In a sharded blockchain, transactions are processed by a number of parallel committees. Thus, the transaction throughput can be largely boosted. A problem is that some groups of blockchain nodes consume large latency to form committees at the beginning of each epoch. Moreover, the heterogeneous processing capabilities of different committees also result in imbalanced consensus latency. Such imbalanced two-phase latency brings a large cumulative age to the transactions pending in transaction pool. Consequently, the blockchain throughput can be significantly degraded. We believe that a good committee-scheduling strategy can reduce the cumulative age of transactions, and thus benefit the throughput. However, we have not yet found a committee-scheduling mechanism that works for accelerating block formation in the context of blockchain sharding. To this end, this paper studies a fine-balanced tradeoff between the transactions’ throughput and their cumulative age in a large-scale sharded blockchain. We formulate this tradeoff as a utility-maximization problem, which is proved NP-hard. To solve this problem, we propose an online distributed Stochastic-Exploration (SE) algorithm, which guarantees a near-optimal system utility. We then rigorously analyze three theoretical properties of the proposed algorithm, including the theoretical convergence time, the probability of committees’ failure due to Sybil attacks, as well as the performance perturbation brought by committees’ offline events. Finally, we evaluate the proposed algorithm using the dataset of real-world blockchain transactions. The simulation results demonstrate that the proposed SE algorithm outperforms other baselines in terms of system utility, the valuable degree of yielded solutions, latency, and throughput performance.