On the Optimality of Dilated Entropy and Lower Bounds for Online Learning in Extensive-Form Games

First-order methods (FOMs) are arguably the most scalable algorithms for equilibrium computation in large extensive-form games. To operationalize these methods, a distance-generating function, acting as a regularizer for the strategy space, must be chosen. The ratio between the strong convexity modulus and the diameter of the regularizer is a key parameter in the analysis of FOMs. A natural question is then: what is the optimal distance-generating function for extensive-form decision spaces? In this paper, we make a number of contributions, ultimately establishing that the weight-one dilated entropy (DilEnt) distance-generating function is optimal up to logarithmic factors. The DilEnt regularizer is notable due to its iterate-equivalence with Kernelized OMWU (KOMWU) -- the algorithm with state-of-the-art dependence on the game tree size in extensive-form games -- when used in conjunction with the online mirror descent (OMD) algorithm. However, the standard analysis for OMD is unable to establish such a result; the only current analysis is by appealing to the iterate equivalence to KOMWU. We close this gap by introducing a pair of primal-dual treeplex norms, which we contend form the natural analytic viewpoint for studying the strong convexity of DilEnt. Using these norm pairs, we recover the diameter-to-strong-convexity ratio that predicts the same performance as KOMWU. Along with a new regret lower bound for online learning in sequence-form strategy spaces, we show that this ratio is nearly optimal. Finally, we showcase our analytic techniques by refining the analysis of Clairvoyant OMD when paired with DilEnt, establishing an $\mathcal{O}(n \log |\mathcal{V}| \log T/T)$ approximation rate to coarse correlated equilibrium in $n$-player games, where $|\mathcal{V}|$ is the number of reduced normal-form strategies of the players, establishing the new state of the art.

CARES: A Comprehensive Benchmark of Trustworthiness in Medical Vision Language Models

Artificial intelligence has significantly impacted medical applications, particularly with the advent of Medical Large Vision Language Models (Med-LVLMs), sparking optimism for the future of automated and personalized healthcare. However, the trustworthiness of Med-LVLMs remains unverified, posing significant risks for future model deployment. In this paper, we introduce CARES and aim to comprehensively evaluate the Trustworthiness of Med-LVLMs across the medical domain. We assess the trustworthiness of Med-LVLMs across five dimensions, including trustfulness, fairness, safety, privacy, and robustness. CARES comprises about 41K question-answer pairs in both closed and open-ended formats, covering 16 medical image modalities and 27 anatomical regions. Our analysis reveals that the models consistently exhibit concerns regarding trustworthiness, often displaying factual inaccuracies and failing to maintain fairness across different demographic groups. Furthermore, they are vulnerable to attacks and demonstrate a lack of privacy awareness. We publicly release our benchmark and code in https://github.com/richard-peng-xia/CARES.

Calibrated Self-Rewarding Vision Language Models

Large Vision-Language Models (LVLMs) have made substantial progress by integrating pre-trained large language models (LLMs) and vision models through instruction tuning. Despite these advancements, LVLMs often exhibit the hallucination phenomenon, where generated text responses appear linguistically plausible but contradict the input image, indicating a misalignment between image and text pairs. This misalignment arises because the model tends to prioritize textual information over visual input, even when both the language model and visual representations are of high quality. Existing methods leverage additional models or human annotations to curate preference data and enhance modality alignment through preference optimization. These approaches may not effectively reflect the target LVLM's preferences, making the curated preferences easily distinguishable. Our work addresses these challenges by proposing the Calibrated Self-Rewarding (CSR) approach, which enables the model to self-improve by iteratively generating candidate responses, evaluating the reward for each response, and curating preference data for fine-tuning. In the reward modeling, we employ a step-wise strategy and incorporate visual constraints into the self-rewarding process to place greater emphasis on visual input. Empirical results demonstrate that CSR enhances performance and reduces hallucinations across ten benchmarks and tasks, achieving substantial improvements over existing methods by 7.62%. Our empirical results are further supported by rigorous theoretical analysis, under mild assumptions, verifying the effectiveness of introducing visual constraints into the self-rewarding paradigm. Additionally, CSR shows compatibility with different vision-language models and the ability to incrementally improve performance through iterative fine-tuning. Our data and code are available at https://github.com/YiyangZhou/CSR.

Settling Constant Regrets in Linear Markov Decision Processes

We study the constant regret guarantees in reinforcement learning (RL). Our objective is to design an algorithm that incurs only finite regret over infinite episodes with high probability. We introduce an algorithm, Cert-LSVI-UCB, for misspecified linear Markov decision processes (MDPs) where both the transition kernel and the reward function can be approximated by some linear function up to misspecification level $\zeta$. At the core of Cert-LSVI-UCB is an innovative certified estimator, which facilitates a fine-grained concentration analysis for multi-phase value-targeted regression, enabling us to establish an instance-dependent regret bound that is constant w.r.t. the number of episodes. Specifically, we demonstrate that for an MDP characterized by a minimal suboptimality gap $\Delta$, Cert-LSVI-UCB has a cumulative regret of $\tilde{\mathcal{O}}(d^3H^5/\Delta)$ with high probability, provided that the misspecification level $\zeta$ is below $\tilde{\mathcal{O}}(\Delta / (\sqrt{d}H^2))$. Remarkably, this regret bound remains constant relative to the number of episodes $K$. To the best of our knowledge, Cert-LSVI-UCB is the first algorithm to achieve a constant, instance-dependent, high-probability regret bound in RL with linear function approximation for infinite runs without relying on prior distribution assumptions. This not only highlights the robustness of Cert-LSVI-UCB to model misspecification but also introduces novel algorithmic designs and analytical techniques of independent interest.

Efficient Data Learning for Open Information Extraction with Pre-trained Language Models

Open Information Extraction (OpenIE) is a fundamental yet challenging task in Natural Language Processing, which involves extracting all triples (subject, predicate, object) from a given sentence. While labeling-based methods have their merits, generation-based techniques offer unique advantages, such as the ability to generate tokens not present in the original sentence. However, these generation-based methods often require a significant amount of training data to learn the task form of OpenIE and substantial training time to overcome slow model convergence due to the order penalty. In this paper, we introduce a novel framework, OK-IE, that ingeniously transforms the task form of OpenIE into the pre-training task form of the T5 model, thereby reducing the need for extensive training data. Furthermore, we introduce an innovative concept of Anchor to control the sequence of model outputs, effectively eliminating the impact of order penalty on model convergence and significantly reducing training time. Experimental results indicate that, compared to previous SOTA methods, OK-IE requires only 1/100 of the training data (900 instances) and 1/120 of the training time (3 minutes) to achieve comparable results.

On the Interplay Between Misspecification and Sub-optimality Gap in Linear Contextual Bandits

We study linear contextual bandits in the misspecified setting, where the expected reward function can be approximated by a linear function class up to a bounded misspecification level $\zeta>0$. We propose an algorithm based on a novel data selection scheme, which only selects the contextual vectors with large uncertainty for online regression. We show that, when the misspecification level $\zeta$ is dominated by $\tilde O (\Delta / \sqrt{d})$ with $\Delta$ being the minimal sub-optimality gap and $d$ being the dimension of the contextual vectors, our algorithm enjoys the same gap-dependent regret bound $\tilde O (d^2/\Delta)$ as in the well-specified setting up to logarithmic factors. In addition, we show that an existing algorithm SupLinUCB (Chu et al., 2011) can also achieve a gap-dependent constant regret bound without the knowledge of sub-optimality gap $\Delta$. Together with a lower bound adapted from Lattimore et al. (2020), our result suggests an interplay between misspecification level and the sub-optimality gap: (1) the linear contextual bandit model is efficiently learnable when $\zeta \leq \tilde O(\Delta / \sqrt{d})$; and (2) it is not efficiently learnable when $\zeta \geq \tilde \Omega({\Delta} / {\sqrt{d}})$. Experiments on both synthetic and real-world datasets corroborate our theoretical results.

OpenFE: Automated Feature Generation beyond Expert-level Performance

The goal of automated feature generation is to liberate machine learning experts from the laborious task of manual feature generation, which is crucial for improving the learning performance of tabular data. The major challenge in automated feature generation is to efficiently and accurately identify useful features from a vast pool of candidate features. In this paper, we present OpenFE, an automated feature generation tool that provides competitive results against machine learning experts. OpenFE achieves efficiency and accuracy with two components: 1) a novel feature boosting method for accurately estimating the incremental performance of candidate features. 2) a feature-scoring framework for retrieving effective features from a large number of candidates through successive featurewise halving and feature importance attribution. Extensive experiments on seven benchmark datasets show that OpenFE outperforms existing baseline methods. We further evaluate OpenFE in two famous Kaggle competitions with thousands of data science teams participating. In one of the competitions, features generated by OpenFE with a simple baseline model can beat 99.3\% data science teams. In addition to the empirical results, we provide a theoretical perspective to show that feature generation is beneficial in a simple yet representative setting. The code is available at https://github.com/ZhangTP1996/OpenFE.

Efficient Algorithms for Sparse Moment Problems without Separation

We consider the sparse moment problem of learning a $k$-spike mixture in high dimensional space from its noisy moment information in any dimension. We measure the accuracy of the learned mixtures using transportation distance. Previous algorithms either assume certain separation assumptions, use more recovery moments, or run in (super) exponential time. Our algorithm for the 1-dimension problem (also called the sparse Hausdorff moment problem) is a robust version of the classic Prony's method, and our contribution mainly lies in the analysis. We adopt a global and much tighter analysis than previous work (which analyzes the perturbation of the intermediate results of Prony's method). A useful technical ingredient is a connection between the linear system defined by the Vandermonde matrix and the Schur polynomial, which allows us to provide tight perturbation bound independent of the separation and may be useful in other contexts. To tackle the high dimensional problem, we first solve the 2-dimensional problem by extending the 1-dimension algorithm and analysis to complex numbers. Our algorithm for the high dimensional case determines the coordinates of each spike by aligning a 1-d projection of the mixture to a random vector and a set of 2d-projections of the mixture. Our results have applications to learning topic models and Gaussian mixtures, implying improved sample complexity results or running time over prior work.