstein distance, which represents distance between probability distribution of a trajectory of an expert and probability distribution of a trajectory determined based on parameters of the reward function. An update means 93 updates the parameters of the reward function to maximize the Wasserstein distance based on the estimated trajectory.