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

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.

• The paper presents a statistically defined action of defer to improve decision-making in continual-learning expert pools that decide to reuse, spawn, or defer for incoming data chunks, providing distinct reliability rather than a heuristic fallback.
• The study compares systems using single-axis triggers and CJSD-based gates while exploring a two-axis system with a covariate shift mode and functional axis estimated by discriminator outputs.
• Findings showcase that CJSD gate outperforms others with considerable expert economy and improved accuracy on various regimes, particularly differentiating decision quality in expert pools.

Overview

"Evidence Before Expansion: Reuse, Spawn, or Defer in Lifelong Expert Pools" (2608.19888) addresses the decision layer of continual-learning systems that maintain a pool of expert models over a nonstationary stream. At each incoming chunk, the system must choose among three actions: absorb the chunk into an existing expert (reuse), create a new expert (spawn), or wait for more evidence (defer). The paper's central contribution is to elevate defer from a heuristic fallback to a statistically defined action: defer is exactly the state in which neither of two one-sided sequential tests has accumulated sufficient evidence. The design rests on a two-axis task comparison built from the conditional Jensen–Shannon discrepancy (CJSD), decomposed into a covariate axis $I_x$ and a functional axis estimated by two discriminators, with the theory of the discrepancy itself deferred to a companion paper.

The work is positioned against one-axis triggers used in prior systems—input novelty (SEMA-style), loss jumps (DDM-style), and model-exchange regret (CLS-style)—arguing that each confounds at least two of the three underlying situations: covariate shift, mechanism change, and insufficient evidence. The paper contributes three things: decision semantics with an indifference zone, sequential evidence processes with anytime-validity guarantees under streaming constraints, and systems mechanics that make the layer run at stream rate.

Decision semantics: reuse, spawn, and defer as sequential hypotheses

Reuse and spawn are posed as one-sided sequential hypotheses separated by an indifference zone $[\tau, 3\tau]$: spawn is tested against $H_0^{\mathrm{sp}}: \le \tau$ and reuse against $H_0^{\mathrm{re}}: \ge 3\tau$. The indifference zone makes the reuse-side test well posed; without it, the reuse boundary would be statistically unreachable. A comparability gate blocks reuse claims when covariate supports barely overlap ($I_x$ above a ceiling), since the functional axis is honestly zero off-overlap.

Per-expert betting e-processes are maintained on per-point loss-difference increments scored by discriminators frozen before the chunk arrives—a predictable scoring rule, so the increments constitute the new randomness. Actions fire at threshold $K_{\max}/\alpha$, where $K_{\max}$ is a declared design capacity on simultaneously monitored experts ($K_{\max}=16$). The union bound must be over this declared capacity rather than the data-dependent pool size, since thresholds growing with each spawn do not control familywise error when experts are created indefinitely. For unbounded lifetimes, the paper implements $\alpha$-spending over creation events with weights $\alpha_c = 6\alpha/(\pi^2 c^2)$. Notably, re-running the full benchmark under spending costs nothing measurable: false-spawn moves only from 0.01 to 0.02, pools remain comparable (6.3 → 7.0 experts on INSECTS-reoccurring), and prequential accuracy is equal or slightly higher everywhere (0.86 → 0.88 synthetic; 0.77 → 0.79 Covertype).

A sensitivity ablation localizes all tuning sensitivity in $[\tau, 3\tau]$0: at $[\tau, 3\tau]$1 combined error is 0.01 with 1.3 experts, while $[\tau, 3\tau]$2 widens the indifference zone past the concept gap and mis-reuses the new concept in half the runs (combined error 0.50). Window length is inert across $[\tau, 3\tau]$3, so the practical guidance is simply to set $[\tau, 3\tau]$4 below the smallest drift mass worth reacting to.

Sequential validity for learned discriminators

Because increments come from learned discriminators, the guarantee must be stated for the observable score rather than assumed for the population quantity. The paper defines a surrogate discrepancy—the conditional population log-loss gap achieved by the predictable discriminator pair scoring each chunk—and proves two propositions:

• Finite-time validity for the observable score: under clipping and predictable betting with a capital constraint, the e-process is a nonnegative supermartingale whenever the surrogate null holds pointwise over its lifetime, giving Ville-bounded anytime validity at any stopping time.
• One-sided transfer to the population quantity: unconditionally, excess risks bound each direction separately, so a spawn-side rejection certifies the population functional axis exceeds $[\tau, 3\tau]$5 with no condition on the second discriminator, and symmetrically for reuse. Under a downward-bias regularity ($[\tau, 3\tau]$6), observed in every lifecycle benchmark reported here, the spawn slack vanishes and conservativeness is exact. This regularity is explicitly an empirical refinement—an engineered misspecified-marginal exception exists within the proven slack—so it sharpens but does not carry the validity claim. Exact zero-slack population conservativeness otherwise requires threshold correction via a valid high-probability excess-risk bound.

In summary, surrogate-level sequential validity is exact; population-level decisions inherit one-sided, discriminator-specific slacks unconditionally.

Recency without windows: the restarted e-detector

A single unwindowed e-process accumulated over a long stationary stretch can absorb a concept switch, mis-firing reuse at a measured rate of 0.5 after switches. A sliding window fixes behavior (mis-reuse 0.1) but breaks the supermartingale property, placing the windowed heuristic outside the validity theorem. The resolution is a restarted e-detector: a bank of unwindowed betting processes with geometrically spaced restart times, occupying $[\tau, 3\tau]$7 memory. Error budget is spent over restart instances (not active slots) with weights $[\tau, 3\tau]$8, preserving lifetime familywise control. The price is logarithmic: instance $[\tau, 3\tau]$9's log-threshold exceeds the uniform threshold by $H_0^{\mathrm{sp}}: \le \tau$0, recoverable in $H_0^{\mathrm{sp}}: \le \tau$1 chunks under any alternative with log-evidence growth rate $H_0^{\mathrm{sp}}: \le \tau$2.

Empirically the correct accounting is nearly free: post-switch mis-reuse drops to 0.00 and false-spawn to 0.00 on the synthetic stream, accuracy is within one point of the windowed heuristic there (0.846 vs 0.856), and equal or better elsewhere—including the best accuracy of any evidence variant on INSECTS-reoccurring (0.616 → 0.675) and Covertype (0.770 → 0.790). The windowed variant is retired, so the deployed system and the guarantee coincide.

Systems mechanics

Three mechanisms make the layer stream-rate. Shortlisting compares only the top-$H_0^{\mathrm{sp}}: \le \tau$3 experts by previous-chunk error, using labels predictably, yielding a $H_0^{\mathrm{sp}}: \le \tau$4 speedup on INSECTS with no measured decision change. Mini-batch test-then-train routing cuts switch lag from one chunk to one mini-batch, lifting every adaptive policy to the same accuracy ceiling and isolating decision quality as the differentiator. Merging closes the loop for recurring concepts; reservoir recency caps prevent regime pollution, which the authors identify as the true cause of over-spawning on fast-mixing streams.

Benchmark findings

Across four stream regimes and seven policies (single, spawn-always, input-novelty, loss-jump, exchange score, CPD-family gate, CJSD gate), with routing equalized, accuracy differences between adaptive policies nearly vanish (synthetic: 0.939–0.945); the differentiators are decision quality and expert economy. Key results:

Finding	Result
Synthetic stream	CJSD gate: zero false spawns, zero missed concepts, ideal expert count
Gradual-drift phase	Spawn rates 0.10 (CJSD) vs 0.16–0.22 (loss/CPD) vs 1.0 (spawn-always)
INSECTS-reoccurring	13 experts (CJSD) vs 18–52 (exchange-based); non-spawn at recurrent change points is correct reuse
Electricity (continuous drift)	No pool helps (all 0.74–0.78); boundary of applicability diagnosed by persistently high reservoir-vs-chunk functional axis
Streaming default config	False-spawn 0.00 / false-reuse 0.00 at 1.0 experts, accuracy 0.85 (batch gate: 0.91 — the explicit price of family-level error control)

The paper characterizes where expert pools pay off—discrete, recurring concepts—and where they cannot: continuous drift. On controlled drift boundaries near $H_0^{\mathrm{sp}}: \le \tau$5, naive repeated confidence intervals commit 64% of borderline cases to effectively coin-flip decisions, whereas valid schemes defer 90–97% of them while paying only a 1.8–2.6× delay factor on clear cases; the e-process variant adds a 0.00 false-alarm rate at detection delays 20% above the invalid naive monitor.

Limitations and open questions

The paper concedes several boundaries plainly. Continuous-drift streams remain out of scope for any discrete-concept pool. Discriminator cost, though bounded by shortlisting, still exceeds loss-trigger baselines by roughly $H_0^{\mathrm{sp}}: \le \tau$6. The downward-bias regularity enabling exact zero-slack transfer is empirical, not guaranteed, and the companion paper exhibits an engineered exception within the proven slack. Open problems include sharper-than-union-bound multiplicity control via mixture e-values and finite-sample theory for the underlying estimator, both left to future or companion work.

Conclusion

This paper reframes the reuse/spawn/defer trichotomy of lifelong expert pools as a pair of one-sided sequential tests separated by an indifference zone, making abstention a precisely defined statistical state. Its technical core—predictable-discriminator e-processes with exact surrogate-level validity, one-sided population transfer, and a restarted e-detector providing bounded-memory recency inside a lifetime anytime-validity guarantee—is validated empirically: zero false spawns and missed concepts on synthetic streams, substantial expert economy on recurrence-heavy real streams, and honest diagnosis of the continuous-drift regime where the approach does not apply. The result is a deployed system whose mechanics and validity guarantees coincide, at negligible measured cost relative to invalid shortcuts.