Artificial intelligence commonly refers to the science and engineering of artificial systems that can carry out tasks generally associated with requiring aspects of human intelligence, such as playing games, translating languages, and driving cars. In recent years, there have been exciting advances in learning-based, data-driven approaches towards AI, and machine learning and deep learning have enabled computer systems to perceive the world in unprecedented ways. Reinforcement learning has enabled breakthroughs in complex games such as Go and challenging robotics tasks such as quadrupedal locomotion. A key aspect of intelligence is to not only make predictions, but reason about the uncertainty in these predictions, and to consider this uncertainty when making decisions. This is what this manuscript on "Probabilistic Artificial Intelligence" is about. The first part covers probabilistic approaches to machine learning. We discuss the differentiation between "epistemic" uncertainty due to lack of data and "aleatoric" uncertainty, which is irreducible and stems, e.g., from noisy observations and outcomes. We discuss concrete approaches towards probabilistic inference and modern approaches to efficient approximate inference. The second part of the manuscript is about taking uncertainty into account in sequential decision tasks. We consider active learning and Bayesian optimization -- approaches that collect data by proposing experiments that are informative for reducing the epistemic uncertainty. We then consider reinforcement learning and modern deep RL approaches that use neural network function approximation. We close by discussing modern approaches in model-based RL, which harness epistemic and aleatoric uncertainty to guide exploration, while also reasoning about safety.

Online restless bandits extend classic contextual bandits by incorporating state transitions and budget constraints, representing each agent as a Markov Decision Process (MDP). This framework is crucial for finite-horizon strategic resource allocation, optimizing limited costly interventions for long-term benefits. However, learning the underlying MDP for each agent poses a major challenge in finite-horizon settings. To facilitate learning, we reformulate the problem as a scalable budgeted thresholding contextual bandit problem, carefully integrating the state transitions into the reward design and focusing on identifying agents with action benefits exceeding a threshold. We establish the optimality of an oracle greedy solution in a simple two-state setting, and propose an algorithm that achieves minimax optimal constant regret in the online multi-state setting with heterogeneous agents and knowledge of outcomes under no intervention. We numerically show that our algorithm outperforms existing online restless bandit methods, offering significant improvements in finite-horizon performance.

This paper presents Deep Dynamic Probabilistic Canonical Correlation Analysis (D2PCCA), a model that integrates deep learning with probabilistic modeling to analyze nonlinear dynamical systems. Building on the probabilistic extensions of Canonical Correlation Analysis (CCA), D2PCCA captures nonlinear latent dynamics and supports enhancements such as KL annealing for improved convergence and normalizing flows for a more flexible posterior approximation. D2PCCA naturally extends to multiple observed variables, making it a versatile tool for encoding prior knowledge about sequential datasets and providing a probabilistic understanding of the system's dynamics. Experimental validation on real financial datasets demonstrates the effectiveness of D2PCCA and its extensions in capturing latent dynamics.

In cooperative multi-agent reinforcement learning (MARL), learning effective policies is challenging when global rewards are sparse and delayed. This difficulty arises from the need to assign credit across both agents and time steps, a problem that existing methods often fail to address in episodic, long-horizon tasks. We propose Temporal-Agent Reward Redistribution $TAR^2$, a novel approach that decomposes sparse global rewards into agent-specific, time-step-specific components, thereby providing more frequent and accurate feedback for policy learning. Theoretically, we show that $TAR^2$ (i) aligns with potential-based reward shaping, preserving the same optimal policies as the original environment, and (ii) maintains policy gradient update directions identical to those under the original sparse reward, ensuring unbiased credit signals. Empirical results on two challenging benchmarks, SMACLite and Google Research Football, demonstrate that $TAR^2$ significantly stabilizes and accelerates convergence, outperforming strong baselines like AREL and STAS in both learning speed and final performance. These findings establish $TAR^2$ as a principled and practical solution for agent-temporal credit assignment in sparse-reward multi-agent systems.

Spin systems form an important class of undirected graphical models. For two Gibbs distributions $\mu$ and $\nu$ induced by two spin systems on the same graph $G = (V, E)$, we study the problem of approximating the total variation distance $d_{TV}(\mu,\nu)$ with an $\epsilon$-relative error. We propose a new reduction that connects the problem of approximating the TV-distance to sampling and approximate counting. Our applications include the hardcore model and the antiferromagnetic Ising model in the uniqueness regime, the ferromagnetic Ising model, and the general Ising model satisfying the spectral condition. Additionally, we explore the computational complexity of approximating the total variation distance $d_{TV}(\mu_S,\nu_S)$ between two marginal distributions on an arbitrary subset $S \subseteq V$. We prove that this problem remains hard even when both $\mu$ and $\nu$ admit polynomial-time sampling and approximate counting algorithms.

This position paper argues that AI agents should be regulated based on the sequence of actions they autonomously take. AI agents with long-term planning and strategic capabilities can pose significant risks of human extinction and irreversible global catastrophes. While existing regulations often focus on computational scale as a proxy for potential harm, we contend that such measures are insufficient for assessing the risks posed by AI agents whose capabilities arise primarily from inference-time computation. To support our position, we discuss relevant regulations and recommendations from AI scientists regarding existential risks, as well as the advantages of action sequences over existing impact measures that require observing environmental states.

The humanoid robot (Unitree G1) demonstrates diverse agile whole-body skills, showcasing the control policies' agility: (a) Cristiano Ronaldo's signature celebration involving a jump with a 180-degree mid-air rotation; (b) LeBron James's "Silencer" celebration involving single-leg balancing; and (c) Kobe Bryant's famous fadeaway jump shot involving single-leg jumping and landing; (d) 1.5m-forward jumping; (e) Leg stretching; (f) 1.3m-side jumping. Abstract -- Humanoid robots hold the potential for unparalleled versatility for performing human-like, whole-body skills. However, achieving agile and coordinated whole-body motions remains a significant challenge due to the dynamics mismatch between simulation and the real world. Existing approaches, such as system identification (SysID) and domain randomization (DR) methods, often rely on labor-intensive parameter tuning or result in overly conservative policies that sacrifice agility. In this paper, we present ASAP (Aligning Simulation and Real Physics), a two-stage framework designed to tackle the dynamics mismatch and enable agile humanoid whole-body skills. Then ASAP fine-tunes pre-trained policies with the delta action model integrated into the simulator to align effectively with real-world dynamics. We evaluate ASAP across three transfer scenarios--IsaacGym to IsaacSim, IsaacGym to Genesis, and IsaacGym to the real-world Unitree G1 humanoid robot. Our approach significantly improves agility and whole-body coordination across various dynamic motions, reducing tracking error compared to SysID, DR, and delta dynamics learning baselines. ASAP enables highly agile motions that were previously difficult to achieve, demonstrating the potential of delta action learning in bridging simulation and real-world dynamics. These results suggest a promising sim-to-real direction for developing more expressive and agile humanoids. I NTRODUCTION For decades, we have envisioned humanoid robots achieving or even surpassing human-level agility. However, most prior work [46, 74, 47, 73, 107, 19, 95, 50] has primarily focused on locomotion, treating the legs as a means of mobility. Recent studies [10, 25, 24, 26, 32] have introduced whole-body expressiveness in humanoid robots, but these efforts have primarily focused on upper-body motions and have yet to achieve the agility seen in human movement.

Weaknesses: A few comments that are needed to be addressed: 1) The first comment is about the presentation of the derivations. There are steps in the appendix, and also in the main text that are skipped. Some of them took me a while to rederive, some I couldn't spend more time to rederive. Some steps are also taken as granted in the main text. It is useful to elaborate on them more.

Summary and Contributions: This paper establishes a concentration inequality in operator norm for the sample co-occurrence matrix C of a regular finite-state Markov chain. This is the matrix whose (i,j) entry counts the fraction of times states i and j co-occur within a time window of fixed size T, with a potential weighting by the difference of their occurrence times. The probability that C-E[C] exceeds eps is shown to be exponentially small in eps 2 * L, where L is the sample size (i.e. the total length of the chain). This concentration inequality is established as a corollary of a general result for the concentration of sample averages for a bounded symmetric-matrix-valued function applied to samples from an ergodic Markov chain. This general result is of independent interest.

This work tackles the problem of estimating the co-occurrence matrix of a Markov chain. The referees were unanimous in the assessment that this is a solid contribution, worthy of being accepted. The only reservations were some missing references in related work, which the authors agreed to discuss in the revision.