New Algorithms Improve Replicability in Multi-Armed and Linear Bandit Problems
Researchers have proposed a family of replicable bandit algorithms—RepUCB, RepLinUCB, and RepGLMUCB—based on Upper Confidence Bound (UCB) exploration, achieving improved regret bounds over prior elimination-based methods. Replicability in bandit algorithms requires that two independent runs sharing internal randomness produce identical action sequences with high probability, a property important for scientific reproducibility in machine learning. The work is notable for being the first linear-bandit algorithm with optimal dependence on the replicability parameter ρ for large action spaces, reducing the price of replicability by a factor of O(d/ρ) over previous best results.
A new preprint on arXiv introduces optimistic, UCB-based algorithms designed to satisfy formal replicability guarantees in stochastic bandit settings. The paper addresses a gap in prior work, which relied on elimination-based strategies and discretization techniques that led to suboptimal scaling with dimension d and the replicability parameter ρ. For multi-armed bandits, the proposed RepUCB algorithm achieves a regret bound of O(K²log²T/ρ² · Σ(Δ_a + log(KTlogT)/Δ_a)), while for linear bandits, RepLinUCB achieves Õ((d + d³/ρ)√T), improving on the best prior guarantee by a factor of O(d/ρ). A key technical contribution is RepRidge, a replicable ridge regression estimator that simultaneously satisfies confidence and replicability guarantees, which the authors note may have independent utility in statistical estimation beyond bandits. The framework is further extended to generalized linear bandits via RepGLM and RepGLMUCB. The paper was submitted in April 2026 and revised in June 2026, and has not yet undergone formal peer review.
What's missing
As a preprint, this work has not yet been peer-reviewed. The paper does not report empirical experiments comparing the proposed algorithms against baselines in practice; the improvements are established theoretically. It is also unclear how the algorithms perform under model misspecification or non-stationary reward distributions, which are common real-world concerns.
What different sources said
- arXiv cs.LGCenter
Residual-Controlled Multiplier Learning for Stochastic Constrained Decision-Making
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