Accelerated Point-Wise Maximum Approach to Approximate Dynamic Programming

Abstract

We describe an approximate dynamic programming approach to compute lower bounds on the optimal value function for a discrete time, continuous space, infinite horizon setting. The approach iteratively constructs a family of lower bounding approximate value functions by using the so-called Bellman inequality. The novelty of our approach is that, at each iteration, we aim to compute an approximate value function that maximizes the point-wise maximum taken with the family of approximate value functions computed thus far. This leads to a non-convex objective, and we propose a gradient ascent algorithm to find stationary points by solving a sequence of convex optimization problems. We provide convergence guarantees for our algorithm and an interpretation for how the gradient computation relates to the state-relevance weighting parameter appearing in related approximate dynamic programming approaches. We demonstrate through numerical examples that, when compared to existing approaches, the algorithm we propose computes tighter suboptimality bounds with comparable computation time.

A Mode of Intelligent Equipment Monitoring Optimization Based on Dynamic Programming Algorithm

“…The integration of intelligent equipment and modern technology not only enhances the intelligence of monitoring but also realizes its own function optimization. Continuous and dynamic intelligent equipment monitoring and analysis of the public can help the government make health decisions and improve the disease resistance and physical quality of the public Beuchat et al [ 2 ]. In the past, the public monitoring method was mainly planning algorithm.…”