Minimax Regret Optimisation for Robust Planning in Uncertain Markov
  Decision Processes
  The parameters for a Markov Decision Process (MDP) often cannot be specified
exactly. Uncertain MDPs (UMDPs) capture this model ambiguity by defining sets
which the parameters belong to. Minimax regret has been proposed as an
objective for planning in UMDPs to find robust policies which are not overly
conservative. In this work, we focus on planning for Stochastic Shortest Path
(SSP) UMDPs with uncertain cost and transition functions. We introduce a
Bellman equation to compute the regret for a policy. We propose a dynamic
programming algorithm that utilises the regret Bellman equation, and show that
it optimises minimax regret exactly for UMDPs with independent uncertainties.
For coupled uncertainties, we extend our approach to use options to enable a
trade off between computation and solution quality. We evaluate our approach on
both synthetic and real-world domains, showing that it significantly
outperforms existing baselines.
