跟随近似稀疏领导者以实现无悔在线稀疏线性逼近
Follow The Approximate Sparse Leader for No-Regret Online Sparse Linear Approximation
- IIT (ISM) Dhanbad（印度理工学院（达姆达德印度矿业学院））
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
针对在线稀疏线性逼近问题，提出 Follow-The-Approximate-Sparse-Leader 元策略，并证明其静态遗憾具有从对数到平方根范围的依赖数据次线性界，仿真验证了有效性。
AI中文摘要：
我们研究在线稀疏线性逼近问题：在该问题中，需要依据给定测量矩阵各列的线性组合，预测一系列测量的最佳稀疏逼近。此类在线预测问题广泛存在于医学试验、网络缓存和资源分配等场景。离线恢复固有的难度也使在线问题颇具挑战。在这封信中，我们提出 Follow-The-Approximate-Sparse-Leader，这是一种用于解决该在线问题的高效在线元策略。通过详细的理论分析，我们证明在关于测量序列的某些假设下，所提策略在静态遗憾上具有依赖于数据的次线性上界，其范围可从对数量级到平方根量级。数值仿真验证了理论发现，并展示了所提在线策略的有效性。
英文摘要：
We consider the problem of \textit{online sparse linear approximation}, where one predicts the best sparse approximation of a sequence of measurements in terms of linear combination of columns of a given measurement matrix. Such online prediction problems are ubiquitous, ranging from medical trials to web caching to resource allocation. The inherent difficulty of offline recovery also makes the online problem challenging. In this letter, we propose Follow-The-Approximate-Sparse-Leader, an efficient online meta-policy to address this online problem. Through a detailed theoretical analysis, we prove that under certain assumptions on the measurement sequence, the proposed policy enjoys a data-dependent sublinear upper bound on the static regret, which can range from logarithmic to square-root. Numerical simulations are performed to corroborate the theoretical findings and demonstrate the efficacy of the proposed online policy.
