Model-Based Reinforcement Learning with Value-Targeted Regression

This paper studies model-based reinforcement learning (RL) for regret minimization. We focus on finite-horizon episodic RL where the transition model P belongs to a known family of models P, a special case of which is when models in P take the form of linear mixtures: Pθ = Pd i=1 θiPi . We propose a model based RL algorithm that is based on the optimism principle: In each episode, the set of models that are ‘consistent’ with the data collected is constructed. The criterion of consistency is based on the total squared error that the model incurs on the task of predicting state values as determined by the last value estimate along the transitions. The next value function is then chosen by solving the optimistic planning problem with the constructed set of models. We derive a bound on the regret, which, in the special case of linear mixtures, takes the form O˜(d √ H3T), where H, T and d are the horizon, the total number of steps and the dimension of θ, respectively. In particular, this regret bound is independent of the total number of states or actions, and is close to a lower bound Ω(√ HdT). For a general model family P, the regret bound is derived based on the Eluder dimension.

Acknowledgements
Csaba Szepesvari gratefully acknowledges funding from ´ the Canada CIFAR AI Chairs Program, Amii and NSERC. Mengdi Wang gratefully acknowledges funding from the U.S. National Science Foundation (NSF) grant CMMI1653435, Air Force Office of Scientific Research (AFOSR) grant FA9550-19-1-020, and C3.ai DTI.