Continuous Inverse Optimal Control with Locally Optimal Examples (1206.4617v1)

Abstract: Inverse optimal control, also known as inverse reinforcement learning, is the problem of recovering an unknown reward function in a Markov decision process from expert demonstrations of the optimal policy. We introduce a probabilistic inverse optimal control algorithm that scales gracefully with task dimensionality, and is suitable for large, continuous domains where even computing a full policy is impractical. By using a local approximation of the reward function, our method can also drop the assumption that the demonstrations are globally optimal, requiring only local optimality. This allows it to learn from examples that are unsuitable for prior methods.

• The paper introduces a novel probabilistic IOC algorithm that leverages locally optimal demonstrations to efficiently recover unknown reward functions.
• By using a Laplace approximation, the method scales to high-dimensional continuous domains without requiring full policy computations.
• Experimental results in robotic and simulated driving tasks showcase superior performance over traditional IOC methods with suboptimal expert trajectories.

Overview of Continuous Inverse Optimal Control with Locally Optimal Examples

The paper "Continuous Inverse Optimal Control with Locally Optimal Examples" presents a novel approach in the area of Inverse Optimal Control (IOC), also referred to as Inverse Reinforcement Learning (IRL). It addresses the computational challenges involved in recovering unknown reward functions from expert demonstrations within continuous and high-dimensional Markov Decision Processes (MDPs). The introduced method, which departs from the global optimality assumption prevalent in prior IOC algorithms, demonstrates efficacy even when expert trajectories are only locally optimal.

The authors propose a probabilistic IOC algorithm that scales efficiently with task dimensionality and is particularly suitable for continuous domains, where a full policy computation is often infeasible. Unlike conventional approaches that necessitate the trajectory to manifest global optimality, this algorithm leverages a local approximation to relax this assumption. Consequently, it facilitates learning from locally optimal demonstrations that are otherwise inadequate for existing methods.

Key Contributions

The primary contributions are encapsulated in the algorithmic design that optimizes the likelihood of achieving expert-like trajectories across different parameterized reward functions. The paper outlines the following advancements:

• Local Optimality: By reallocating focus from global to local optimality, the presented method can utilize demonstrations that are not globally optimal, thereby expanding the dataset applicable for learning.
• Scalability and Efficiency: The use of a Laplace approximation circumvents the need to repeatedly solve complex forward control problems, leading to a computationally efficient method suitable for high-dimensional state spaces.

• Flexible Reward Representations: Two variants of the algorithm are introduced:

  1. Linear Reward Learning: Involves learning reward functions as linear combinations of provided features.
  2. Nonlinear Reward Learning: Employs Gaussian Processes to capture nonlinear dependencies within the reward functions.

Numerical Results and Implications

The paper demonstrates through experiments on tasks, such as robotic arm control and simulated driving, that the algorithm successfully reconstructs reward functions from locally optimal examples. The linear variant shows proficiency when features form a suitable linear basis, while the nonlinear variant excels without such basis, illustrating the versatility and robustness of the approach.

Significant numerical results highlight the approach's efficiency and its ability to retain accuracy in high dimensions. Notably, the method exhibits superior performance compared to MaxEnt and OptV when the expert demonstrations lack global optimality. These findings suggest practical applications in domains where human experts might provide suboptimal trajectories or in situations where computational simplicity and efficiency are paramount.

Future Directions

The relaxation of global optimality constraints hints at broader future applications across more complex continuous control tasks. Further research could explore integrating this approach with more sophisticated feature construction methodologies that inherently provide better generalization across state spaces. Additionally, extending the algorithm to stochastic environments or infinite-horizon problems could enrich its applicability.

The paper serves as a notable step forward in IOC research, offering a potentially transformative tool for real-world scenarios where only locally optimal human demonstrations are available. Embracing local information without incurring substantial computational overhead establishes a solid foundation for subsequent innovations in control and learning systems.