Jianyu Xu

Jianyu Xu, Yining Wang, Xi Chen et al.

We study an online dynamic pricing problem where the potential demand at each time period $t=1,2,\ldots, T$ is stochastic and dependent on the price. However, a perishable inventory is imposed at the beginning of each time $t$, censoring the potential demand if it exceeds the inventory level. To address this problem, we introduce a pricing algorithm based on the optimistic estimates of derivatives. We show that our algorithm achieves $\tilde{O}(\sqrt{T})$ optimal regret even with adversarial inventory series. Our findings advance the state-of-the-art in online decision-making problems with censored feedback, offering a theoretically optimal solution against adversarial observations.

Jianyu Xu, Xuan Wang, Yu-Xiang Wang et al.

We study an online learning problem on dynamic pricing and resource allocation, where we make joint pricing and inventory decisions to maximize the overall net profit. We consider the stochastic dependence of demands on the price, which complicates the resource allocation process and introduces significant non-convexity and non-smoothness to the problem. To solve this problem, we develop an efficient algorithm that utilizes a "Lower-Confidence Bound (LCB)" meta-strategy over multiple OCO agents. Our algorithm achieves $\tilde{O}(\sqrt{Tmn})$ regret (for $m$ suppliers and $n$ consumers), which is optimal with respect to the time horizon $T$. Our results illustrate an effective integration of statistical learning methodologies with complex operations research problems.

Jundong Xu, Hao Fei, Yuhui Zhang et al.

Multimodal symbolic logical reasoning, which aims to deduce new facts from multimodal input via formal logic, is critical in high-stakes applications such as autonomous driving and medical diagnosis, as its rigorous, deterministic reasoning helps prevent serious consequences. To evaluate such capabilities of current state-of-the-art vision language models (VLMs), we introduce the first benchmark MuSLR for multimodal symbolic logical reasoning grounded in formal logical rules. MuSLR comprises 1,093 instances across 7 domains, including 35 atomic symbolic logic and 976 logical combinations, with reasoning depths ranging from 2 to 9. We evaluate 7 state-of-the-art VLMs on MuSLR and find that they all struggle with multimodal symbolic reasoning, with the best model, GPT-4.1, achieving only 46.8%. Thus, we propose LogiCAM, a modular framework that applies formal logical rules to multimodal inputs, boosting GPT-4.1's Chain-of-Thought performance by 14.13%, and delivering even larger gains on complex logics such as first-order logic. We also conduct a comprehensive error analysis, showing that around 70% of failures stem from logical misalignment between modalities, offering key insights to guide future improvements. All data and code are publicly available at https://llm-symbol.github.io/MuSLR.

Jianyu Xu, Bin Liu, Huadong Mo et al.

The cybersecurity of smart grids has become one of key problems in developing reliable modern power and energy systems. This paper introduces a non-stationary adversarial cost with a variation constraint for smart grids and enables us to investigate the problem of optimal smart grid protection against cyber attacks in a relatively practical scenario. In particular, a Bayesian multi-node bandit (MNB) model with adversarial costs is constructed and a new regret function is defined for this model. An algorithm called Thompson-Hedge algorithm is presented to solve the problem and the superior performance of the proposed algorithm is proven in terms of the convergence rate of the regret function. The applicability of the algorithm to real smart grid scenarios is verified and the performance of the algorithm is also demonstrated by numerical examples.

Jianyu Xu, Yu-Xiang Wang

Feature-based dynamic pricing is an increasingly popular model of setting prices for highly differentiated products with applications in digital marketing, online sales, real estate and so on. The problem was formally studied as an online learning problem [Javanmard & Nazerzadeh, 2019] where a seller needs to propose prices on the fly for a sequence of $T$ products based on their features $x$ while having a small regret relative to the best -- "omniscient" -- pricing strategy she could have come up with in hindsight. We revisit this problem and provide two algorithms (EMLP and ONSP) for stochastic and adversarial feature settings, respectively, and prove the optimal $O(d\log{T})$ regret bounds for both. In comparison, the best existing results are $O\left(\min\left\{\frac{1}{λ_{\min}^2}\log{T}, \sqrt{T}\right\}\right)$ and $O(T^{2/3})$ respectively, with $λ_{\min}$ being the smallest eigenvalue of $\mathbb{E}[xx^T]$ that could be arbitrarily close to $0$. We also prove an $Ω(\sqrt{T})$ information-theoretic lower bound for a slightly more general setting, which demonstrates that "knowing-the-demand-curve" leads to an exponential improvement in feature-based dynamic pricing.