Provable regret guarantee for the CMAB capacity controller

Prove a regret bound for the contextual multi-armed bandit (CMAB) capacity controller used by COMET, and establish that such a bound yields a sub-linear rate of false expert expansions under the stated margin condition.

Background

COMET uses a contextual multi-armed bandit to decide whether each newly trained task expert should be retained or merged with an existing expert. The theoretical analysis shows that sub-linear expert growth follows from sub-linear cumulative novelty, but practical CMAB decisions may violate the idealized assumption that expansion occurs only for sufficiently novel tasks.

The appendix explains that converting a no-regret guarantee into a sub-linear count of false expansions requires a positive reward-gap margin. However, the implemented CMAB update is projected and EMA-smoothed rather than a standard no-regret algorithm, and the paper does not establish a regret guarantee for it. Proving the required guarantee would provide formal control over capacity growth beyond the sufficient-condition analysis.

References

CMAB updates its weights with a projected, EMA-smoothed advantage step, which is not a standard no-regret algorithm, and we do not prove a regret bound for it. Eq. (15) thus names the property CMAB would need for a sub-linear false-expansion term; proving it is left to future work.

— COMET: Decoupled Distillation, Routing, and Capacity Control for Task-Agnostic Continual Vision--Language Learning  (2610.22907 - Woo et al., 16 Oct 2026) in Appendix A.5, “From regret to false-expansion count” and “Applicability to CMAB,” p. 17; Limitations, p. 10