New Lower Bound and Upper Bounds on the Regret for Online Sparse Linear Regression
We study online sparse linear regression (OSLR) where any algorithm is restricted to accessing only $b$ out of $d$ attributes per instance for prediction and $b0\geq 0$ additional attributes after prediction, which was proved to be NP-hard.
ProofPaper ↗
Key points
- Previous work focused on designing computationally efficient algorithms under regularity assumptions, but did not characterize its information theoretic complexity.
- In this work, we give the first lower bound on the minimax regret of OSLR and design algorithms with better upper bounds without regularity assumptions.
- We characterize how minimax regret scales with problem-dependent parameters, capturing the information theoretic complexity of OSLR.
Sources (1)
- [1]New Lower Bound and Upper Bounds on the Regret for Online Sparse Linear RegressionarXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 8, 09:15 AM
We study online sparse linear regression (OSLR) where any algorithm is restricted to accessing only $b$ out of $d$ attributes per instance for prediction and $b_0\geq 0$ additional attributes after prediction, which was proved to be NP-hard.
Previous work focused on designing computationally efficient algorithms under regularity assumptions, but did not characterize its information theoretic complexity.
Extractive summary: sentences quoted from the sources.
Before this
- Oct 8, 2026Parametric Trajectory Distillation for Few-Step Video Generation
- Oct 8, 2026WorldGuide: Goal-Directed Video World Model for Procedural Task Execution
- Oct 7, 2026Policy Learning with Weak Signals
- Oct 7, 2026Sharp Asymptotic Theory of Maximum Likelihood Estimation for Gaussian Processes with an RBF Kernel
- Oct 7, 2026Online Resource Allocation with an Endogenous Markov State: Fewer LP Solves Earn More
- Oct 6, 2026Reinforcement Learning for Hierarchical Reasoning Rewards: Minimax-Optimal Rates with Transformers