Tractable contextual bandits beyond realizability
This work addresses the bias-variance trade-off in contextual bandits for machine learning practitioners, offering a more robust alternative to methods reliant on the often-unrealistic realizability assumption.
The paper tackles the problem of contextual bandits under model misspecification, presenting a tractable algorithm that reduces to constrained regression and achieves regret guarantees comparable to realizability-based methods, with an additive term proportional to the misspecification error.
Tractable contextual bandit algorithms often rely on the realizability assumption - i.e., that the true expected reward model belongs to a known class, such as linear functions. In this work, we present a tractable bandit algorithm that is not sensitive to the realizability assumption and computationally reduces to solving a constrained regression problem in every epoch. When realizability does not hold, our algorithm ensures the same guarantees on regret achieved by realizability-based algorithms under realizability, up to an additive term that accounts for the misspecification error. This extra term is proportional to T times a function of the mean squared error between the best model in the class and the true model, where T is the total number of time-steps. Our work sheds light on the bias-variance trade-off for tractable contextual bandits. This trade-off is not captured by algorithms that assume realizability, since under this assumption there exists an estimator in the class that attains zero bias.