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New lower bound shows bandit convex optimization is harder than linear bandits

By PulseAugur Editorial · [2 sources] ·

Researchers have established a new lower bound for bandit convex optimization, demonstrating that it is fundamentally more complex than linear bandits. The study introduces a novel class of convex functions that reveal a trade-off: learners must either discover a specific 'tube' without knowing a key linear transformation or expend observations to learn it. This leads to a sample complexity lower bound of $\widetilde{\Omega}(d^{5/2}/\varepsilon^2)$ for finding an $\varepsilon$-optimal action, translating to a regret lower bound of $\widetilde{\Omega}(d^{5/4}\sqrt{T})$. The findings extend to unconstrained action spaces. AI

IMPACT Establishes a theoretical limit on learning efficiency for certain optimization problems, potentially guiding future algorithm development.

RANK_REASON The cluster contains an academic paper detailing theoretical research with new mathematical bounds.

Read on Hugging Face Daily Papers →

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

New lower bound shows bandit convex optimization is harder than linear bandits

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The cluster contains an academic paper detailing theoretical research with new mathematical bounds.
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COVERAGE [2]

  1. arXiv cs.LG TIER_1 English(EN) · Nived Rajaraman ·

    The Price of Hidden Curvature: An $\widetilde{\Omega} (d^{5/4} \sqrt{T})$ Lower Bound for Bandit Convex Optimization

    arXiv:2607.18652v1 Announce Type: cross Abstract: We establish a $\widetilde\Omega(d^{5/4}\sqrt T)$ lower bound on the minimax expected regret of stochastic bandit convex optimization of $1$-Lipschitz functions on the Euclidean ball. This presents the first nontrivial regret lowe…

  2. Hugging Face Daily Papers TIER_1 English(EN) ·

    The Price of Hidden Curvature: An $\widetildeΩ (d^{5/4} \sqrt{T})$ Lower Bound for Bandit Convex Optimization

    We establish a $\widetildeΩ(d^{5/4}\sqrt T)$ lower bound on the minimax expected regret of stochastic bandit convex optimization of $1$-Lipschitz functions on the Euclidean ball. This presents the first nontrivial regret lower bound that grows faster than $d\sqrt{T}$ for this pro…

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