What policy should be employed in a Markov decision process with uncertain parameters? Robust optimization answer to this question is to use rectangular uncertainty sets, which independently reflect available knowledge about each state, and then obtains a decision policy that maximizes expected reward for the worst-case decision process parameters from these uncertainty sets. While this rectangularity is convenient computationally and leads to tractable solutions, it often produces policies that are too conservative in practice, and does not facilitate knowledge transfer between portions of the state space or across related decision processes. In this work, we propose non-rectangular uncertainty sets that bound marginal moments of state-action features defined over entire trajectories through a decision process. This enables generalization to different portions of the state space while retaining appropriate uncertainty of the decision process. We develop algorithms for solving the resulting robust decision problems, which reduce to finding an optimal policy for a mixture of decision processes, and demonstrate the benefits of our approach experimentally.

Neural Information Processing Systems http://nips.cc/

An important challenge in Markov decision processes is to ensure robustness with respect to unexpected or adversarial system behavior while taking advantage of well-behaving parts of the system. We consider a problem setting where some unknown parts of the state space can have arbitrary transitions while other parts are purely stochastic. We devise an algorithm that is adaptive to potentially adversarial behavior and show that it achieves similar regret bounds as the purely stochastic case.

We study the evaluation of a policy under best- and worst-case perturbations to a Markov decision process (MDP), using transition observations from the original MDP, whether they are generated under the same or a different policy. This is an important problem when there is the possibility of a shift between historical and future environments, \emph{e.g.} due to unmeasured confounding, distributional shift, or an adversarial environment. We propose a perturbation model that allows changes in the transition kernel densities up to a given multiplicative factor or its reciprocal, extending the classic marginal sensitivity model (MSM) for single time-step decision-making to infinite-horizon RL. We characterize the sharp bounds on policy value under this model -- \emph{i.e.}, the tightest possible bounds based on transition observations from the original MDP -- and we study the estimation of these bounds from such transition observations. We develop an estimator with several important guarantees: it is semiparametrically efficient, and remains so even when certain necessary nuisance functions, such as worst-case Q-functions, are estimated at slow, nonparametric rates.

The authors consider distributionally robust finite MDPs over a finite horizon. The transition probabilities conditionally to a state-action pair should remain at L1-bounded distance from a base measure, which is feasible as being generated using a given reference policy. This is a nice idea. A few comments are mentioned next. Related to that question, why the requirement of staying "close" to this policy would be beneficial.

We present a novel $Q$-learning algorithm to solve distributionally robust Markov decision problems, where the corresponding ambiguity set of transition probabilities for the underlying Markov decision process is a Wasserstein ball around a (possibly estimated) reference measure. We prove convergence of the presented algorithm and provide several examples also using real data to illustrate both the tractability of our algorithm as well as the benefits of considering distributional robustness when solving stochastic optimal control problems, in particular when the estimated distributions turn out to be misspecified in practice.

What policy should be employed in a Markov decision process with uncertain parameters? Robust optimization answer to this question is to use rectangular uncertainty sets, which independently reflect available knowledge about each state, and then obtains a decision policy that maximizes expected reward for the worst-case decision process parameters from these uncertainty sets. While this rectangularity is convenient computationally and leads to tractable solutions, it often produces policies that are too conservative in practice, and does not facilitate knowledge transfer between portions of the state space or across related decision processes. In this work, we propose non-rectangular uncertainty sets that bound marginal moments of state-action features defined over entire trajectories through a decision process. This enables generalization to different portions of the state space while retaining appropriate uncertainty of the decision process.

An important challenge in Markov decision processes is to ensure robustness with respect to unexpected or adversarial system behavior while taking advantage of well-behaving parts of the system. We consider a problem setting where some unknown parts of the state space can have arbitrary transitions while other parts are purely stochastic. We devise an algorithm that is adaptive to potentially adversarial behavior and show that it achieves similar regret bounds as the purely stochastic case. Papers published at the Neural Information Processing Systems Conference.