Previous work has focused primarily on developing ML-based "meta-learners" that can provide point estimates of the conditional

Large Language Models that are evaluated on multiple metrics.

Stochastic dominance is an important concept in probability theory, econometrics and social choice theory for robustly modeling agents' preferences between random outcomes. While many works have been dedicated to the univariate case,little has been done in the multivariate scenario, wherein an agent has to decide between different multivariate outcomes. By exploiting a characterization of multivariate first stochastic dominance in terms of couplings, we introduce a statistic that assesses multivariate almost stochastic dominance under the framework of Optimal Transport with a smooth cost. Further, we introduce an entropic regularization of this statistic, and establish a central limit theorem (CLT) and consistency of the bootstrap procedure for the empirical statistic. Armed with this CLT, we propose a hypothesis testing framework as well as an efficient implementation using the Sinkhorn algorithm. We showcase our method in comparing and benchmarking Large Language Models that are evaluated on multiple metrics. Our multivariate stochastic dominance test allows us to capture the dependencies between the metrics in order to make an informed and statistically significant decision on the relative performance of the models.

We investigate the static portfolio selection problem of S-shaped and non-concave utility maximization under first-order and second-order stochastic dominance (SD) constraints. In many S-shaped utility optimization problems, one should require a liquidation boundary to guarantee the existence of a finite concave envelope function. A first-order SD (FSD) constraint can replace this requirement and provide an alternative for risk management. We explicitly solve the optimal solution under a general S-shaped utility function with a first-order stochastic dominance constraint. However, the second-order SD (SSD) constrained problem under non-concave utilities is difficult to solve analytically due to the invalidity of Sion's maxmin theorem. For this sake, we propose a numerical algorithm to obtain a plausible and sub-optimal solution for general non-concave utilities. The key idea is to detect the poor performance region with respect to the SSD constraints, characterize its structure and modify the distribution on that region to obtain (sub-)optimality. A key financial insight is that the decision maker should follow the SD constraint on the poor performance scenario while conducting the unconstrained optimal strategy otherwise. We provide numerical experiments to show that our algorithm effectively finds a sub-optimal solution in many cases. Finally, we develop an algorithm-guided piecewise-neural-network framework to learn the solution of the SSD problem, which demonstrates accelerated convergence compared to standard neural network approaches.

Stochastic multi-objective optimization (SMOOP) requires ranking multivariate distributions; yet, most empirical studies perform scalarization, which loses information and is unreliable. Based on the optimal transport theory, we introduce the center-outward q-dominance relation and prove it implies strong first-order stochastic dominance (FSD). Also, we develop an empirical test procedure based on q-dominance, and derive an explicit sample size threshold, $n^*(δ)$, to control the Type I error. We verify the usefulness of our approach in two scenarios: (1) as a ranking method in hyperparameter tuning; (2) as a selection method in multi-objective optimization algorithms. For the former, we analyze the final stochastic Pareto sets of seven multi-objective hyperparameter tuners on the YAHPO-MO benchmark tasks with q-dominance, which allows us to compare these tuners when the expected hypervolume indicator (HVI, the most common performance metric) of the Pareto sets becomes indistinguishable. For the latter, we replace the mean value-based selection in the NSGA-II algorithm with $q$-dominance, which shows a superior convergence rate on noise-augmented ZDT benchmark problems. These results establish center-outward q-dominance as a principled, tractable foundation for seeking truly stochastically dominant solutions for SMOOPs.

Ouyang et al., 2022, Bai et al., 2022], achieves this by learning a reward model on human preference

Large Language Models that are evaluated on multiple metrics.

Previous work has focused primarily on developing ML-based "meta-learners" that can provide point estimates of the conditional

The ability to discern subtle emotional cues is fundamental to human social intelligence. As artificial intelligence (AI) becomes increasingly common, AI's ability to recognize and respond to human emotions is crucial for effective human-AI interactions. In particular, whether such systems can match or surpass human experts remains to be seen. However, the emotional intelligence of AI, particularly multimodal large language models (MLLMs), remains largely unexplored. This study evaluates the emotion recognition abilities of MLLMs using the Reading the Mind in the Eyes Test (RMET) and its multiracial counterpart (MRMET), and compares their performance against human participants. Results show that, on average, MLLMs outperform humans in accurately identifying emotions across both tests. This trend persists even when comparing performance across low, medium, and expert-level performing groups. Yet when we aggregate independent human decisions to simulate collective intelligence, human groups significantly surpass the performance of aggregated MLLM predictions, highlighting the wisdom of the crowd. Moreover, a collaborative approach (augmented intelligence) that combines human and MLLM predictions achieves greater accuracy than either humans or MLLMs alone. These results suggest that while MLLMs exhibit strong emotion recognition at the individual level, the collective intelligence of humans and the synergistic potential of human-AI collaboration offer the most promising path toward effective emotional AI. We discuss the implications of these findings for the development of emotionally intelligent AI systems and future research directions.