Inverse Reinforcement Learning via Wasserstein Distance Minimization
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Solution Overview
Problem
Existing inverse reinforcement learning methods, such as Maximum Entropy Inverse Reinforcement Learning (ME-IRL) and Guided Cost Learning (GCL), face difficulties in calculating the sum of rewards for all trajectories, especially in combinatorial optimization problems where setting the sampling distribution is challenging, leading to indefiniteness issues.
Innovation Solution
A learning device and method that estimates a trajectory minimizing the Wasserstein distance between expert and reward function distributions, updating the reward function parameters to maximize the log-likelihood of a Boltzmann distribution by subtracting an entropy regularization term from the Wasserstein distance, ensuring the reward function satisfies the Lipschitz continuity condition.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If Maximum Entropy Inverse Reinforcement Learning (ME-IRL) is used to learn the reward function by maximizing log-likelihood, then the indefiniteness of multiple reward functions is resolved, but it becomes necessary to calculate the sum of rewards for all possible trajectories which is computationally difficult
Solution Approach 1:
The patent applies partial action by replacing the intractable sum over all trajectories with a tractable lower bound computation. Instead of calculating the exact log-likelihood which requires summing rewards across all possible trajectories, the invention computes a lower bound using only the maximum reward trajectory, making the computation feasible while preserving the essential learning objective
Solution Approach 2:
The patent transforms the objective function by changing from maximizing the exact log-likelihood to maximizing a lower bound of the log-likelihood. This parameter change in the optimization objective enables computational tractability by replacing the intractable partition function with a computationally manageable expression involving only the maximum reward path
2Device complexity
If Guided Cost Learning (GCL) is used to approximate the sum of rewards by weighted sampling, then computational complexity is reduced, but it requires assuming a sampling distribution which is not known for combinatorial optimization problems
Solution Approach 1:
The patent extracts the essential component needed for computation by removing the requirement for a sampling distribution assumption. Instead of using GCL's weighted sampling approach which depends on knowing the data distribution, the invention extracts only the maximum reward trajectory information needed to compute the lower bound, eliminating the need for distributional assumptions
Solution Approach 2:
The patent segments the intractable sum over all trajectories into two parts: the maximum reward trajectory (which can be computed) and the rest (which is omitted in the lower bound). This segmentation allows the method to focus computational resources on the most informative portion of the trajectory space without requiring knowledge of the complete distribution
3Measurement precision
If the reward function parameters are updated to maximize the exact log-likelihood, then the learning accuracy is improved, but the computational burden increases significantly due to the need to calculate all trajectory rewards
Solution Approach 1:
The patent applies partial action by computing only the necessary portion of the log-likelihood (the lower bound based on maximum reward trajectories) rather than the complete log-likelihood requiring all trajectories. This reduces training time significantly while maintaining sufficient learning accuracy for practical applications
Data Source
AI summary
The function input means 91 accepts input of a reward function whose feature is set to satisfy Lipschitz continuity condition. The estimation means 92 estimates a trajectory that minimizes Wasserstein distance, which represents distance between a probability distribution of a trajectory of an expert and a probability distribution of a trajectory determined based on a parameter of the reward function. The updating means 93 updates, based on the estimated trajectory, the parameter of the reward function to maximize the log-likelihood of Boltzmann distribution derived from a principle of a maximum entropy.