Haoyuan Sun

Haoyuan Sun, Navid Azizan, Akash Srivastava et al. · mit

When machine learning models are trained on synthetic data and then deployed on real data, there is often a performance drop due to the distribution shift between synthetic and real data. In this paper, we introduce a new ensemble strategy for training downstream models, with the goal of enhancing their performance when used on real data. We generate multiple synthetic datasets by applying a differential privacy (DP) mechanism several times in parallel and then ensemble the downstream models trained on these datasets. While each synthetic dataset might deviate more from the real data distribution, they collectively increase sample diversity. This may enhance the robustness of downstream models against distribution shifts. Our extensive experiments reveal that while ensembling does not enhance downstream performance (compared with training a single model) for models trained on synthetic data generated by marginal-based or workload-based DP mechanisms, our proposed ensemble strategy does improve the performance for models trained using GAN-based DP mechanisms in terms of both accuracy and calibration of downstream models.

Yiwen Hou, Haoyuan Sun, Jinming Ma et al.

Offline reinforcement learning (RL) provides a promising approach to avoid costly online interaction with the real environment. However, the performance of offline RL highly depends on the quality of the datasets, which may cause extrapolation error in the learning process. In many robotic applications, an inaccurate simulator is often available. However, the data directly collected from the inaccurate simulator cannot be directly used in offline RL due to the well-known exploration-exploitation dilemma and the dynamic gap between inaccurate simulation and the real environment. To address these issues, we propose a novel approach to combine the offline dataset and the inaccurate simulation data in a better manner. Specifically, we pre-train a generative adversarial network (GAN) model to fit the state distribution of the offline dataset. Given this, we collect data from the inaccurate simulator starting from the distribution provided by the generator and reweight the simulated data using the discriminator. Our experimental results in the D4RL benchmark and a real-world manipulation task confirm that our method can benefit more from both inaccurate simulator and limited offline datasets to achieve better performance than the state-of-the-art methods.

Xufei Lv, Kehai Chen, Haoyuan Sun et al.

Alignment of large language models (LLMs) with human values has recently garnered significant attention, with prominent examples including the canonical yet costly Reinforcement Learning from Human Feedback (RLHF) and the simple Direct Preference Optimization (DPO). In this work, we demonstrate that both RLHF and DPO can be interpreted from the perspective of mutual information (MI) maximization, uncovering a profound connection to contrastive learning. Within this framework, both RLHF and DPO can be interpreted as methods that performing contrastive learning based on the positive and negative samples derived from base model, leveraging the Donsker-Varadhan (DV) lower bound on MI (equivalently, the MINE estimator). Such paradigm further illuminates why RLHF may not intrinsically incentivize reasoning capacities in LLMs beyond what is already present in the base model. Building on the perspective, we replace the DV/MINE bound with the Jensen-Shannon (JS) MI estimator and propose the Mutual Information Optimization (MIO). Comprehensive theoretical analysis and extensive empirical evaluations demonstrate that MIO mitigates the late-stage decline in chosen-likelihood observed in DPO, achieving competitive or superior performance across various challenging reasoning and mathematical benchmarks.

Haoyuan Sun, Ali Jadbabaie

The focus of this paper is on linear system identification in the setting where it is known that the underlying partially-observed linear dynamical system lies within a finite collection of known candidate models. We first consider the problem of identification from a given trajectory, which in this setting reduces to identifying the index of the true model with high probability. We characterize the finite-time sample complexity of this problem by leveraging recent advances in the non-asymptotic analysis of linear least-square methods in the literature. In comparison to the earlier results that assume no prior knowledge of the system, our approach takes advantage of the smaller hypothesis class and leads to the design of a learner with a dimension-free sample complexity bound. Next, we consider the switching control of linear systems, where there is a candidate controller for each of the candidate models and data is collected through interaction of the system with a collection of potentially destabilizing controllers. We develop a dimension-dependent criterion that can detect those destabilizing controllers in finite time. By leveraging these results, we propose a data-driven switching strategy that identifies the unknown parameters of the underlying system. We then provide a non-asymptotic analysis of its performance and discuss its implications on the classical method of estimator-based supervisory control.

Pablo Moscato, Haoyuan Sun, Mohammad Nazmul Haque

We present an approach for regression problems that employs analytic continued fractions as a novel representation. Comparative computational results using a memetic algorithm are reported in this work. Our experiments included fifteen other different machine learning approaches including five genetic programming methods for symbolic regression and ten machine learning methods. The comparison on training and test generalization was performed using 94 datasets of the Penn State Machine Learning Benchmark. The statistical tests showed that the generalization results using analytic continued fractions provides a powerful and interesting new alternative in the quest for compact and interpretable mathematical models for artificial intelligence.

Gautam Goel, Yiheng Lin, Haoyuan Sun et al.

We study online convex optimization in a setting where the learner seeks to minimize the sum of a per-round hitting cost and a movement cost which is incurred when changing decisions between rounds. We prove a new lower bound on the competitive ratio of any online algorithm in the setting where the costs are $m$-strongly convex and the movement costs are the squared $\ell_2$ norm. This lower bound shows that no algorithm can achieve a competitive ratio that is $o(m^{-1/2})$ as $m$ tends to zero. No existing algorithms have competitive ratios matching this bound, and we show that the state-of-the-art algorithm, Online Balanced Decent (OBD), has a competitive ratio that is $Ω(m^{-2/3})$. We additionally propose two new algorithms, Greedy OBD (G-OBD) and Regularized OBD (R-OBD) and prove that both algorithms have an $O(m^{-1/2})$ competitive ratio. The result for G-OBD holds when the hitting costs are quasiconvex and the movement costs are the squared $\ell_2$ norm, while the result for R-OBD holds when the hitting costs are $m$-strongly convex and the movement costs are Bregman Divergences. Further, we show that R-OBD simultaneously achieves constant, dimension-free competitive ratio and sublinear regret when hitting costs are strongly convex.