Performance guarantees for model-based Approximate Dynamic Programming in continuous spaces
For researchers in reinforcement learning and control, this work offers theoretical guarantees and computational improvements for linear programming approaches to dynamic programming in continuous spaces.
The paper provides performance guarantees for model-based Approximate Dynamic Programming in continuous spaces, including fitting error and online policy performance, and introduces a condition to simplify the Q-function formulation for improved computational efficiency.
We study both the value function and Q-function formulation of the Linear Programming approach to Approximate Dynamic Programming. The approach is model-based and optimizes over a restricted function space to approximate the value function or Q-function. Working in the discrete time, continuous space setting, we provide guarantees for the fitting error and online performance of the policy. In particular, the online performance guarantee is obtained by analyzing an iterated version of the greedy policy, and the fitting error guarantee by analyzing an iterated version of the Bellman inequality. These guarantees complement the existing bounds that appear in the literature. The Q-function formulation offers benefits, for example, in decentralized controller design, however it can lead to computationally demanding optimization problems. To alleviate this drawback, we provide a condition that simplifies the formulation, resulting in improved computational times.