arXiv subjects

Guokai Li

Publications and source records attributed to Guokai Li.

4 recordsLinked to original sources

arXiv2026

Infrequent Resolving Algorithm for Online Linear Programming

Online linear programming (OLP) has gained significant attention from both researchers and practitioners due to its extensive applications such as online auctions, network revenue management, order fulfillment and advertising. Existing OLP algorithms fall into two categories: LP-based algorithms and LP-free algorithms. The former typically guarantees better performance but requires solving a large number of LPs, which could be computationally expensive. In contrast, LP-free algorithms only require first-order computations but induce a worse performance. In this work, we bridge the gap between these two extremes by proposing a well-performing algorithm that solves LPs at a few selected time points and conducts first-order computations at other time points. Specifically, for the case where the inputs are drawn from an unknown finite-support distribution, the proposed algorithm achieves a constant regret (even for the hard "degenerate" case) while solving LPs only $O(\log\log T)$ times over the time horizon $T$. Moreover, when we are allowed to solve LPs only $M$ times, we design the corresponding schedule such that the proposed algorithm can guarantee a nearly $O\left(T^{(1/2)^{M-1}}\right)$ regret. Our work highlights the value of resolving both at the beginning and the end of the selling horizon, and provides a novel framework to prove the performance guarantee of the proposed policy under different infrequent resolving schedules. Numerical experiments are conducted to demonstrate the efficiency of the proposed algorithms.

cs.DS↗

arXiv2026

Self-Improving Neural-Guided Pruning: A Graph Neural Network Framework for Scalable Mixed Bundle Pricing

Mixed bundle pricing is a classic revenue management problem arising in industries such as e-commerce, tourism, and video games. It refers to designing product combinations (i.e., bundles) and determining their prices to maximize expected profit. Exact mixed bundling models capture this structure but become computationally intractable because the number of candidate bundles grows exponentially with the number of products. We develop a graph neural network (GNN)-guided pruning-then-optimization framework for bundle pricing with (non-)additive valuations. The method represents each instance as a compact segment-product graph, predicts segment-product inclusion probabilities, and accordingly prunes the exponential bundle space into a small candidate family; the final prices and bundle offerings are obtained by solving the mixed bundling formulation over the retained bundles, possibly refined by a GNN-guided local search. Because exact labels are available only at small scales, we further propose an iterative self-improvement procedure: the current GNN policies generate high-quality solutions on large-scale instances, which serve as near-optimal labels for training a stronger model at larger scales. Theoretically, we show that under mild conditions the proposed edge-output GNN class is expressive enough to represent the optimal product-assignment mapping, justifying the edge-level learning target. Numerical experiments show that the fastest proposed policy delivers 13-21% higher profit than bundle-size pricing on instances with up to 100 products at about 2% of its runtime.

cs.LG↗

arXiv2026

From Small to Large: A Graph Convolutional Network Approach for Solving Assortment Optimization Problems

Assortment optimization seeks to select a subset of substitutable products, subject to constraints, to maximize expected revenue. The problem is NP-hard due to its combinatorial and nonlinear nature and arises frequently in industries such as e-commerce, where platforms must solve thousands of such problems each minute. We propose a graph convolutional network (GCN) framework to efficiently solve constrained assortment optimization problems. Our approach constructs a graph representation of the problem, trains a GCN to learn the mapping from problem parameters to optimal assortments, and develops three inference policies based on the GCN's output. Owing to the GCN's ability to generalize across instance sizes, patterns learned from small-scale samples can be transferred to large-scale problems. Theoretical results are established to show the expressive power of the proposed GCN, and explain the underlying mechanism of the size generalization ability. Numerical experiments show that a GCN trained on instances with 20 products achieves over 85% of the optimal revenue on problems with up to 2,000 products within seconds, outperforming existing heuristics in both accuracy and efficiency. We further extend the framework to settings with an unknown choice model using transaction data and demonstrate similar performance and scalability.

cs.LG↗

arXiv2026

Asymptotically Optimal Sequential Testing with Heterogeneous LLMs

We study a Bayesian binary sequential hypothesis testing problem with multiple large language models (LLMs). Each LLM $j$ has per-query cost $c_j>0$, random waiting time with mean $μ_j>0$ and sub-Gaussian tails, and \emph{asymmetric} accuracies: the probability of returning the correct label depends on the true hypothesis $θ\in\{A,B\}$ and needs not be the same under $A$ and $B$. This asymmetry induces two distinct information rates $(I_{j,A}, I_{j,B})$ per LLM, one under each hypothesis. The decision-maker chooses LLMs sequentially, observes their noisy binary answers, and stops when the posterior probability of one hypothesis exceeds $1-α$. The objective is to minimize the sum of expected query cost and expected waiting cost, $\mathbb{E}[C_π] + \mathbb{E}[g(W_π)]$, where $C_π$ is the total query cost, $W_π$ is the total waiting time and $g$ is a polynomial function (e.g., $g(x)=x^ρ$ with $ρ\ge 1$). We prove that as the error tolerance $α\to0$, the optimal policy is asymptotically equivalent to one that uses at most two LLMs. In this case, a single-LLM policy is \emph{not} generically optimal: optimality now requires exploiting a two-dimensional tradeoff between information under $A$ and information under $B$. Any admissible policy induces an expected information-allocation vector in $\mathbb{R}_+^2$, and we show that the optimal allocation lies at an extreme point of the associated convex set when $α$ is relatively small, and hence uses at most two LLMs. We construct belief-dependent policies that first mix between two LLMs when the posterior is ambiguous, and then switch to a single "specialist" LLM when the posterior is sufficiently close to one of the hypotheses. These policies match the universal lower bound up to a $(1+o(1))$ factor as $α\rightarrow 0$.

cs.DS↗