We study the online routing problem in large language model serving, where requests arrive sequentially and must be dispatched to parallel decode workers under tight batch-size and KV-cache constraints. Unlike widely used routing heuristics that are not tied to explicit service-level objectives (SLOs) and offer limited control over latency-throughput trade-offs, we introduce a multi-objective optimization framework that formulates routing as an online linear programming with interpretable decision rewards. We apply an efficient bid-price control policy based on the online linear programming that admits requests when their SLO-weighted benefit exceeds their shadow prices. To meet millisecond decision requirements, we develop a warm-started, projected first-order updates that track the evolving dual shadow prices online with predictable runtime. We integrate our router into the Vidur simulator and demonstrate substantial improvements over standard baselines across multiple SLO regimes, including end-to-end latency, time-to-first-token, throughput, and tail performance. A big picture from our result: a science-based approach outperforms others based on heuristics.
A data-driven inverse optimization problem (DDIOP) is the problem of estimating the objective-function parameters (weights) that explain observed optimal-solution data, and it arises in many applications, including integer linear programming (ILP). It is known that, by applying g…
Portfolio optimization under uncertainty is inherently a multi-objective decision problem involving complex interactions among return, risk, market dynamics, and practical investment constraints. Existing reliability based portfolio optimization approaches primarily rely on stati…
Large Language Models (LLMs) offer a natural interface for translating human objectives into reward signals for cooperative multi-agent reinforcement learning (MARL), yet the training-time dynamics of this integration remain poorly understood. We show that dynamically updating LL…
A truckload carrier must accept or reject each load tender within seconds. The decision depends on fleet state, hours-of-service (HOS) clocks, and appointment windows. We model this as a weakly coupled dynamic program in which the resources relocate and carry clocks: serving a re…
Neural autoregressive solvers for the Multi-Attribute Vehicle Routing Problem (MAVRP) reach competitive cost but offer no per-step justification, a problem when dispatchers must validate, accept, or compare them. We open two complementary black boxes in one protocol. On the encod…
This paper studies real-time robust optimal control for uncertain nonlinear systems, where linear time-varying (LTV) approximations make planning tractable but require sound linearization error bounds (LEBs) to guarantee robust constraint satisfaction. We develop tight, different…