arXiv subjects

John C. S. Lui

Publications and source records attributed to John C. S. Lui.

At least 19 recordsLinked to original sources

arXiv2026

Quality-Aware Cross-Model Computation Reuse

An intermediate result computed by one model can be reused by other models to perform their tasks. Existing work mainly focuses on practical execution, leaving a theoretical gap in optimizing reuse decisions. This optimization faces two challenges: quality uncertainty, because the effect of reuse on task quality is uncertain across models, and coupled scheduling, because tasks need to share the cost of preparing reusable results. These challenges compound each other: quality must be learned online, but the shared preparation structure makes scheduling NP-hard even with known quality, breaking the key assumption in existing methods. We formulate cross-model computation reuse as an online decision problem and develop the Quality-Aware Reuse Scheduling (QARS) algorithm to address it. For quality uncertainty, QARS learns task-dependent reuse quality from selected, possibly delayed feedback and uses optimistic estimates to guide decisions. For coupled scheduling, it jointly chooses which results to prepare and which tasks should use them, adapting scheduling accuracy to the remaining quality uncertainty. For the considered problem, our analysis separates learning and optimization error in regret and quantifies the tradeoff between scheduling accuracy and computation. Completing the quality-aware stopping rule yields $\widetilde O(\sqrt{T})$ regret while preserving feasibility. Experiments demonstrate the effectiveness of QARS in optimizing cross-model reuse, reducing the combined cost of computation and quality loss by up to 18.0%, and mean regret by 63.9% over the strongest scheduling baseline.

cs.IR↗

arXiv2026

On the Convergence of Stochastic Low-Rank Adaptation

Low-rank adaptation (LoRA) optimizes $J(B,A)=\mathcal L(W_\mathrm{base}+sBA)$ over two adapters $B \in \mathbb{R}^{m \times r}$ and $A \in \mathbb{R}^{r \times n}$ that form a low-rank update to a frozen pretrained weight matrix $W_\mathrm{base} \in \mathbb{R}^{m \times n}$. The prior analysis shows LoRA-GD takes $\exp\{\mathcal{O}(ε^{-2})\}$ oracle calls to find an $ε$-stationary point such that $\|\nabla J(B,A)\|\leq ε$ in the deterministic setting. We sharpen the analysis and show that $\mathcal{O}(ε^{-4})$ full-gradient evaluations suffice for the same first-order criterion. We further study stochastic LoRA under unbiased gradient estimates and finite variance. We propose LoRA-NSGDM, which finds an $ε$-stationary point with $\mathcal{O}(ε^{-8})$ stochastic oracle complexity. Under the additional mean-square smoothness condition, we use variance reduction strategy and propose LoRA-STORM, which improves the stochastic oracle complexity to $\mathcal{O}(ε^{-6})$.

cs.LG↗

arXiv2026

Quantum Multi-Armed Bandits and Linear Bandits: Lower Bounds and Algorithms

We study quantum multi-armed bandits (QMAB) and quantum linear bandits (QLB) in the model of Wan et al. [2023], where the learner queries each arm or action through a quantum reward oracle or its inverse. Prior work gives algorithms over horizon $T$ with regret $O(K\log T)$ for QMAB with $K$ arms and $O(d^2\operatorname{polylog} T)$ for $d$-dimensional QLB. This leaves open whether the $K\log T$ scale is unavoidable and whether the $d^2$ dependence can be improved. We prove the first minimax lower bounds of $Ω(K\log(T/K))$ for QMAB and $Ω(d\log(T/d))$ for finite-action QLB, resolving the question raised by Wan et al. [2023] of whether regret independent of $T$ is achievable. At the heart of our argument is a high-confidence single-arm quantum testing lower bound for distinguishing a fixed reward mean from an interval of alternatives, proved by the polynomial method and a Remez-type inequality for trigonometric polynomials. A bandit-to-testing reduction then lifts it to the QMAB lower bound, while a linear embedding gives the finite-action QLB lower bound. Complementing the lower bounds, we give a design-based elimination algorithm for finite-action QLB. When the action set has size $\operatorname{poly}(d)$, its regret is linear in $d$, improving the prior $d^2$ dependence and matching our lower bound up to polylogarithmic factors. The algorithm couples a low-bias low-variance quantum mean estimator with a small-support $G$-optimal design through a query allocation matched to the design weights. The design-based elimination reduces the dimension dependence from $d^2$ to $d^{3/2}$ when using Quantum Monte Carlo estimates. The low-variance estimator then makes reconstruction error aggregate through variance rather than worst-case absolute error, removing the remaining $\sqrt d$ factor.

cs.LG↗

arXiv2026

Optimal Convex Optimization with Inexact Second-Order Oracles

In this paper, we present a novel second-order method called Accelerated Inexact Newton Extragradient (AINE) for convex optimization using $δ$-inexact Hessians. We show that AINE can find an $ε$-solution in the inexact second-order oracle (ISO) complexity of $\mathcal{O}( (δ/ε)^{1/2} + (L_2/ε)^{2/7} )$ when the Hessian is $L_2$-Lipschitz continuous, and a better complexity of $\mathcal{O}( (δ/ε)^{1/2} + (L_3/ε)^{1/5} )$ when the third-order derivative is $L_3$-Lipschitz continuous. Notably, each iteration of our method can be conducted in the same running time as matrix multiplication up to logarithmic factors. In addition, we also establish matching oracle complexity lower bounds for both setups, demonstrating the optimality of our methods.

math.OC↗

arXiv2026

Quantum Speedups for Stochastic Optimization with Heavy-Tailed Noise

We study stochastic optimization with heavy-tailed gradient noise. We first propose a novel quantum mean estimator for multivariate heavy-tailed random variables that achieves lower query complexity than optimal classical estimators in the low-dimensional regime. We further develop an unbiased quantum mean estimator by applying a generalized multi-level Monte Carlo technique. We prove quantum lower bounds showing that, when the dimension $d$ of the random vector is small and can be viewed as a constant, our quantum estimators are optimal up to logarithmic factors. We further derive stronger dimension-dependent lower bounds for tail index $p>4/3$, showing that a nontrivial dependence on the dimension is unavoidable in the low-dimensional regime. Based on these estimators, we propose a quantum normalized stochastic gradient descent method ($\texttt{QNSGD}$), which finds an $ε$-stationary point using $\tilde{\mathcal{O}}\big(\sqrt d\,ε^{-\frac{5p-4}{2p-2}}\big)$ queries to the quantum stochastic gradient oracle. For a convex objective function, we propose a quantum projected stochastic gradient descent method ($\texttt{QPSGD}$), which computes a solution with $ε$-optimal solution using $\tilde{\mathcal{O}}\big(\sqrt d\,ε^{-\frac{3p-2}{2p-2}}+ε^{-2}\big)$ queries in expectation. These sharper bounds improve upon the classical lower bounds $Ω\big(ε^{-\frac{3p-2}{p-1}}\big)$ for nonconvex problems and $Ω\big(ε^{-\frac{p}{p-1}}\big)$ for convex problems in the low-dimensional regimes $d\lesssimε^{-\frac{p}{p-1}}$ and $d\lesssimε^{-\frac{2-p}{p-1}}$, respectively.

cs.LG↗

arXiv2026

Formal Verification for Deep Learning-based Power Control in Massive MIMO

Deep learning is a promising approach to optimize wireless communication by simplifying the search for near-optimal solutions. Prior studies on deep learning-based wireless communication optimization have explored supervised learning approaches that map raw user information, such as location or channel state information, to optimal power allocation vectors. While this approach demonstrates competitive performance, it is susceptible to adversarial attacks via input perturbations. Current defense mechanisms primarily rely on empirical methods, which do not provide formal guarantees of robustness. We fill this gap by proposing a formal verification framework to evaluate the robustness of deep learning-based power allocation in multi-cell massive multiple-input multiple-output (MIMO) systems against a wide range of potential adversarial input manipulations. To the best of our knowledge, this is the first attempt to formally verify deep neural networks in a regression setting with non-linear output constraints. We model the adversary's capabilities using hyper-rectangle constraints on their perturbation, adopt the abstraction-based bound-propagation technique (DeepPoly) to bound the interval of potential allocated powers, and formulate the minimum performance requirements as a constrained program for numerical feasibility analysis. Evaluation on publicly available datasets for power allocation in multi-cell massive MIMO indicates that a well-trained model can guarantee the local robustness under location perturbation by +-1m while retaining a maximum 1% optimality gap.

cs.NI↗

arXiv2026

Universal Tensor Methods for Monotone Variational Inequalities

We study monotone variational inequalities whose operators have Hölder continuous higher-order derivatives. For a fixed order $p\geq 2$, we assume that the $(p-1)$-th derivative of the monotone operator is Hölder continuous with parameter $ν\in[0,1]$ on a bounded closed convex set. We develop regularized tensor extragradient methods that combine a high-order Taylor approximation of the operator with an extragradient correction step. When the Hölder parameter $ν$ is known, our regularized tensor extragradient method finds an $ε$-weak solution using $\mathcal{O}(ε^{-2/(p+ν)})$ tensor-oracle calls. When $ν$ is unknown, we propose a universal tensor extragradient method whose tensor-oracle complexity is $\mathcal{O}(ε^{-2p/((p+1)(p-1+ν))})$.

math.OC↗

arXiv2026

Second-Order Bilevel Optimization with Accelerated Convergence Rates

This paper studies second-order methods for nonconvex-strongly-convex bilevel optimization. We propose a novel fully second-order bilevel approximation method (FSBA) that achieves an iteration complexity of $\tilde{\mathcal{O}}(ε^{-1.5})$ for finding the $(ε, \mathcal{O}(\sqrtε))$ second-order stationary point of the hyper-objective function. Our results demonstrate that second-order methods can achieve an accelerated convergence rate than first-order methods in bilevel optimization. To address the heavy computational cost associated with the second-order oracle, we introduce a lazy variant of FSBA, called LFSBA, which reuses second-order information across several iterations. We prove that LFSBA exhibits better computational complexity than FSBA by a factor of $\sqrt{d}$, where $d$ is the dimension of the problem. We also apply a similar idea to nonconvex strongly-concave minimax optimization and propose the lazy minimax cubic-regularized Newton (LMCN) method with better computational complexity compared to existing second-order methods.

math.OC↗

arXiv2026

Stochastic Non-Smooth Non-Convex Optimization with Decision-Dependent Distributions

We study stochastic zeroth-order optimization with decision-dependent distributions, where the sampling law depends on the current decision and only noisy function values are available. For the non-smooth non-convex setting, we establish an explicit convergence guarantee for finding a $(δ,ε)$-Goldstein stationary point with stochastic zeroth-order oracle (SZO) complexity of $\mathcal{O}(d^2δ^{-3}ε^{-3})$. In addition, we show that the above complexity can be achieved with single SZO feedback per iteration. We further extend the analysis to smooth and Hessian-Lipschitz objectives, obtaining complexities $\mathcal{O}(d^2ε^{-6})$ and $\mathcal{O}(d^2ε^{-9/2})$, respectively. In the Hessian-Lipschitz case, this improves the best-known dependence on $ε$ for decision-dependent zeroth-order methods by a factor of $ε^{-1/2}$.

math.OC↗

arXiv2026

A Scalable Distributed Quantum Optimization Framework via Factor Graph Paradigm

Distributed quantum computing (DQC) connects many small quantum processors into a single logical machine, offering a practical route to scalable quantum computation. However, most existing DQC paradigms are structure-agnostic. Circuit cutting proposed by Peng et al. in [Phys. Rev. Lett., Oct. 2020] reduces per-device qubits at the cost of exponential classical post-processing, while search-space partitioning proposed by Avron et al. in [Phys. Rev. A., Nov. 2021] distributes the workload but weakens Grover's ideal quadratic speedup. In this paper, we introduce a structure-aware framework for distributed quantum optimization that resolves this complexity-resource trade-off. We model the objective function as a factor graph and expose its sparse interaction structure. We cut the graph along its natural ``seams'', i.e., a separator of boundary variables, to obtain loosely coupled subproblems that fit on resource-constrained processors. We coordinate these subproblems with shared entanglement, so the network executes a single globally coherent search rather than independent local searches. We prove that this design preserves Grover-like scaling: for a search space of size $N$, our framework achieves $O(\sqrt{N})$ query complexity up to processors and separator dependent factors, while relaxing the qubit requirement of each processor. We extend the framework with a hierarchical divide-and-conquer strategy that scales to large-scale optimization problems and supports two operating modes: a fully coherent mode for fault-tolerant networks and a hybrid mode that inserts measurements to cap circuit depth on near-term devices. We validate the predicted query-entanglement trade-offs through simulations over diverse network topologies, and we show that structure-aware decomposition delivers a practical path to scalable distributed quantum optimization on quantum networks.

quant-ph↗

arXiv2026

Steering Frozen LLMs: Adaptive Social Alignment via Online Prompt Routing

Large language models (LLMs) are typically governed by post-training alignment (e.g., RLHF or DPO), which yields a largely static policy during deployment and inference. However, real-world safety is a full-lifecycle problem: static defenses degrade against evolving jailbreak behaviors, and fixed weights cannot adapt to pluralistic, time-varying safety norms. This motivates inference-time governance that steers behavior without costly retraining. To address this, we introduce the Consensus Clustering LinUCB Bandit (CCLUB), a unified framework for adaptive social alignment via system-prompt routing. CCLUB employs a conservative consensus clustering mechanism: it pools data only within the intersection of utility and safety similarity graphs, effectively preventing unsafe generalization across semantically proximal but risk-divergent contexts. Our theoretical analysis yields a sublinear regret guarantee, demonstrating near-optimal performance of CCLUB. Extensive experiments validate that CCLUB outperforms strong baselines, achieving a 10.98% improvement in cumulative reward and a 14.42% reduction in the average suboptimality gap.

cs.LG↗

arXiv2026

FGGM: Formal Grey-box Gradient Method for Attacking DRL-based MU-MIMO Scheduler

In 5G mobile communication systems, MU-MIMO has been applied to enhance spectral efficiency and support high data rates. To maximize spectral efficiency while providing fairness among users, the base station (BS) needs to selects a subset of users for data transmission. Given that this problem is NP-hard, DRL-based methods have been proposed to infer the near-optimal solutions in real-time, yet this approach has an intrinsic security problem. This paper investigates how a group of adversarial users can exploit unsanitized raw CSIs to launch a throughput degradation attack. Most existing studies only focused on systems in which adversarial users can obtain the exact values of victims' CSIs, but this is impractical in the case of uplink transmission in LTE/5G mobile systems. We note that the DRL policy contains an observation normalizer which has the mean and variance of the observation to improve training convergence. Adversarial users can then estimate the upper and lower bounds of the local observations including the CSIs of victims based solely on that observation normalizer. We develop an attacking scheme FGGM by leveraging polytope abstract domains, a technique used to bound the outputs of a neural network given the input ranges. Our goal is to find one set of intentionally manipulated CSIs which can achieve the attacking goals for the whole range of local observations of victims. Experimental results demonstrate that FGGM can determine a set of adversarial CSI vector controlled by adversarial users, then reuse those CSIs throughout the simulation to reduce the network throughput of a victim up to 70\% without knowing the exact value of victims' local observations. This study serves as a case study and can be applied to many other DRL-based problems, such as a knapsack-oriented resource allocation problems.

cs.NI↗

arXiv2026

Semantic Caching for Low-Cost LLM Serving: From Offline Learning to Online Adaptation

Large Language Models (LLMs) are revolutionizing how users interact with information systems, yet their high inference cost poses serious scalability and sustainability challenges. Caching inference responses, allowing them to be retrieved without another forward pass through the LLM, has emerged as one possible solution. Traditional exact-match caching, however, overlooks the semantic similarity between queries, leading to unnecessary recomputation. Semantic caching addresses this by retrieving responses based on semantic similarity, but introduces a fundamentally different cache eviction problem: one must account for mismatch costs between incoming queries and cached responses. Moreover, key system parameters, such as query arrival probabilities and serving costs, are often unknown and must be learned over time. Existing semantic caching methods are largely ad-hoc, lacking theoretical foundations and unable to adapt to real-world uncertainty. In this paper, we present a principled, learning-based framework for semantic cache eviction under unknown query and cost distributions. We formulate both offline optimization and online learning variants of the problem, and develop provably efficient algorithms with state-of-the-art guarantees. We also evaluate our framework on a synthetic dataset, showing that our proposed algorithms perform matching or superior performance compared with baselines.

cs.LG↗

arXiv2026

Faster, Smaller, and Smarter: Task-Aware Expert Merging for Online MoE Inference

Sparse Mixture of Experts (SMoE) has become a preferred architecture for scaling Transformer capacity without increasing computational cost, as it activates only a small subset of experts for each input. However, deploying such an approach for \textit{online inference} remains challenging due to the large size of a full SMoE model and the complexity of expert routing, especially in resource-constrained edge networks. Moreover, during the online inference, task information is often unavailable, making the task-level routing error-prone. In this work, we propose a novel tree-structured adaptive neural bandit router, \texttt{Tanbr}, to enable efficient and reliable online MoE inference. Instead of relying on explicit task tags, \texttt{Tanbr} estimates the task distribution over time from historical data and uses it to guide task-aware expert merging within a given pre-trained MoE. To handle the large continuous space of merging weights, \texttt{Tanbr} employs a binary tree to progressively partition the space and generate finer candidate weights. It then applies a neural bandit to learn the non-linear mapping from merging weight to model performance and decides optimal expert merging. We prove that \texttt{Tanbr} achieves a sublinear regret bound of {\small $\mathcal{O}(\sqrt{T} \log(T))$} over {\small $T$} rounds, despite operating over a continuous decision space, matching regret bounds compared to existing methods. Extensive experiments show that \texttt{Tanbr} reduces inference latency by at least {\small $45\%$} and memory usage by up to {\small $25\%$}, while maintaining a high accuracy compared to many state-of-the-art methods.

cs.LG↗

arXiv2025

FM-EAC: Feature Model-based Enhanced Actor-Critic for Multi-Task Control in Dynamic Environments

Model-based reinforcement learning (MBRL) and model-free reinforcement learning (MFRL) evolve along distinct paths but converge in the design of Dyna-Q [1]. However, modern RL methods still struggle with effective transferability across tasks and scenarios. Motivated by this limitation, we propose a generalized algorithm, Feature Model-Based Enhanced Actor-Critic (FM-EAC), that integrates planning, acting, and learning for multi-task control in dynamic environments. FM-EAC combines the strengths of MBRL and MFRL and improves generalizability through the use of novel feature-based models and an enhanced actor-critic framework. Simulations in both urban and agricultural applications demonstrate that FM-EAC consistently outperforms many state-of-the-art MBRL and MFRL methods. More importantly, different sub-networks can be customized within FM-EAC according to user-specific requirements.

cs.LG↗

arXiv2025

Time Matters: Enhancing Sequential Recommendations with Time-Guided Graph Neural ODEs

Sequential recommendation (SR) is widely deployed in e-commerce platforms, streaming services, etc., revealing significant potential to enhance user experience. However, existing methods often overlook two critical factors: irregular user interests between interactions and highly uneven item distributions over time. The former factor implies that actual user preferences are not always continuous, and long-term historical interactions may not be relevant to current purchasing behavior. Therefore, relying only on these historical interactions for recommendations may result in a lack of user interest at the target time. The latter factor, characterized by peaks and valleys in interaction frequency, may result from seasonal trends, special events, or promotions. These externally driven distributions may not align with individual user interests, leading to inaccurate recommendations. To address these deficiencies, we propose TGODE to both enhance and capture the long-term historical interactions. Specifically, we first construct a user time graph and item evolution graph, which utilize user personalized preferences and global item distribution information, respectively. To tackle the temporal sparsity caused by irregular user interactions, we design a time-guided diffusion generator to automatically obtain an augmented time-aware user graph. Additionally, we devise a user interest truncation factor to efficiently identify sparse time intervals and achieve balanced preference inference. After that, the augmented user graph and item graph are fed into a generalized graph neural ordinary differential equation (ODE) to align with the evolution of user preferences and item distributions. This allows two patterns of information evolution to be matched over time. Experimental results demonstrate that TGODE outperforms baseline methods across five datasets, with improvements ranging from 10% to 46%.

cs.IR↗

arXiv2025

A Multi-Agent Conversational Bandit Approach to Online Evaluation and Selection of User-Aligned LLM Responses

Prompt-based offline methods are commonly used to optimize large language model (LLM) responses, but evaluating these responses is computationally intensive and often fails to accommodate diverse response styles. This study introduces a novel online evaluation framework that employs a multi-agent conversational bandit model to select optimal responses while aligning with user preferences dynamically. To tackle challenges such as high-dimensional features, large response sets, adaptive conversational needs, and multi-device access, we propose MACO, Multi-Agent Conversational Online Learning, which comprises two key components: (1) \texttt{MACO-A}: Executed by local agents, it employs an online elimination mechanism to filter out low-quality responses. (2) \texttt{MACO-S}: Executed by the cloud server, it adaptively adjusts selection strategies based on aggregated preference data. An adaptive preference mechanism triggers asynchronous conversations to enhance alignment efficiency. Theoretical analysis demonstrates that MACO achieves near-optimal regret bounds, matching state-of-the-art performance in various degenerate cases. Extensive experiments utilizing Google and OpenAI text embedding models on the real-world datasets with different response styles, combined with Llama and GPT-4o, show that MACO consistently outperforms baseline methods by at least 8.29\% across varying response set sizes and numbers of agents.

cs.HC↗

arXiv2025

Trading Vector Data in Vector Databases

Vector data trading is essential for cross-domain learning with vector databases, yet it remains largely unexplored. We study this problem under online learning, where sellers face uncertain retrieval costs and buyers provide stochastic feedback to posted prices. Three main challenges arise: (1) heterogeneous and partial feedback in configuration learning, (2) variable and complex feedback in pricing learning, and (3) inherent coupling between configuration and pricing decisions. We propose a hierarchical bandit framework that jointly optimizes retrieval configurations and pricing. Stage I employs contextual clustering with confidence-based exploration to learn effective configurations with logarithmic regret. Stage II adopts interval-based price selection with local Taylor approximation to estimate buyer responses and achieve sublinear regret. We establish theoretical guarantees with polynomial time complexity and validate the framework on four real-world datasets, demonstrating consistent improvements in cumulative reward and regret reduction compared with existing methods.

cs.DB↗