Variance-Aware Non-Stationary Bandits:All-Budget Regret Bounds and Adaptation Costs
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...
| Authors | Xiaojin Zhang |
|---|---|
| Primary category | cs.LG |
| Published | 19 October 2026 |
| Last updated at source | 19 October 2026 |
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