Robust Control and Reinforcement Learning in Uncertain Systems with Partial Observations

Core Concepts

This paper presents a general framework for decision-making in uncertain systems with partially observed states. It introduces the notion of information states and approximate information states to facilitate computationally efficient control and provide a principled approach to reinforcement learning using partial observations.

Abstract

The paper investigates discrete-time decision-making problems in uncertain systems with partially observed states. It considers a non-stochastic model where uncontrolled disturbances take values in bounded sets with unknown distributions.
The key highlights are:

Introduction of the notion of information states, which can replace the agent's memory to compute an optimal control strategy through a dynamic program (DP).

Relaxation of the conditions for information states to define approximate information states, which can be learned from output data without knowledge of system dynamics.

Formulation of an approximate DP that computes a control strategy with a bounded performance loss compared to the optimal strategy.

Presentation of examples of approximate information states with corresponding theoretical guarantees on the approximation loss.

Illustration of the application of the results in control and reinforcement learning using numerical examples.

The paper provides a general framework to address decision-making under incomplete information, which is a fundamental problem in modern engineering applications involving cyber-physical systems. The non-stochastic approach used in the paper ensures robustness against worst-case disturbances, making it suitable for safety-critical applications.

Stats

The paper does not contain any explicit numerical data or statistics. It focuses on the theoretical development of the framework for decision-making in uncertain systems with partial observations.

Quotes

"We present a general framework for decision-making in such problems by using the notion of the information state and approximate information state, and introduce conditions to identify an uncertain variable that can be used to compute an optimal strategy through a dynamic program (DP)."
"Next, we relax these conditions and define approximate information states that can be learned from output data without knowledge of system dynamics. We use approximate information states to formulate a DP that yields a strategy with a bounded performance loss."

Key Insights Distilled From

Approximate Information States for Worst-Case Control and Learning in Uncertain Systems

by Aditya Dave,... at arxiv.org 04-09-2024

https://arxiv.org/pdf/2301.05089.pdf

Deeper Inquiries

How can the proposed framework be extended to handle time-varying or nonlinear system dynamics

To extend the proposed framework to handle time-varying or nonlinear system dynamics, we can incorporate adaptive techniques that update the information states and approximate value functions as the system evolves. This can involve using online learning algorithms to continuously update the approximate information states based on new observations and control actions. Additionally, we can introduce non-parametric or neural network-based approximations to capture the nonlinearities in the system dynamics. By adapting the framework to dynamically adjust to changes in the system behavior, we can effectively handle time-varying and nonlinear dynamics.

What are the potential challenges in applying the approximate information state approach to high-dimensional or continuous-state systems

Applying the approximate information state approach to high-dimensional or continuous-state systems may face several challenges. One major challenge is the curse of dimensionality, where the size of the state space grows exponentially with the number of dimensions, making it computationally expensive to maintain and update the information states. Additionally, ensuring the Lipschitz continuity of the approximate value functions in high-dimensional spaces can be challenging. Another issue is the scalability of the approach, as the complexity of the computations increases with the dimensionality of the system. Handling continuous-state systems also requires careful discretization or approximation techniques to represent the state space effectively while maintaining accuracy.

Can the ideas presented in this paper be adapted to address multi-agent decision-making problems in uncertain environments with partial observations

The ideas presented in the paper can be adapted to address multi-agent decision-making problems in uncertain environments with partial observations by extending the concept of information states to each agent in the system. Each agent can maintain its own information state based on its observations and actions, allowing them to make decisions independently while considering the interactions with other agents. By incorporating communication protocols or shared information among agents, the approximate information state approach can be used to coordinate decision-making strategies in a decentralized manner. Additionally, techniques from game theory and multi-agent reinforcement learning can be integrated to handle the complexities of interactions between multiple agents in uncertain environments.