优化大模型推理的缓存调度，降低延迟并提升资源利用率。

Large Language Model (LLM) inference, where a trained model generates text one word at a time in response to user prompts, is a computationally intensive process requiring efficient scheduling to optimize latency and resource utilization. A key challenge in LLM inference is the management of the Key-Value (KV) cache, which reduces redundant computations but introduces memory constraints. In this work, we model LLM inference with KV cache constraints theoretically and propose a novel batching and scheduling algorithm that minimizes inference latency while effectively managing the KV cache's memory. More specifically, we make the following contributions. First, to evaluate the performance of online algorithms for scheduling in LLM inference, we introduce a hindsight optimal benchmark, formulated as an integer program that computes the minimum total inference latency under full future information. Second, we prove that no deterministic online algorithm can achieve a constant competitive ratio when the arrival process is arbitrary. Third, motivated by the computational intractability of solving the integer program at scale, we propose a polynomial-time online scheduling algorithm and show that under certain conditions it can achieve a constant competitive ratio. We also demonstrate our algorithm's strong empirical performance by comparing it to the hindsight optimal in a synthetic dataset. Finally, we conduct empirical evaluations on a real-world public LLM inference dataset, simulating the Llama2-70B model on A100 GPUs, and show that our algorithm significantly outperforms the benchmark algorithms. Overall, our results offer a path toward more sustainable and cost-effective LLM deployment.