Simple Projection-Free Algorithm for Contextual Recommendation with Logarithmic Regret and Robustness

We propose an algorithmic framework, Offline Estimation to Decisions (OE2D), that efficiently 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 $O(\log\log T)$ 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 finds an action distribution that we term ``exploitative F-design'' that simultaneously guarantees low regret and good coverage, striking a balance between exploration and exploitation. Central to our regret analysis is a new complexity measure, the Decision-Offline Estimation Coefficient (DOEC), which we show is small in many settings, including bounded Eluder dimension per-context and the smoothed regret setting. 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.

Contextual bandits are incredibly useful in many practical problems. We go one step further by devising a more realistic problem that combines: (1) contextual bandits with dense arm features, (2) non-linear reward functions, and (3) a generalization of correlated bandits where reward distributions change over time but the degree of correlation maintains. This formulation lends itself to a wider set of applications such as recommendation tasks. To solve this problem, we introduce conditionally coupled contextual C3 Thompson sampling for Bernoulli bandits. It combines an improved Nadaraya-Watson estimator on an embedding space with Thompson sampling that allows online learning without retraining. Empirical results show that C3 outperforms the next best algorithm by 5.7% lower average cumulative regret on four OpenML tabular datasets as well as demonstrating a 12.4% click lift on Microsoft News Dataset (MIND) compared to other algorithms.

We study stochastic contextual bandits with an unknown context-lumpable structure. The $S$ contexts are partitioned into $r$ blocks, and every arm has the same mean reward across contexts in the same block. Under arbitrary context distributions and without separation assumptions, we design an algorithm with expected regret $\widetilde{O}(\sqrt{r(S+K)T})$, matching the lower bound of Lee et al. (2023) up to logarithmic factors and improving their previous upper bound by a factor of $r$. The algorithm operates over dyadic accuracy levels, using a baseline policy and confidence-based early stopping to control exploration. It then performs cross-context elimination: since rewards are identical within a block, one selected arm eliminates all surviving records from that block, requiring at most $r$ selections at each level. Multi-scale exploration assigns finer accuracies to frequent blocks and coarser accuracies to rare blocks, yielding a near-optimal arm for every block while keeping the weighted policy error small.