BALANCE: Hybrid Autoregressive-Speculative LLM Inference in Wireless Edge Networks

Speculative decoding accelerates large language model (LLM) inference by using a lightweight draft model to propose tokens and a larger target model to verify them in parallel. In distributed edge-cloud inference, however, draft length must be controlled online: longer drafts amortize communication delay but reduce token acceptance, whereas shorter drafts preserve acceptance but trigger more communication rounds. We formulate this tradeoff as a ratio-type optimal stopping problem and prove that the optimal draft length is a finite delay-monotone threshold. The analysis identifies a critical delay below which single-token speculation is optimal and shows that the optimal length grows only logarithmically with communication delay. For time-varying networks, we extend the model to Markov-modulated channels and establish, under a bounded horizon and monotone stopping-region conditions, a state-dependent threshold policy. For unknown environments, we propose UCB-SpecStop, an online control algorithm with gap-free and gap-dependent expected regret bounds of $O(L_{\max}\sqrt{K_{\max}T\log(K_{\max}T)})$ and $O(\sum_{k:Δ_k>0}L_{\max}^2\log(K_{\max}T)/Δ_k)$. We implement the method on a real edge-cloud testbed with a Jetson Orin Nano Super edge node and an RTX3090 Ti cloud node, using Qwen and Llama draft--target pairs. Experiments validate the predicted phase transition, with transition points near 83ms and 111~ms. Qwen matches the geometric prediction, while Llama requires empirical-prefix calibration due to heavy-head acceptance. Across the tested delay grid, UCB-SpecStop reduces per-token latency over SpecDec++ by up to 22.4%, approaches an offline oracle within 0.2--2.4% in communication-dominated regimes, improves over naive UCB by up to 7.5%, removes the 14.0--18.7% gap caused by static tuning under delay drift, and gains 3.0--6.8% with contextual channel-state information.

The recent growth of on-device Large Language Model (LLM) inference has driven significant interest in device-edge collaborative LLM inference. As a promising architecture, Speculative Decoding (SD) is increasingly adopted where a lightweight draft model rapidly generates candidate tokens to be verified by a powerful target model. However, a fundamental challenge lies in achieving per-token resource scheduling to effectively adapt SD paradigm to resource-constrained edge environment. This paper proposes a Generative Entropy- and Lyapunov-based Adaptive Token Offloading framework, named GELATO, to maximize decoding throughput under energy constraints in a device-edge collaborative SD system. Specifically, an outer drift-plus-penalty loop makes online decisions to establish a reference drafting budget, managing long-term energy-throughput trade-off. Further, a nested entropy-driven generation mechanism executes early exiting to adapt to per-token dynamic generative uncertainty. Theoretical analysis establishes a rigorous performance bound on long-term throughput for GELATO. Extensive evaluations demonstrate that GELATO achieves a globally optimal tradeoff, outperforming state-of-the-art distributed SD architectures by 64.98% in token throughput and reducing energy consumption by 47.47% under resource-constrained environments, while preserving LLM decoding quality.

Large Language Models (LLMs) have achieved remarkable success in natural language understanding and generation, but their deployment is constrained by high computational demands. Deploying smaller LLMs directly on the edge can circumvent this, but with degraded accuracy. Deploying smaller cloud-based big LLMs preserves performance, but at the cost of expensive per-token computation. We present a distributed inference framework, \our{}, that integrates speculative decoding (SD) across edge and cloud. A compact draft model deployed on the edge generates candidate tokens rapidly, and a large verifier model on the cloud validates these tokens in parallel. Accepted tokens are retained, while only rejections trigger verifier correction, substantially reducing the number of cloud queries. Our plug-and-play design shifts the bulk of computation to the edge, significantly lowers inference time and cloud cost, and preserves the accuracy of the big model without any retraining requirement. Our approach demonstrates a practical path toward scalable, cost-efficient, and accurate deployment of LLMs in real-world environments. Experimental results across multiple Natural Language Processing tasks using SpecBench and CNN/Dailymail datasets demonstrate that \our{} reduces the cloud model calls by $76\%$ with zero loss in accuracy as compared to the full model.