arXiv subjects

Liner Xiang

Publications and source records attributed to Liner Xiang.

3 recordsLinked to original sources

arXiv2026

Policy Optimization and Statistical Inference for Online Contextual Matrix Games

Online decision making often requires navigating a landscape shaped by both dynamic contexts and strategic interactions. In competitive pricing, for example, hotels must account for both dynamic contextual factors and rivals' strategic responses. Existing approaches address only part of this challenge: contextual bandits optimize single-agent decisions using observable features but ignore multi-player interactions, while online matrix games capture strategic behavior through Nash equilibrium but assume fixed payoffs, ignoring contextual information. How should agents act then when strategic payoffs evolve with contextual signals? We introduce \emph{online contextual matrix games} to integrate contextual information into multi-player online games. We further propose \emph{OnGameLearn}, an online learning algorithm that efficiently balances exploration and exploitation across both player actions and contexts. This approach comes with statistical guarantees: tail bounds for the estimated payoff matrix, the convergence of the estimated Nash equilibrium, the asymptotic normality of the parameter estimators, and the sublinear regret bound. We also develop the notion of \emph{policy value} in matrix games and develop a doubly robust, $\sqrt{T}$-consistent estimator for it. Across simulated studies and a real-world hotel pricing application, we find that OnGameLearn effectively navigates the intertwined challenges of strategic and contextual decision-making.

stat.ML↗

arXiv2026

Reasoning Is Not Free: Robust Adaptive Cost-Efficient Routing for LLM-as-a-Judge

Reasoning-capable large language models (LLMs) have recently been adopted as automated judges, but their benefits and costs in LLM-as-a-Judge settings remain unclear. Through controlled comparisons between reasoning and non-reasoning judges, we show that explicit reasoning substantially improves judgment accuracy on tasks requiring structured verification (e.g., math and coding), while offering limited or even negative gains on simpler evaluations and incurring significantly higher computational cost. These findings motivate that reasoning should be used selectively rather than universally, with awareness of possible distribution shift. We propose a Robust Adaptive Cost-Efficient Routing (RACER), which dynamically selects between reasoning and non-reasoning judges under a fixed budget by formulating routing as a constrained distributionally robust optimization problem. RACER explicitly accounts for distribution shift via a KL-divergence uncertainty set, admits an efficient primal--dual algorithm, and enjoys theoretical guarantees including uniqueness of the optimal policy and linear convergence. Extensive experiments show that RACER achieves superior accuracy--cost trade-offs under distribution shift.

cs.AI↗

arXiv2025

Foresighted Online Policy Optimization with Interference

Contextual bandits, which leverage the baseline features of sequentially arriving individuals to optimize cumulative rewards while balancing exploration and exploitation, are critical for online decision-making. Existing approaches typically assume no interference, where each individual's action affects only their own reward. Yet, such an assumption can be violated in many practical scenarios, and the oversight of interference can lead to short-sighted policies that focus solely on maximizing the immediate outcomes for individuals, which further results in suboptimal decisions and potentially increased regret over time. To address this significant gap, we introduce the foresighted online policy with interference (FRONT) that innovatively considers the long-term impact of the current decision on subsequent decisions and rewards. The proposed FRONT method employs a sequence of exploratory and exploitative strategies to manage the intricacies of interference, ensuring robust parameter inference and regret minimization. Theoretically, we establish a tail bound for the online estimator and derive the asymptotic distribution of the parameters of interest under suitable conditions on the interference network. We further show that FRONT attains sublinear regret under two distinct definitions, capturing both the immediate and consequential impacts of decisions, and we establish these results with and without statistical inference. The effectiveness of FRONT is further demonstrated through extensive simulations and a real-world application to urban hotel profits.

stat.ML↗