Machine Learning

, Volume 85, Issue 3, pp 299-332

First online:

Model selection in reinforcement learning

  • Amir-massoud FarahmandAffiliated withDepartment of Computing Science, University of Alberta
  • , Csaba SzepesváriAffiliated withDepartment of Computing Science, University of Alberta Email author 


We consider the problem of model selection in the batch (offline, non-interactive) reinforcement learning setting when the goal is to find an action-value function with the smallest Bellman error among a countable set of candidates functions. We propose a complexity regularization-based model selection algorithm, \(\ensuremath{\mbox{\textsc {BErMin}}}\), and prove that it enjoys an oracle-like property: the estimator’s error differs from that of an oracle, who selects the candidate with the minimum Bellman error, by only a constant factor and a small remainder term that vanishes at a parametric rate as the number of samples increases. As an application, we consider a problem when the true action-value function belongs to an unknown member of a nested sequence of function spaces. We show that under some additional technical conditions \(\ensuremath{\mbox{\textsc {BErMin}}}\) leads to a procedure whose rate of convergence, up to a constant factor, matches that of an oracle who knows which of the nested function spaces the true action-value function belongs to, i.e., the procedure achieves adaptivity.


Reinforcement learning Model selection Complexity regularization Adaptivity Offline learning Off-policy learning Finite-sample bounds