Bayesian Best-Arm Identification with Abstention: A Polynomial-to-Exponential Phase Transition
A new theoretical result reveals that allowing learners to abstain from predictions fundamentally reshapes the error-convergence landscape in best-arm identification tasks. The finding demonstrates a sharp phase transition where abstention budgets flip error decay from polynomial to exponential rates, with matching lower and upper bounds for Gaussian settings. This work clarifies how uncertainty quantification and selective prediction interact in sequential decision-making, a principle increasingly relevant to AI systems that must balance accuracy against the cost of deferring to humans or abstaining entirely.
Modelwire context
ExplainerThe paper's core contribution is proving that abstention creates a sharp threshold rather than a gradual trade-off. Below a critical budget, deferring predictions helps only marginally; above it, error rates collapse exponentially. This isn't just a quantitative improvement but a qualitative regime change.
This connects directly to the PolicyGuard work from the same week, which reframes agent compliance as a dialogue-grounded verification problem rather than a binary gate. Both papers treat deferral and human-in-the-loop decisions as first-class design choices rather than failure modes. Where PolicyGuard shows how to architect systems that know when to ask for help, this theoretical result explains what happens to error rates when you actually budget for that help. The phase transition finding also echoes the evaluation fragility exposed in the diffusion LLM study, where small methodological choices (prompt templates there, abstention budgets here) flip performance regimes entirely.
If practitioners implementing selective prediction systems observe the predicted exponential decay threshold in their own bandit experiments within the next 6 months, that validates the theory on non-Gaussian data. If the threshold holds only for Gaussian arms but collapses under real-world reward distributions, that signals the bounds are tight but not practically universal.
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