Recent studies on visual reinforcement learning (visual RL) have explored the use of 3D visual representations. However, none of these work has systematically compared the efficacy of 3D representations with 2D representations across different tasks, nor have they analyzed 3D representations from the perspective of agent-object / object-object relationship reasoning. In this work, we seek answers to the question of when and how do 3D neural networks that learn features in the 3D-native space provide a beneficial inductive bias for visual RL. We specifically focus on 3D point clouds, one of the most common forms of 3D representations. We systematically investigate design choices for 3D point cloud RL, leading to the development of a robust algorithm for various robotic manipulation and control tasks. Furthermore, through comparisons between 2D image vs 3D point cloud RL methods on both minimalist synthetic tasks and complex robotic manipulation tasks, we find that 3D point cloud RL can significantly outperform the 2D counterpart when agent-object / object-object relationship encoding is a key factor.

Recent successful generative models are trained by fitting a neural network to an a-priori defined tractable probability density path taking noise to training examples. In this paper we investigate the space of Gaussian probability paths, which includes diffusion paths as an instance, and look for an optimal member in some useful sense. In particular, minimizing the Kinetic Energy (KE) of a path is known to make particles' trajectories simple, hence easier to sample, and empirically improve performance in terms of likelihood of unseen data and sample generation quality. We investigate Kinetic Optimal (KO) Gaussian paths and offer the following observations: (i) We show the KE takes a simplified form on the space of Gaussian paths, where the data is incorporated only through a single, one dimensional scalar function, called the \emph{data separation function}. (ii) We characterize the KO solutions with a one dimensional ODE. (iii) We approximate data-dependent KO paths by approximating the data separation function and minimizing the KE. (iv) We prove that the data separation function converges to $1$ in the general case of arbitrary normalized dataset consisting of $n$ samples in $d$ dimension as $n/\sqrt{d}\rightarrow 0$. A consequence of this result is that the Conditional Optimal Transport (Cond-OT) path becomes \emph{kinetic optimal} as $n/\sqrt{d}\rightarrow 0$. We further support this theory with empirical experiments on ImageNet.

We introduce a principled study on establishing Gaussian processes (GPs) with inputs on the product of directional manifolds. A circular kernel is first presented according to the von Mises distribution. Based thereon, the so-called hypertoroidal von Mises (HvM) kernel is proposed to establish GPs on hypertori with consideration of correlational circular components. The proposed HvM kernel is demonstrated with multi-output GP regression for learning vector-valued functions defined on hypertori using the intrinsic coregionalization model. Analytical derivatives in hyperparameter optimization are provided for runtime-critical applications. For evaluation, we synthesize a ranging-based sensor network and employ the HvM-based GPs for data-driven recursive localization. The numerical results show that the HvM-based GP achieves superior tracking accuracy compared to parametric model and GPs based on conventional kernel designs.

We study preferential Bayesian optimization (BO) where reliable feedback is limited to pairwise comparison called duels. An important challenge in preferential BO, which uses the preferential Gaussian process (GP) model to represent flexible preference structure, is that the posterior distribution is a computationally intractable skew GP. The most widely used approach for preferential BO is Gaussian approximation, which ignores the skewness of the true posterior. Alternatively, Markov chain Monte Carlo (MCMC) based preferential BO is also proposed. In this work, we first verify the accuracy of Gaussian approximation, from which we reveal the critical problem that the predictive probability of duels can be inaccurate. This observation motivates us to improve the MCMC-based estimation for skew GP, for which we show the practical efficiency of Gibbs sampling and derive the low variance MC estimator. However, the computational time of MCMC can still be a bottleneck in practice. Towards building a more practical preferential BO, we develop a new method that achieves both high computational efficiency and low sample complexity, and then demonstrate its effectiveness through extensive numerical experiments.

Causal disentanglement seeks a representation of data involving latent variables that relate to one another via a causal model. A representation is identifiable if both the latent model and the transformation from latent to observed variables are unique. In this paper, we study observed variables that are a linear transformation of a linear latent causal model. Data from interventions are necessary for identifiability: if one latent variable is missing an intervention, we show that there exist distinct models that cannot be distinguished. Conversely, we show that a single intervention on each latent variable is sufficient for identifiability. Our proof uses a generalization of the RQ decomposition of a matrix that replaces the usual orthogonal and upper triangular conditions with analogues depending on a partial order on the rows of the matrix, with partial order determined by a latent causal model. We corroborate our theoretical results with a method for causal disentanglement that accurately recovers a latent causal model.

We propose policy gradient algorithms for solving a risk-sensitive reinforcement learning (RL) problem in on-policy as well as off-policy settings. We consider episodic Markov decision processes, and model the risk using the broad class of smooth risk measures of the cumulative discounted reward. We propose two template policy gradient algorithms that optimize a smooth risk measure in on-policy and off-policy RL settings, respectively. We derive non-asymptotic bounds that quantify the rate of convergence of our proposed algorithms to a stationary point of the smooth risk measure. As special cases, we establish that our algorithms apply to optimization of mean-variance and distortion risk measures, respectively.

This work deals with the heterogeneous semantic-native communication (SNC) problem. When agents do not share the same communication context, the effectiveness of contextual reasoning (CR) is compromised calling for agents to infer other agents' context. This article proposes a novel framework for solving the inverse problem of CR in SNC using two Bayesian inference methods, namely: Bayesian inverse CR (iCR) and Bayesian inverse linearized CR (iLCR). The first proposed Bayesian iCR method utilizes Markov Chain Monte Carlo (MCMC) sampling to infer the agent's context while being computationally expensive. To address this issue, a Bayesian iLCR method is leveraged which obtains a linearized CR (LCR) model by training a linear neural network. Experimental results show that the Bayesian iLCR method requires less computation and achieves higher inference accuracy compared to Bayesian iCR. Additionally, heterogeneous SNC based on the context obtained through the Bayesian iLCR method shows better communication effectiveness than that of Bayesian iCR. Overall, this work provides valuable insights and methods to improve the effectiveness of SNC in situations where agents have different contexts.

Researchers have integrated exploration techniques into multi-agent reinforcement learning (MARL) algorithms, drawing on their remarkable success in deep reinforcement learning. Nonetheless, exploration in MARL presents a more substantial challenge, as agents need to coordinate their efforts in order to achieve comprehensive state coverage. Reaching a unanimous agreement on which kinds of states warrant exploring can be a struggle for agents in this context. We introduce \textbf{M}ulti-agent \textbf{E}xploration based on \textbf{S}ub-state \textbf{E}ntropy (MESE) to address this limitation. This novel approach incentivizes agents to explore states cooperatively by directing them to achieve consensus via an extra team reward. Calculating the additional reward is based on the novelty of the current sub-state that merits cooperative exploration. MESE employs a conditioned entropy approach to select the sub-state, using particle-based entropy estimation to calculate the entropy. MESE is a plug-and-play module that can be seamlessly integrated into most existing MARL algorithms, which makes it a highly effective tool for reinforcement learning. Our experiments demonstrate that MESE can substantially improve the MAPPO's performance on various tasks in the StarCraft multi-agent challenge (SMAC).

Capturing stochastic behaviors in business and work processes is essential to quantitatively understand how nondeterminism is resolved when taking decisions within the process. This is of special interest in process mining, where event data tracking the actual execution of the process are related to process models, and can then provide insights on frequencies and probabilities. Variants of stochastic Petri nets provide a natural formal basis for this. However, when capturing processes, such nets need to be labelled with (possibly duplicated) activities, and equipped with silent transitions that model internal, non-logged steps related to the orchestration of the process. At the same time, they have to be analyzed in a finite-trace semantics, matching the fact that each process execution consists of finitely many steps. These two aspects impede the direct application of existing techniques for stochastic Petri nets, calling for a novel characterization that incorporates labels and silent transitions in a finite-trace semantics. In this article, we provide such a characterization starting from generalized stochastic Petri nets and obtaining the framework of labelled stochastic processes (LSPs). On top of this framework, we introduce different key analysis tasks on the traces of LSPs and their probabilities. We show that all such analysis tasks can be solved analytically, in particular reducing them to a single method that combines automata-based techniques to single out the behaviors of interest within a LSP, with techniques based on absorbing Markov chains to reason on their probabilities. Finally, we demonstrate the significance of how our approach in the context of stochastic conformance checking, illustrating practical feasibility through a proof-of-concept implementation and its application to different datasets.

The information transmission rate (ITR), or effective bit rate, is a popular and widely used information measurement metric, particularly popularized for SSVEP-based Brain-Computer (BCI) interfaces. By combining speed and accuracy into a single-valued parameter, this metric aids in the evaluation and comparison of various target identification algorithms across different BCI communities. In order to calculate ITR, it is customary to assume a uniform input distribution and an oversimplified channel model that is memoryless, stationary, and symmetrical in nature with discrete alphabet sizes. To accurately depict performance and inspire an end-to-end design for futuristic BCI designs, a more thorough examination and definition of ITR is therefore required. We model the symbiotic communication medium, hosted by the retinogeniculate visual pathway, as a discrete memoryless channel and use the modified capacity expressions to redefine the ITR. We leverage a result for directed graphs to characterize the relationship between the asymmetry of the transition statistics and the ITR gain due to the new definition, leading to potential bounds on data rate performance. On two well-known SSVEP datasets, we compared two cutting-edge target identification methods. Results indicate that the induced DM channel asymmetry has a greater impact on the actual perceived ITR than the change in input distribution. Moreover, it is demonstrated that the ITR gain under the new definition is inversely correlated with the asymmetry in the channel transition statistics. Individual input customizations are further shown to yield perceived ITR performance improvements. Finally, an algorithm is proposed to find the capacity of binary classification and further discussions are given to extend such results to multi-class case through ensemble techniques.