Adaptive Estimation and Optimal Control in Offline Contextual MDPs without Stationarity
This work provides a theoretically grounded method for offline learning in contextual MDPs, addressing a key bottleneck in applications like biostatistics and machine learning.
The paper introduces a novel adaptive estimator for offline contextual MDPs that provides strong optimality guarantees, overcoming challenges like non-stationarity and model irregularity. It derives oracle risk bounds and finite-sample guarantees for optimal control, achieving the first estimator of its kind.
Contextual MDPs are powerful tools with wide applicability in areas from biostatistics to machine learning. However, specializing them to offline datasets has been challenging due to a lack of robust, theoretically backed methods. Our work tackles this problem by introducing a new approach towards adaptive estimation and cost optimization of contextual MDPs. This estimator, to the best of our knowledge, is the first of its kind, and is endowed with strong optimality guarantees. We achieve this by overcoming the key technical challenges evolving from the endogenous properties of contextual MDPs; such as non-stationarity, or model irregularity. Our guarantees are established under complete generality by utilizing the relatively recent and powerful statistical technique of $T$-estimation (Baraud, 2011). We first provide a procedure for selecting an estimator given a sample from a contextual MDP and use it to derive oracle risk bounds under two distinct, but nevertheless meaningful, loss functions. We then consider the problem of determining the optimal control with the aid of the aforementioned density estimate and provide finite sample guarantees for the cost function.