Linear Bandits under Exact Sliding-Window Constraints

Practical Tips

Practical tips and how-to guidance will be added by our editorial team.

中文解读

中文解读待补充：本站将优先为睡眠改善、失眠治疗、助眠方法等高价值文章补充中文说明。

Article Summary

We study linear bandits under exact sliding-window constraints, where every consecutive block of actions must belong to a prescribed feasible set. In the offline setting, where the reward function is known, we show that convexity and cyclic-shift invariance make a stationary solution optimal when $w\mid T$ and within an additive $O(w)$ gap otherwise. In the online setting, we show that geometric structure alone is insufficient for learning, and sublinear regret can be impossible. We introduce a transition diameter $τ$ that quantifies feasible reachability and develop a rare-switching OFUL algorithm with regret $\widetilde{O}(d\sqrt{T}+τd+w)$ against the offline-optimal feasible trajectory. Finally, we remove cyclic invariance and consider general sliding-window constraints, where optimal behavior may be non-stationary. We represent recent action history as the state of a finite-memory control problem and introduce a history-state diameter $D$ that measures feasible communication between viable histories. Combining optimistic remaining-horizon planning with rare policy updates, we obtain a regret bound of $\widetilde{O}(d\sqrt{T}+dD+w)$. We evaluate our approach on real-world and synthetic benchmarks, showing that it maintains exact feasibility while achieving reward and regret comparable to baselines with substantially fewer policy updates.

Sources & References

• Original source
• Full article (PDF)

Comments