Ensuring Feasibility in Constrained Reinforcement Learning: A Comprehensive Analysis

Core Concepts

Satisfying safety constraints is a critical challenge in solving optimal control problems. This paper proposes a comprehensive feasibility theory that applies to both model predictive control (MPC) and reinforcement learning (RL) by decoupling policy solving and implementation into virtual-time and real-time domains. The theory defines different types of feasibility, analyzes their containment relationships, and provides guidelines for designing virtual-time constraints to achieve the maximum feasible region.

Abstract

The paper addresses the feasibility problem in constrained optimal control problems, where the policy must satisfy safety constraints at every time step. It proposes a feasibility theory that applies to both MPC and RL by decoupling the problem into virtual-time and real-time domains.
The key insights are:

Initial feasibility describes whether a state can satisfy the virtual-time constraints at the current step, while endless feasibility describes whether all future states can satisfy the constraints.

The paper analyzes the containment relationships between different feasible regions, such as the initially feasible region (IFR), the endlessly feasible region (EFR), and the maximum EFR. This provides a tool for analyzing the feasibility of an arbitrary policy.

The paper introduces the concept of a feasibility function, which is a practical design tool for constructing virtual-time constraints that can achieve the maximum EFR. It reviews existing constraint formulations and shows they are applications of feasibility functions.

The paper demonstrates the feasibility theory through an emergency braking control example, visualizing the feasible regions under both MPC and RL policies.

Overall, the feasibility theory fills an important gap in the literature by providing a unified framework for analyzing feasibility in constrained optimal control for both MPC and RL.

Stats

Satisfying safety constraints is a priority concern when solving optimal control problems.
Due to the existence of infeasibility phenomenon, where a constraint-satisfying solution cannot be found, it is necessary to identify a feasible region before implementing a policy.
Existing feasibility theories built for model predictive control (MPC) only consider the feasibility of optimal policy, but reinforcement learning (RL) solves the optimal policy in an iterative manner, which comes with a series of non-optimal intermediate policies.

Quotes

"Feasibility analysis of these non-optimal policies is also necessary for iteratively improving constraint satisfaction; but that is not available under existing MPC feasibility theories."
"The basis of our theory is to decouple policy solving and implementation into two temporal domains: virtual-time domain and real-time domain."
"We further provide virtual-time constraint design rules along with a practical design tool called feasibility function that helps to achieve the maximum feasible region."

Key Insights Distilled From

The Feasibility of Constrained Reinforcement Learning Algorithms: A Tutorial Study

by Yujie Yang,Z... at arxiv.org 04-17-2024

https://arxiv.org/pdf/2404.10064.pdf

Deeper Inquiries

How can the proposed feasibility theory be extended to handle stochastic dynamics or partially observable environments

The proposed feasibility theory can be extended to handle stochastic dynamics or partially observable environments by incorporating probabilistic models and belief states into the analysis. In the case of stochastic dynamics, the feasibility function can be adapted to consider the uncertainty in state transitions and constraints. This may involve defining probabilistic constraints that capture the likelihood of satisfying constraints under different state transitions. Additionally, the concept of feasibility in partially observable environments can be addressed by incorporating belief states into the analysis. By considering the uncertainty in observations and inferring the underlying states, the feasibility theory can be extended to ensure that policies are feasible even in partially observable settings.

What are the potential limitations of the feasibility function approach, and how can it be improved to handle more complex constraint structures

One potential limitation of the feasibility function approach is its reliance on a single scalar value to represent feasibility. This may oversimplify the complexity of constraint structures, especially in cases where constraints are interdependent or have non-linear relationships. To improve the approach for handling more complex constraint structures, the feasibility function can be expanded to include multiple dimensions or vectors to capture the nuances of different constraints. By incorporating a more comprehensive representation of feasibility, the approach can better handle intricate constraint structures and provide a more accurate assessment of policy feasibility.

What are the implications of the feasibility theory for the design of safe exploration strategies in reinforcement learning

The feasibility theory has significant implications for the design of safe exploration strategies in reinforcement learning. By understanding the feasible regions of policies and the maximum feasible region, researchers can develop exploration strategies that prioritize safety while exploring the environment. Safe exploration strategies can leverage the knowledge of feasible regions to guide the exploration process towards states and actions that are more likely to lead to safe outcomes. This can help mitigate the risk of encountering infeasible states or violating constraints during the learning process, ultimately improving the safety and efficiency of reinforcement learning algorithms.