Approximate Control for Continuous-Time POMDPs: Decision-Making Framework for Partially Observable Systems

Основні поняття

The authors propose a scalable algorithm for solving continuous-time discrete-state space POMDPs by approximating the filtering distribution and separating the control problem, enabling effective decision-making in partially observable systems.

Анотація

This work introduces a decision-making framework for partially observable systems in continuous time with discrete state and action spaces. The authors employ approximation methods to scale well with increasing numbers of states, demonstrating effectiveness on various systems. They propose a new scalable algorithm that divides into two parts: approximating the filtering distribution and adapting a historical heuristic to continuous-time POMDPs.

The content discusses the challenges of partial observability in dynamical systems and presents Bayesian filtering as a solution. It explores optimal control strategies, historical settings, and modern deep learning techniques applied to discrete-time problems. The article highlights the limitations of existing approaches and proposes a novel method based on entropic matching for approximate inference in continuous-time POMDPs.

The experiments section evaluates the proposed method on queueing networks, predator-prey systems, and chemical reaction networks. It showcases the effectiveness of the approach through comparisons with benchmark methods like particle filters. Results demonstrate improved stability and performance in controlled trajectories compared to uncontrolled scenarios.

Статистика

X = {0, 1, ..., N}n where N = 1000
λ1, λ2 are constant arrival rates for packets in queues
Observation model uses Gaussian discrete-time measurements
Reward function favors empty queues

Цитати

"The stochastic filtering approach is especially appealing for controlling partially observed dynamical systems." - Content
"Many problems cannot be modeled using traditional approaches due to their unique characteristics." - Content

Ключові висновки, отримані з

Approximate Control for Continuous-Time POMDPs

by Yannick Eich... о arxiv.org 03-01-2024

https://arxiv.org/pdf/2402.01431.pdf

Глибші Запити

How can this scalable algorithm be adapted to other complex systems beyond those tested

The scalable algorithm proposed in the research can be adapted to other complex systems by adjusting the modeling and approximation techniques to suit the specific characteristics of the system. For instance, in systems with a larger state space or more intricate dynamics, one could explore different parametric families for approximating the filtering distribution or incorporate additional features into the value function approximation method. Additionally, incorporating domain-specific knowledge and constraints into the algorithm can enhance its performance in diverse applications. By customizing the algorithm's components based on the unique requirements of each system, it can be effectively applied to a wide range of complex systems beyond those tested.

What are potential drawbacks or limitations of using approximation methods in decision-making frameworks

While approximation methods offer scalability and efficiency benefits in decision-making frameworks for large-scale problems, they also come with potential drawbacks and limitations. One limitation is that approximations may introduce errors or inaccuracies compared to exact solutions, leading to suboptimal decisions under certain conditions. Additionally, depending on how well-suited the chosen parametric family is for representing complex distributions accurately, there may be challenges in capturing all nuances of the underlying system dynamics. Another drawback is that some approximation methods may require tuning hyperparameters or assumptions that could impact their effectiveness across different scenarios. It's essential to carefully consider these limitations when applying approximation methods in decision-making frameworks.

How can insights from this research be applied to real-world applications outside of engineering

Insights from this research can be applied to real-world applications outside of engineering by leveraging similar principles and methodologies for decision-making under uncertainty. For example:

Finance: The algorithms developed for partially observable systems could be utilized in financial markets for making trading decisions based on noisy data.
Healthcare: Similar approaches could assist healthcare providers in optimizing treatment plans by considering uncertain patient outcomes.
Supply Chain Management: Decision-making frameworks inspired by this research could help optimize inventory management strategies under uncertain demand patterns.
Environmental Monitoring: Applying these insights could improve resource allocation decisions related to environmental monitoring and conservation efforts.
By adapting concepts such as Bayesian filtering, optimal control theory, and approximate inference techniques from this research, various industries can benefit from more effective decision-making processes amidst uncertainty and complexity.