Worst-case Performance of Greedy Policies in Bandits with Imperfect Context Observations
This work addresses the immature study of imperfect context observations in sequential decision-making, providing theoretical guarantees for greedy policies in this setting, which is incremental as it extends classical bandit models.
The paper tackles the problem of contextual bandits with imperfectly observed contexts, establishing that greedy policies achieve non-asymptotic worst-case regret that grows poly-logarithmically with time horizon and failure probability, and linearly with the number of arms, as supported by numerical analysis.
Contextual bandits are canonical models for sequential decision-making under uncertainty in environments with time-varying components. In this setting, the expected reward of each bandit arm consists of the inner product of an unknown parameter with the context vector of that arm. The classical bandit settings heavily rely on assuming that the contexts are fully observed, while study of the richer model of imperfectly observed contextual bandits is immature. This work considers Greedy reinforcement learning policies that take actions as if the current estimates of the parameter and of the unobserved contexts coincide with the corresponding true values. We establish that the non-asymptotic worst-case regret grows poly-logarithmically with the time horizon and the failure probability, while it scales linearly with the number of arms. Numerical analysis showcasing the above efficiency of Greedy policies is also provided.