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Linear regression regret bounds analyzed for scale-invariance in new paper

By PulseAugur Editorial · [2 sources] ·

Researchers have characterized scale-invariant upper bounds for self-normalized martingales in linear regression, finding that such bounds are generally only possible in one dimension. For dimensions greater than one, nontrivial scale-invariant bounds are shown to be impossible without additional assumptions. The study also resolves an open question regarding doubly-uniform regret in online linear regression, providing an algorithm with $O(\log T)$ regret in $d=1$ and demonstrating its impossibility for $d>1$. AI

IMPACT Advances theoretical understanding of regret bounds in online learning, potentially impacting future algorithm design.

RANK_REASON Academic paper detailing theoretical advancements in statistical learning.

Read on arXiv stat.ML →

AI-generated summary · Google Gemini · from 2 sources. How we write summaries →

Linear regression regret bounds analyzed for scale-invariance in new paper

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COVERAGE [2]

  1. arXiv stat.ML TIER_1 English(EN) · Fan Chen, Jian Qian, Alexander Rakhlin, Nikita Zhivotovskiy ·

    Self-Normalized Martingales and Uniform Regret Bounds for Linear Regression

    arXiv:2605.01628v1 Announce Type: new Abstract: Self-normalized martingale inequalities lie at the heart of confidence ellipsoids for online least squares and, more broadly, many bandit and reinforcement-learning results. Yet existing vector and scalar results typically rely on b…

  2. arXiv stat.ML TIER_1 English(EN) · Nikita Zhivotovskiy ·

    Self-Normalized Martingales and Uniform Regret Bounds for Linear Regression

    Self-normalized martingale inequalities lie at the heart of confidence ellipsoids for online least squares and, more broadly, many bandit and reinforcement-learning results. Yet existing vector and scalar results typically rely on bounded covariates and an explicit regularization…

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