aiqbench analysis
This paper advances theoretical bounds for non-stationary multi-armed bandits by refining the tradeoff between reward variance and variation budgets, offering new minimax regret formulas and adaptation cost analyses. It provides rigorous mathematical characterizations for algorithms that must monitor arms improving while unobserved, including specific strategies for handling small-budget noisy regimes via observation clipping. The work contributes directly to the foundational understanding of dynamic regret in machine learning environments where data distributions shift over time.
Variance-Aware Non-Stationary Bandits:All-Budget Regret Bounds and Adaptation Costs
arXiv:2610.26116v1 Announce Type: new Abstract: Low reward variance reduces estimation cost, but does not eliminate monitoring of arms that may improve while unobserved. We refine the variance--variation tradeoff and characterize how both costs depend on supplied variance and variation budgets in bounded, non-stationary multi-armed bandits. Let $A$ be the number of arms, $T$ the horizon, $B$ a bound on consecutive mean variation excluding the initial vector, and $Q$ a bound on the sum of the largest per-round reward variances. For every admissible pair $Q,B$, the minimax expected dynamic regret is, within a single logarithmic factor, \[ \min\{T,\;A+\sqrt{AQ}+(AQBT)^{1/3} +\sqrt{AT}\min\{B,\sqrt B\}\}. \] The deterministic boundary $Q=0$ is characterized without logarithms. For small positive budgets, a safe calibration phase identifies a common interval containing all future means of surviving arms. Clipping observations to a wider interval reduces the cost of restarting a prior hybrid static-regret algorithm; an original-mean analytical reference controls its residuals without charging the variation of clipped means. Balancing clipping bias and monitoring closes the small-budget noisy regime. Fixed oblivious constructions give the matching lower bound. We also quantify adaptation costs: on a disclosed deterministic one-improvement family, a stationary-regret budget has a matching worst-case change-regret frontier, including a finite improvement pulse. This implies an $\Omega((T/A)^{1/4})$ loss when one policy competes with all supplied-budget deterministic oracle rates. The budget-free low-noise scheduling problem remains separate.
Abstract:Low reward variance reduces estimation cost, but does not eliminate monitoring of arms that may improve while unobserved. We refine the variance--variation tradeoff and characterize how both costs depend on supplied variance and variation budgets in bounded, non-stationary multi-armed bandits. Let $A$ be the number of arms, $T$ the horizon, $B$ a bound on consecutive mean variation excluding the initial vector, and $Q$ a bound on the sum of the largest per-round reward variances. For every admissible pair $Q,B$, the minimax expected dynamic regret is, within a single logarithmic factor, \[ \min\{T,\;A+\sqrt{AQ}+(AQBT)^{1/3} +\sqrt{AT}\min\{B,\sqrt B\}\}. \] The deterministic boundary $Q=0$ is characterized without logarithms. For small positive budgets, a safe calibration phase identifies a common interval containing all future means of surviving arms. Clipping observations to a wider interval reduces the cost of restarting a prior hybrid static-regret algorithm; an original-mean analytical reference controls its residuals without charging the variation of clipped means. Balancing clipping bias and monitoring closes the small-budget noisy regime. Fixed oblivious constructions give the matching lower bound. We also quantify adaptation costs: on a disclosed deterministic one-improvement family, a stationary-regret budget has a matching worst-case change-regret frontier, including a finite improvement pulse. This implies an $\Omega((T/A)^{1/4})$ loss when one policy competes with all supplied-budget deterministic oracle rates. The budget-free low-noise scheduling problem remains separate.
Machine Learning (cs.LG)
arXiv:2610.26116 [cs.LG]
(or arXiv:2610.26116v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2610.26116 Focus to learn more arXiv-issued DOI via DataCite
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Full text under the publisher's open licence · 309 words