Tingyu Zhu

Yuhang Wu, Zeyu Zheng, Tingyu Zhu

We formulate, analyze and solve the problem of best arm identification with fairness constraints on subpopulations (BAICS). Standard best arm identification problems aim at selecting an arm that has the largest expected reward where the expectation is taken over the entire population. The BAICS problem requires that an selected arm must be fair to all subpopulations (e.g., different ethnic groups, age groups, or customer types) by satisfying constraints that the expected reward conditional on every subpopulation needs to be larger than some thresholds. The BAICS problem aims at correctly identify, with high confidence, the arm with the largest expected reward from all arms that satisfy subpopulation constraints. We analyze the complexity of the BAICS problem by proving a best achievable lower bound on the sample complexity with closed-form representation. We then design an algorithm and prove that the algorithm's sample complexity matches with the lower bound in terms of order. A brief account of numerical experiments are conducted to illustrate the theoretical findings.

Tingyu Zhu, Yuhang Wu, Zeyu Zheng

Many high-stakes decisions in health care, public policy, and clinical development require committing to a single policy that will be applied uniformly across a heterogeneous population. Regulatory and fairness standards sometime requires that the chosen policy performs adequately in every pre-specified subpopulation, not only on average. We formalize this as a Selection of the Best with Fairness Constraints (SBFC) problem, in order to identify the policy with the highest average performance among those policies that meet a minimum per-subpopulation threshold. We establish an instance-specific lower bound on sample complexity of the SBFC problem. We then develop a Track-and-Stop with Constraints on Subpopulation (T-a-S-CS) algorithm that achieves the lower bound asymptotically. We extend the framework to general closed-set and penalty-based fairness specifications with matching guarantees. Numerical experiments and a case study using the International Stroke Trial demonstrate substantial efficiency gains over policy-level allocation baselines.

Nanshan Jia, Tingyu Zhu, Haoyu Liu et al.

We propose a class of structured diffusion models, in which the prior distribution is chosen as a mixture of Gaussians, rather than a standard Gaussian distribution. The specific mixed Gaussian distribution, as prior, can be chosen to incorporate certain structured information of the data. We develop a simple-to-implement training procedure that smoothly accommodates the use of mixed Gaussian as prior. Theory is provided to quantify the benefits of our proposed models, compared to the classical diffusion models. Numerical experiments with synthetic, image and operational data are conducted to show comparative advantages of our model. Our method is shown to be robust to mis-specifications and in particular suits situations where training resources are limited or faster training in real time is desired.

Tingyu Zhu, Haoyu Liu, Ziyu Wang et al.

Developing generative models to create or conditionally create symbolic music presents unique challenges due to the combination of limited data availability and the need for high precision in note pitch. To address these challenges, we introduce an efficient Fine-Grained Guidance (FGG) approach within diffusion models. FGG guides the diffusion models to generate music that aligns more closely with the control and intent of expert composers, which is critical to improve the accuracy, listenability, and quality of generated music. This approach empowers diffusion models to excel in advanced applications such as improvisation, and interactive music creation. We derive theoretical characterizations for both the challenges in symbolic music generation and the effects of the FGG approach. We provide numerical experiments and subjective evaluation to demonstrate the effectiveness of our approach. We have published a demo page to showcase performances, which enables real-time interactive generation.