Detecting symmetry from data is a fundamental problem in signal analysis, providing insight into underlying structure and constraints. When data emerge as trajectories of dynamical systems, symmetries encode structural properties of the dynamics that enable model reduction, principled comparison across conditions, and detection of regime changes. While recent optimal transport methods provide practical tools for data-driven symmetry detection in this setting, they rely on deterministic thresholds and lack uncertainty quantification, limiting robustness to noise and ability to resolve hierarchical symmetry structures. We present a Bayesian framework that formulates symmetry detection as probabilistic model selection over a lattice of candidate subgroups, using a Gibbs posterior constructed from Wasserstein distances between observed data and group-transformed copies. We establish three theoretical guarantees: $(i)$ a Bayesian Occam's razor favoring minimal symmetry consistent with data, $(ii)$ conjugation equivariance ensuring frame-independence, and $(iii)$ stability bounds under perturbations for robustness to noise. Posterior inference is performed via Metropolis-Hastings sampling and numerical experiments on equivariant dynamical systems and synthetic point clouds demonstrate accurate symmetry recovery under high noise and small sample sizes. An application to human gait dynamics reveals symmetry changes induced by mechanical constraints, demonstrating the framework's utility for statistical inference in biomechanical and dynamical systems.

Timely and reliable decision-making is vital for flood emergency response, yet it remains severely hindered by limited and imprecise situational awareness due to various budget and data accessibility constraints. Traditional flood management systems often rely on in-situ sensors to calibrate remote sensing-based large-scale flood depth forecasting models, and further take flood depth estimates to optimize flood response decisions. However, these approaches often take fixed, decision task-agnostic strategies to decide where to put in-situ sensors (e.g., maximize overall information gain) and train flood forecasting models (e.g., minimize average forecasting errors), but overlook that systems with the same sensing gain and average forecasting errors may lead to distinct decisions. To address this, we introduce a novel decision-focused framework that strategically selects locations for in-situ sensor placement and optimize spatio-temporal flood forecasting models to optimize downstream flood response decision regrets. Our end-to-end pipeline integrates four components: a contextual scoring network, a differentiable sensor selection module under hard budget constraints, a spatio-temporal flood reconstruction and forecasting model, and a differentiable decision layer tailored to task-specific objectives. Central to our approach is the incorporation of Implicit Maximum Likelihood Estimation (I-MLE) to enable gradient-based learning over discrete sensor configurations, and probabilistic decision heads to enable differentiable approximation to various constrained disaster response tasks.

Sampling multiple responses is a common way to improve LLM output quality, but it comes at the cost of additional computation. The key challenge is deciding when to stop generating new samples to balance accuracy gains against efficiency. To address this, we introduce BEACON (Bayesian Efficient Adaptive Criterion for Optimal N-stopping), a principled adaptive sampling framework grounded in Sequential Search with Bayesian Learning. BEACON sequentially generates responses from the policy LLM, updates posterior belief over reward distributions in real time without further training, and determines when to stop by weighing expected gains against computational cost. Sampling terminates once the marginal utility of further exploration no longer justifies the expense. We establish both theoretical optimality guarantees and practical tractability, and show empirically that BEACON reduces average sampling by up to 80% while maintaining response quality. We further demonstrate BEACON's utility for cost-efficient preference data generation and outline practical extensions, offering actionable insights for future researchers.

Reinforcement Learning with V erifiable Reward (RL VR) has significantly advanced the complex reasoning abilities of Large Language Models (LLMs). However, it struggles to break through the inherent capability boundaries of the base LLM, due to its essentially on-policy strategy coupled with LLM's immense action space and sparse reward. Critically, RL VR can lead to the capability boundary collapse, narrowing the LLM's problem-solving scope. To address this problem, we propose RL-PLUS, a novel hybrid-policy optimization approach for LLMs that synergizes internal exploitation with external data to achieve stronger reasoning capabilities and surpass the boundaries of base models. RL-PLUS integrates two core components, i.e., Multiple Importance Sampling to address distributional mismatch from external data, and Exploration-Based Advantage Function to guide the model towards high-value, unexplored reasoning paths. We provide both theoretical analysis and extensive experiments to demonstrate the superiority and gen-eralizability of our approach. Compared with existing RL VR methods, RL-PLUS achieves 1) state-of-the-art performance on six math reasoning benchmarks; 2) superior performance on six out-of-distribution reasoning tasks; 3) consistent and significant gains across diverse model families, with average relative improvements up to 69.2%. Moreover, the analysis of Pass@k curves indicates that RL-PLUS effectively resolves the capability boundary collapse problem.

The integration of vision-language models (VLMs) is driving a new generation of embodied agents capable of operating in human-centered environments. However, as deployment expands, these systems face growing safety risks, particularly when executing hazardous instructions. Current safety evaluation benchmarks remain limited: they cover only narrow scopes of hazards and focus primarily on final outcomes, neglecting the agent's full perception-planning-execution process and thereby obscuring critical failure modes. Therefore, we present SAFE, a benchmark for systematically assessing the safety of embodied VLM agents on hazardous instructions. SAFE comprises three components: SAFE-THOR, an extensible adversarial simulation sandbox with a universal adapter that maps high-level VLM outputs to low-level embodied controls, supporting diverse agent workflow integration; SAFE-VERSE, a risk-aware task suite inspired by Asimov's Three Laws of Robotics, comprising 45 adversarial scenarios, 1,350 hazardous tasks, and 9,900 instructions that span risks to humans, environments, and agents; and SAFE-DIAGNOSE, a multi-level and fine-grained evaluation protocol measuring agent performance across perception, planning, and execution. Applying SAFE to nine state-of-the-art VLMs and two embodied agent workflows, we uncover systematic failures in translating hazard recognition into safe planning and execution. Our findings reveal fundamental limitations in current safety alignment and demonstrate the necessity of a comprehensive, multi-stage evaluation for developing safer embodied intelligence.

N-agent ad hoc teamwork (NAHT) is a newly introduced challenge in multi-agent reinforcement learning, where controlled subteams of varying sizes must dynamically collaborate with varying numbers and types of unknown teammates without pre-coordination. The existing learning algorithm (POAM) considers only independent learning for its flexibility in dealing with a changing number of agents. However, independent learning fails to fully capture the inter-agent dynamics essential for effective collaboration. Based on our observation that transformers deal effectively with sequences with varying lengths and have been shown to be highly effective for a variety of machine learning problems, this work introduces a centralized, transformer-based method for N-agent ad hoc teamwork. Our proposed approach incorporates historical observations and actions of all controlled agents, enabling optimal responses to diverse and unseen teammates in partially observable environments. Empirical evaluation on a StarCraft II task demonstrates that MAT-NAHT outperforms POAM, achieving superior sample efficiency and generalization, without auxiliary agent-modeling objectives. Keywords: multi-agent reinforcement learning, ad hoc teamwork, transformers, agent modeling Acknowledgements This work has taken place in the Learning Agents Research Group (LARG) at UT Austin.

Graphical User Interface (GUI) agents show promising capabilities for automating computer-use tasks and facilitating accessibility, but existing interactive benchmarks are mostly English-only, covering web-use or Windows, Linux, and Android environments, but not macOS. macOS is a major OS with distinctive GUI patterns and exclusive applications. To bridge the gaps, we present macOSWorld, the first comprehensive benchmark for evaluating GUI agents on macOS. macOSWorld features 202 multilingual interactive tasks across 30 applications (28 macOS-exclusive), with task instructions and OS interfaces offered in 5 languages (English, Chinese, Arabic, Japanese, and Russian). As GUI agents are shown to be vulnerable to deception attacks, macOSWorld also includes a dedicated safety benchmarking subset. Our evaluation on six GUI agents reveals a dramatic gap: proprietary computer-use agents lead at above 30% success rate, while open-source lightweight research models lag at below 5\%, highlighting the need for macOS domain adaptation. Multilingual benchmarks also expose common weaknesses, especially in Arabic, with a 28.8% average degradation compared to English. Results from safety benchmarking also highlight that deception attacks are more general and demand immediate attention. Project page: https://macos-world.github.io.

Time-inhomogeneous finite-horizon Markov decision processes (MDP) are frequently employed to model decision-making in dynamic treatment regimes and other statistical reinforcement learning (RL) scenarios. These fields, especially healthcare and business, often face challenges such as high-dimensional state spaces and time-inhomogeneity of the MDP process, compounded by insufficient sample availability which complicates informed decision-making. To overcome these challenges, we investigate knowledge transfer within time-inhomogeneous finite-horizon MDP by leveraging data from both a target RL task and several related source tasks. We have developed transfer learning (TL) algorithms that are adaptable for both batch and online $Q$-learning, integrating valuable insights from offline source studies. The proposed transfer $Q$-learning algorithm contains a novel {\em re-targeting} step that enables {\em cross-stage transfer} along multiple stages in an RL task, besides the usual {\em cross-task transfer} for supervised learning. We establish the first theoretical justifications of TL in RL tasks by showing a faster rate of convergence of the $Q^*$-function estimation in the offline RL transfer, and a lower regret bound in the offline-to-online RL transfer under stage-wise reward similarity and mild design similarity across tasks. Empirical evidence from both synthetic and real datasets is presented to evaluate the proposed algorithm and support our theoretical results.

Sim2Real aims at training policies in high-fidelity simulation environments and effectively transferring them to the real world. Despite the developments of accurate simulators and Sim2Real RL approaches, the policies trained purely in simulation often suffer significant performance drops when deployed in real environments. This drop is referred to as the Sim2Real performance gap. Current Sim2Real RL methods optimize the simulator accuracy and variability as proxies for real-world performance. However, these metrics do not necessarily correlate with the real-world performance of the policy as established theoretically and empirically in the literature. We propose a novel framework to address this issue by directly adapting the simulator parameters based on real-world performance. We frame this problem as a bi-level RL framework: the inner-level RL trains a policy purely in simulation, and the outer-level RL adapts the simulation model and in-sim reward parameters to maximize real-world performance of the in-sim policy. We derive and validate in simple examples the mathematical tools needed to develop bi-level RL algorithms that close the Sim2Real performance gap.

This dissertation makes three main contributions. First, We identify a new connection between policy gradient and dynamic programming in MMDPs and propose the Coordinate Ascent Dynamic Programming (CADP) algorithm to compute a Markov policy that maximizes the discounted return averaged over the uncertain models. CADP adjusts model weights iteratively to guarantee monotone policy improvements to a local maximum. Second, We establish sufficient and necessary conditions for the exponential ERM Bellman operator to be a contraction and prove the existence of stationary deterministic optimal policies for ERM-TRC and EVaR-TRC. We also propose exponential value iteration, policy iteration, and linear programming algorithms for computing optimal stationary policies for ERM-TRC and EVaR-TRC. Third, We propose model-free Q-learning algorithms for computing policies with risk-averse objectives: ERM-TRC and EVaR-TRC. The challenge is that Q-learning ERM Bellman may not be a contraction. Instead, we use the monotonicity of Q-learning ERM Bellman operators to derive a rigorous proof that the ERM-TRC and the EVaR-TRC Q-learning algorithms converge to the optimal risk-averse value functions. The proposed Q-learning algorithms compute the optimal stationary policy for ERM-TRC and EVaR-TRC.