Taming the Monster Every Context: Complexity Measure and Unified Framework for Offline-Oracle Efficient Contextual Bandits

We propose an algorithmic framework, Offline Estimation to Decisions (OE2D), that reduces contextual bandit learning with general reward function approximation to offline regression. The framework allows near-optimal regret for contextual bandits with large action spaces with $O(log(T))$ calls to an offline regression oracle over $T$ rounds, and makes $O(loglog(T))$ calls when $T$ is known. The design of OE2D algorithm generalizes Falcon~\citep{simchi2022bypassing} and its linear reward version~\citep[][Section 4]{xu2020upper} in that it chooses an action distribution that we term ``exploitative F-design'' that simultaneously guarantees low regret and good coverage that trades off exploration and exploitation. Central to our regret analysis is a new complexity measure, the Decision-Offline Estimation Coefficient (DOEC), which we show is bounded in bounded Eluder dimension per-context and smoothed regret settings. We also establish a relationship between DOEC and Decision Estimation Coefficient (DEC)~\citep{foster2021statistical}, bridging the design principles of offline- and online-oracle efficient contextual bandit algorithms for the first time.