Online truckload bid acceptance is a closed-loop stochastic decision problem in which a carrier or broker must, in real time, accept or reject a tendered load subject to operational feasibility, fleet repositioning costs, and opportunity cost against future demand. Public, reproducible benchmarks for this problem are scarce: existing routing benchmarks are static, while dynamic-fleet studies typically rely on private operator data. We introduce FreightBidBench, a public-calibrated, dependency-free, closed-loop benchmark in which feasibility (pickup reach, appointment windows, simplified hours-of-service, stochastic yard delays) and economics (service-failure penalty, terminal fleet value, daily price-premium window) are explicit, versioned, and reproducible from public Freight Analysis Framework and U.S. Department of Agriculture truck rate data. We develop two full-horizon hindsight ceilings: a simple LP style relaxation and a tighter Lagrangian-per-truck information relaxation that retains per-truck hours-of-service and sequencing structure and is 20.7% tighter than the LP relaxation on a tight-capacity scenario and 39.3% tighter on a scarce-capacity scenario. We introduce a parametric surrogate-rollout cascade with boundary-band and scarcity-pressure escalation triggers. On ten-seed tight and scarce scenarios, the best simple policy retains 91.0% and 86.5% of rollout profit and the standard-library surrogate 94.2% and 89.3%; a cascade at a single escalation band recovers roughly 98% on both at 40-56% of rollout's mean decision latency, and on the tight scenario is statistically indistinguishable from the rollout teacher (paired-bootstrap 95% CI on the profit delta spans zero).
LLM post-training often relies on reinforcement learning methods that sample multiple rollouts per prompt, yet most existing approaches use a fixed rollout budget for every prompt, despite large differences in the training signal different prompts provide. In this paper, we study adaptive rollout allocation under a fixed global budget and formulate the problem as online resource allocation with prompt-level diminishing returns. Our method, CERO, maintains a Beta posterior over each prompt's success probability and uses the posterior expected Bernoulli variance as a Bayesian estimate of the value of additional rollouts. We use this estimate to construct a concave, saturating utility over cumulative allocations, yielding an objective in which decisions across prompts and epochs are coupled by the global budget. Since the resulting objective is temporally nonseparable, we derive a Fenchel-dual reformulation and update both prompt-level and budget-level dual variables via projected online gradient descent. Under fixed prompt utilities, we prove an $O(\sqrt{K})$ regret bound against the offline allocation benchmark. Experiments on mathematical-reasoning problems show that CERO consistently outperforms GRPO across multiple open-weight LLMs and benchmarks, demonstrating that adaptive rollout budgeting can improve sample efficiency.