Online conformal prediction (OCP) seeks prediction intervals that achieve long-run $1-α$ coverage for arbitrary (possibly adversarial) data streams, while remaining as informative as possible. Existing OCP methods often require manual learning-rate tuning to work well, and may also require algorithm-specific analyses. Here, we develop a general regret-to-coverage theory for interval-valued OCP based on the $(1-α)$-pinball loss. Our first contribution is to identify \emph{linearized regret} as a key notion, showing that controlling it implies coverage bounds for any online algorithm. This relies on a black-box reduction that depends only on the Fenchel conjugate of an upper bound on the linearized regret. Building on this theory, we propose UP-OCP, a parameter-free method for OCP, via a reduction to a two-asset portfolio selection problem, leveraging universal portfolio algorithms. We show strong finite-time bounds on the miscoverage of UP-OCP, even for polynomially growing predictions. Extensive experiments support that UP-OCP delivers consistently better size/coverage trade-offs than prior online conformal baselines.
Tao Wang, Shuo Li, Yan Sun, Dongsheng Ding, Edgar Dobriban
原文摘要
Reinforcement learning with verifiable rewards (RLVR) has emerged as a central paradigm for improving the reasoning capabilities of large language models. Group-based policy optimization methods, such as GRPO, typically allocate a fixed number of rollouts to every prompt. This uniform allocation can be inefficient: it over-allocates compute to prompts whose sampled groups are already saturated while under-exploring prompts for which additional samples may reveal useful correct trajectories. To address this limitation, we introduce hit utility, the posterior probability that at least one rollout in a proposed additional allocation for a prompt will be correct. Building on this notion, we propose Hit-Utility Optimal Rollout Allocation (HORA), a learning-free rollout allocation policy that maximizes total posterior hit utility within each allocation batch. HORA adaptively reallocates rollout budgets while leaving the downstream reward evaluation and group-based advantage estimator unchanged. Across two training sets, four mathematical reasoning benchmarks, and three model families at multiple scales, HORA preserves comparable Pass@1 and improves Pass@K over compute-matched GRPO, and it outperforms related allocation baselines at large K. It is also drop-in compatible with other group-based estimators such as RLOO. Ablation studies indicate that the uniform prior used by HORA is competitive with five prompt-conditioned learned-prior alternatives.