Online Reinforcement Learning Control by Direct Heuristic Dynamic Programming: from Time-Driven to Event-Driven

TL;DR

This paper introduces an event-driven version of the direct heuristic dynamic programming algorithm for reinforcement learning control, reducing unnecessary updates caused by insignificant events and ensuring system stability.

Contribution

It proposes a novel event-driven dHDP algorithm with stability guarantees, improving upon traditional time-driven approaches in reinforcement learning control.

Findings

Proves system states and weights are bounded under the new algorithm.

Shows the approximate control approaches Bellman optimality within a finite bound.

Demonstrates the effectiveness of event-driven dHDP compared to time-driven dHDP.

Abstract

In this paper time-driven learning refers to the machine learning method that updates parameters in a prediction model continuously as new data arrives. Among existing approximate dynamic programming (ADP) and reinforcement learning (RL) algorithms, the direct heuristic dynamic programming (dHDP) has been shown an effective tool as demonstrated in solving several complex learning control problems. It continuously updates the control policy and the critic as system states continuously evolve. It is therefore desirable to prevent the time-driven dHDP from updating due to insignificant system event such as noise. Toward this goal, we propose a new event-driven dHDP. By constructing a Lyapunov function candidate, we prove the uniformly ultimately boundedness (UUB) of the system states and the weights in the critic and the control policy networks. Consequently we show the approximate control and cost-to-go function approaching Bellman optimality within a finite bound. We also illustrate how the event-driven dHDP algorithm works in comparison to the original time-driven dHDP.