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

arXiv:2602.09456v1 Announce Type: cross
Abstract: 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.