Evidence Before Expansion: Reuse, Spawn, or Defer in Lifelong Expert Pools

Kentaro Oda

cs.LGAug 20, 2026

Evidence Before Expansion: Reuse, Spawn, or Defer in Lifelong Expert Pools

Authors: Kentaro Oda

Organizations: Center for Management of Information Technologies, Kagoshima University

Abstract

Streaming systems that maintain a pool of expert models must repeatedly decide whether to reuse an existing expert for arriving data, spawn a new one, or defer. We present a decision layer that makes all three outcomes statistically meaningful. Reuse and spawn are posed as one-sided sequential hypotheses on a conditional (mechanism-level) discrepancy, separated by an indifference zone; defer is exactly the state in which neither betting e-process has accumulated sufficient evidence. We prove finite-time anytime validity for the observable surrogate discrepancy of a predictable discriminator sequence, and an unconditional one-sided transfer to the population quantity in which each side's slack is the excess risk of a single discriminator; an empirically observed downward-bias regularity makes the spawn side exactly conservative. Recency without sacrificing the guarantee is obtained by a restarted e-detector: a bank of unwindowed betting supermartingales at geometrically spaced restart times (O(log t) memory), with the error budget spent over restart instances, which preserves lifetime anytime validity; spending over expert-creation order likewise controls multiplicity for unboundedly many experts. On synthetic multi-concept streams, Electricity, Covertype, and the recurrence-heavy INSECTS benchmark, the instance-accounted restarted bank achieves zero false spawns and zero false reuses after switches and matches or exceeds the retired windowed heuristic (INSECTS-reoccurring accuracy 0.675), making the deployed algorithm and the guaranteed algorithm one and the same.

Figures & tables

Panel of Figure 1 — Figure 1: The decision layer as a state machine. Every chunk starts in defer ; the two betting e-processes must earn a transition (threshold $K_{\max}/\alpha$ or the $\alpha_{c}$ spending schedule), the indifference zone $[\tau,3\tau]$ separates the two exits, and the comparability gate blocks reuse claims when supports barely overlap.

Figure 2: Improved streaming benchmark: all seven policies share online routing and pruning; a gradual-drift phase (shaded) and recurrences are included. Bottom: expert counts.

Figure 3: INSECTS (abrupt and reoccurring): prequential accuracy (top) and expert counts (bottom) per decision policy; dotted lines mark documented change points.

Figure 4: Repeated CI peeking commits 64% of borderline cases to a near-coin-flip decision; anytime-valid monitoring keeps them deferred and pays only ${\sim}2\times$ delay on clear cases.

Online Continual Learning

Online continual learning adapts models to sequential data streams while preserving useful knowledge and limiting forgetting.

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Learning to Defer Bandit Learning Multiclass Classification Online Learning

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Learning-to-Defer (L2D) methods route each query either to a predictive model or to external experts. While existing work studies this problem in batch settings, real-world deployments require handling streaming data, changing expert availability, and shifting expert distribution. We introduce the first online L2D algorithm for multiclass classification with bandit feedback and a dynamically varying pool of experts. Our method achieves regret guarantees of

O((n+n_e)T^{2/3})

in general and

O((n+n_e)\sqrt{T})

under a low-noise condition, where

T

is the time horizon,

n

is the number of labels, and

n_e

is the number of distinct experts observed across rounds. The analysis builds on novel

\mathcal{H}

-consistency bounds for the online framework, combined with first-order methods for online convex optimization. Experiments on synthetic and real-world datasets demonstrate that our approach effectively extends standard Learning-to-Defer to settings with varying expert availability and reliability.

Abstract

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