Corrupted Contextual Bandits with Action Order Constraints

We consider a variant of the novel contextual bandit problem with corrupted context, which we call the contextual bandit problem with corrupted context and action correlation, where actions exhibit a relationship structure that can be exploited to guide the exploration of viable next decisions. Our setting is primarily motivated by adaptive mobile health interventions and related applications, where users might transitions through different stages requiring more targeted action selection approaches. In such settings, keeping user engagement is paramount for the success of interventions and therefore it is vital to provide relevant recommendations in a timely manner. The context provided by users might not always be informative at every decision point and standard contextual approaches to action selection will incur high regret. We propose a meta-algorithm using a referee that dynamically combines the policies of a contextual bandit and multi-armed bandit, similar to previous work, as wells as a simple correlation mechanism that captures action to action transition probabilities allowing for more efficient exploration of time-correlated actions. We evaluate empirically the performance of said algorithm on a simulation where the sequence of best actions is determined by a hidden state that evolves in a Markovian manner. We show that the proposed meta-algorithm improves upon regret in situations where the performance of both policies varies such that one is strictly superior to the other for a given time period. To demonstrate that our setting has relevant practical applicability, we evaluate our method on several real world data sets, clearly showing better empirical performance compared to a set of simple algorithms

Off-Policy Evaluation for Action-Dependent Non-Stationary Environments

Methods for sequential decision-making are often built upon a foundational assumption that the underlying decision process is stationary. This limits the application of such methods because real-world problems are often subject to changes due to external factors (passive non-stationarity), changes induced by interactions with the system itself (active non-stationarity), or both (hybrid non-stationarity). In this work, we take the first steps towards the fundamental challenge of on-policy and off-policy evaluation amidst structured changes due to active, passive, or hybrid non-stationarity. Towards this goal, we make a higher-order stationarity assumption such that non-stationarity results in changes over time, but the way changes happen is fixed. We propose, OPEN, an algorithm that uses a double application of counterfactual reasoning and a novel importance-weighted instrument-variable regression to obtain both a lower bias and a lower variance estimate of the structure in the changes of a policy’s past performances. Finally, we show promising results on how OPEN can be used to predict future performances for several domains inspired by real-world applications that exhibit non-stationarity

Delphic Offline Reinforcement Learning under Nonidentifiable Hidden Confounding

A prominent challenge of offline reinforcement learning (RL) is the issue of hidden confounding: unobserved variables may influence both the actions taken by the agent and the observed outcomes. Hidden confounding can compromise the validity of any causal conclusion drawn from data and presents a major obstacle to effective offline RL. In the present paper, we tackle the problem of hidden confounding in the nonidentifiable setting. We propose a definition of uncertainty due to hidden confounding bias, termed delphic uncertainty, which uses variation over world models compatible with the observations, and differentiate it from the well-known epistemic and aleatoric uncertainties. We derive a practical method for estimating the three types of uncertainties, and construct a pessimistic offline RL algorithm to account for them. Our method does not assume identifiability of the unobserved confounders, and attempts to reduce the amount of confounding bias. We demonstrate through extensive experiments and ablations the efficacy of our approach on a sepsis management benchmark, as well as on electronic health records. Our results suggest that nonidentifiable hidden confounding bias can be mitigated to improve offline RL solutions in practice