On-line Learning in Tree MDPs by Treating Policies as Bandit Arms

ArXi:2605.04979v1 Announce Type: new A Tree Marko Decision Problem (T-MDP) is a finite-horizon MDP with a starting state $s_{1}$, in which every state is reachable from $s_{1}$ through exactly one state-action trajectory. T-MDPs arise naturally as abstractions of decision making in sequential games with perfect recall, against stationary opponents. We consider the problem of on-line learning in T-MDPs, both in the PAC and the regret-minimisation regimes. We show that well-known bandit algorithms -- \textsc{Lucb} and \textsc{Ucb} -- can be applied on T-MDPs by treating each policy as an arm.