OptimizedDP: An Efficient, User-friendly Library For Optimal Control and Dynamic Programming (2204.05520v1)

Abstract: This paper introduces OptimizedDP, a high-performance software library that solves time-dependent Hamilton-Jacobi partial differential equation (PDE), computes backward reachable sets with application in robotics, and contains value iterations algorithm implementation for continuous action-state space Markov Decision Process (MDP) while leveraging user-friendliness of Python for different problem specifications without sacrificing efficiency of the core computation. These algorithms are all based on dynamic programming, and hence can both be challenging to implement and have bad execution runtime due to the large high-dimensional tabular arrays. Although there are existing toolboxes for level set methods that are used to solve the HJ PDE, our toolbox makes solving the PDE at higher dimensions possible as well as having an order of magnitude improvement in execution times compared to other toolboxes while keeping the interface easy to specify different dynamical systems description. Our toolbox is available online at https://github.com/SFU-MARS/optimized_dp.

• The paper presents advanced dynamic programming algorithms that enable rapid computation of Hamilton-Jacobi PDEs and backward reachable sets.
• The paper details a dual-layer architecture that separates user-friendly Python interfaces from high-performance HeteroCL-based computation.
• The paper demonstrates up to 75x runtime improvements, efficiently processing systems up to six dimensions for real-time optimal control.

Overview of "OptimizedDP: An Efficient, User-friendly Library For Optimal Control and Dynamic Programming"

The paper presents OptimizedDP, a sophisticated software library designed to enhance computational efficiency and user accessibility in solving time-dependent Hamilton-Jacobi (HJ) partial differential equations (PDEs) and conducting reachability analysis essential for robotics and other domains. The library leverages dynamic programming techniques to operate on continuous action-state spaces within Markov Decision Processes (MDPs). Despite previous challenges associated with high-dimensional tabular computations in dynamic programming, OptimizedDP manages to offer significant efficiency improvements, maintaining Python's ease of use.

Key Contributions and Methodology

This research introduces a toolbox capable of handling the numerical challenges inherent in solving the Hamilton-Jacobi PDEs and conducting MDP value iteration. It significantly reduces the runtime compared to existing MATLAB-based tools like ToolboxLS and HelperOC, and C++/CUDA-based tools such as BEACLS.

1. Dynamic Programming Algorithms: The paper details the algorithms embedded in the library—value iteration for continuous state and action spaces and level-set methods for solving HJ PDEs. Both play a crucial role in autonomy by providing backward reachable sets (BRS) and tubes (BRT) for complex dynamical systems, thus ensuring safety and optimal control behavior over time.
2. Software Architecture: The toolbox separates the user interface from the computational backend, the latter being implemented using HeteroCL, a domain-specific language. This separation ensures that while the core operations are optimized for speed, end-users can define problem specifications in Python, a more accessible language.
3. Performance Improvements: OptimizedDP demonstrates substantial execution time reductions, especially as problem dimensionality increases. This is attributed to efficient memory management practices and parallelization techniques inherent to HeteroCL. The library efficiently processes up to six-dimensional dynamical systems—a notable feat given the computational demands.
4. User-centric Design: While maintaining computational efficiency, the library remains user-friendly, allowing researchers to define system dynamics and problem parameters with ease. This is crucial for prototyping in research that involves varied dynamical models.

Empirical Results

Empirical evaluations reveal that OptimizedDP outperforms existing toolboxes by a factor of up to 75 in runtime efficiency. For instance, the library computes a three-dimensional system in less than a second, a task that takes MATLAB-based tools considerably longer. Moreover, for six-dimensional systems, which are infeasible in some traditional environments, OptimizedDP successfully completes execution within a day.

Implications and Future Directions

The introduction of OptimizedDP has significant implications for the field of robotics, specifically in advancing the real-time capabilities of autonomous systems. By drastically reducing computational overhead, the library enables the integration of sophisticated control algorithms in practical applications.

Theoretically, the library underscores the potential for further optimization in dynamic programming techniques, suggesting a path towards handling even higher-dimensional systems. Future work could focus on expanding the toolbox's capabilities, incorporating more advanced algorithmic techniques, and extending support for additional numerical schemes.

Overall, this paper contributes a valuable resource to the community, paving the way for more robust and practical implementations of dynamic programming in AI research and applications.