Training generative models to sample from unnormalized density functions is an important and challenging task in machine learning. Traditional training methods often rely on the reverse Kullback-Leibler (KL) divergence due to its tractability. However, the mode-seeking behavior of reverse KL hinders effective approximation of multi-modal target distributions. To address this, we propose to minimize the reverse KL along diffusion trajectories of both model and target densities. We refer to this objective as the reverse diffusive KL divergence, which allows the model to capture multiple modes. Leveraging this objective, we train neural samplers that can efficiently generate samples from the target distribution in one step. We demonstrate that our method enhances sampling performance across various Boltzmann distributions, including both synthetic multi-modal densities and n-body particle systems.

Eliciting a high-dimensional probability distribution from an expert via noisy judgments is notoriously challenging, yet useful for many applications, such as prior elicitation and reward modeling. We introduce a method for eliciting the expert's belief density as a normalizing flow based solely on preferential questions such as comparing or ranking alternatives. This allows eliciting in principle arbitrarily flexible densities, but flow estimation is susceptible to the challenge of collapsing or diverging probability mass that makes it difficult in practice. We tackle this problem by introducing a novel functional prior for the flow, motivated by a decision-theoretic argument, and show empirically that the belief density can be inferred as the function-space maximum a posteriori estimate. We demonstrate our method by eliciting multivariate belief densities of simulated experts, including the prior belief of a general-purpose large language model over a real-world dataset.

Graphs are a highly expressive abstraction for modeling entities and their relations, such as molecular structures, social networks, and traffic networks. Deep Graph Networks (DGNs) have emerged as a family of deep learning models that can effectively process and learn such structured information. However, learning effective information propagation patterns within DGNs remains a critical challenge that heavily influences the model capabilities, both in the static domain and in the temporal domain (where features and/or topology evolve). Given this challenge, this thesis investigates the dynamics of information propagation within DGNs for static and dynamic graphs, focusing on their design as dynamical systems. Throughout this work, we provide theoretical and empirical evidence to demonstrate the effectiveness of our proposed architectures in propagating and preserving long-term dependencies between nodes, and in learning complex spatio-temporal patterns from irregular and sparsely sampled dynamic graphs. In summary, this thesis provides a comprehensive exploration of the intersection between graphs, deep learning, and dynamical systems, offering insights and advancements for the field of graph representation learning and paving the way for more effective and versatile graph-based learning models.

This paper addresses the problem of learning optimal control policies for systems with uncertain dynamics and high-level control objectives specified as Linear Temporal Logic (LTL) formulas. Uncertainty is considered in the workspace structure and the outcomes of control decisions giving rise to an unknown Markov Decision Process (MDP). Existing reinforcement learning (RL) algorithms for LTL tasks typically rely on exploring a product MDP state-space uniformly (using e.g., an $\epsilon$-greedy policy) compromising sample-efficiency. This issue becomes more pronounced as the rewards get sparser and the MDP size or the task complexity increase. In this paper, we propose an accelerated RL algorithm that can learn control policies significantly faster than competitive approaches. Its sample-efficiency relies on a novel task-driven exploration strategy that biases exploration towards directions that may contribute to task satisfaction. We provide theoretical analysis and extensive comparative experiments demonstrating the sample-efficiency of the proposed method. The benefit of our method becomes more evident as the task complexity or the MDP size increases.

The Bayesian two-step change point detection method is popular for the Hawkes process due to its simplicity and intuitiveness. However, the non-conjugacy between the point process likelihood and the prior requires most existing Bayesian two-step change point detection methods to rely on non-conjugate inference methods. These methods lack analytical expressions, leading to low computational efficiency and impeding timely change point detection. To address this issue, this work employs data augmentation to propose a conjugate Bayesian two-step change point detection method for the Hawkes process, which proves to be more accurate and efficient. Extensive experiments on both synthetic and real data demonstrate the superior effectiveness and efficiency of our method compared to baseline methods. Additionally, we conduct ablation studies to explore the robustness of our method concerning various hyperparameters.

Recent works have introduced LEAPS and HPRL, systems that learn latent spaces of domain-specific languages, which are used to define programmatic policies for partially observable Markov decision processes (POMDPs). These systems induce a latent space while optimizing losses such as the behavior loss, which aim to achieve locality in program behavior, meaning that vectors close in the latent space should correspond to similarly behaving programs. In this paper, we show that the programmatic space, induced by the domain-specific language and requiring no training, presents values for the behavior loss similar to those observed in latent spaces presented in previous work. Moreover, algorithms searching in the programmatic space significantly outperform those in LEAPS and HPRL. To explain our results, we measured the "friendliness" of the two spaces to local search algorithms. We discovered that algorithms are more likely to stop at local maxima when searching in the latent space than when searching in the programmatic space. This implies that the optimization topology of the programmatic space, induced by the reward function in conjunction with the neighborhood function, is more conducive to search than that of the latent space. This result provides an explanation for the superior performance in the programmatic space.

In reinforcement learning, agents often learn policies for specific tasks without the ability to generalize this knowledge to related tasks. This paper introduces an algorithm that attempts to address this limitation by decomposing neural networks encoding policies for Markov Decision Processes into reusable sub-policies, which are used to synthesize temporally extended actions, or options. We consider neural networks with piecewise linear activation functions, so that they can be mapped to an equivalent tree that is similar to oblique decision trees. Since each node in such a tree serves as a function of the input of the tree, each sub-tree is a sub-policy of the main policy. We turn each of these sub-policies into options by wrapping it with while-loops of varied number of iterations. Given the large number of options, we propose a selection mechanism based on minimizing the Levin loss for a uniform policy on these options. Empirical results in two grid-world domains where exploration can be difficult confirm that our method can identify useful options, thereby accelerating the learning process on similar but different tasks.

We propose a novel tomographic method, nonlinear Gaussian process tomography (nonlinear GPT) that employs the Laplace approximation to ensure the non-negative physical quantity, such as the emissivity of plasma optical diagnostics. This new method implements a logarithmic Gaussian process (log-GP) to model plasma distribution more naturally, thereby expanding the limitations of standard GPT, which are restricted to linear problems and may yield non-physical negative values. The effectiveness of the proposed log-GP tomography is demonstrated through a case study using the Ring Trap 1 (RT-1) device, where log-GPT outperforms existing methods, standard GPT, and the Minimum Fisher Information (MFI) methods in terms of reconstruction accuracy. The result highlights the effectiveness of nonlinear GPT for imposing physical constraints in applications to an inverse problem.

Recently there has been a proliferation of intrinsic motivation (IM) reward-shaping methods to learn in complex and sparse-reward environments. These methods can often inadvertently change the set of optimal policies in an environment, leading to suboptimal behavior. Previous work on mitigating the risks of reward shaping, particularly through potential-based reward shaping (PBRS), has not been applicable to many IM methods, as they are often complex, trainable functions themselves, and therefore dependent on a wider set of variables than the traditional reward functions that PBRS was developed for. We present an extension to PBRS that we prove preserves the set of optimal policies under a more general set of functions than has been previously proven. We also present {\em Potential-Based Intrinsic Motivation} (PBIM) and {\em Generalized Reward Matching} (GRM), methods for converting IM rewards into a potential-based form that are useable without altering the set of optimal policies. Testing in the MiniGrid DoorKey and Cliff Walking environments, we demonstrate that PBIM and GRM successfully prevent the agent from converging to a suboptimal policy and can speed up training. Additionally, we prove that GRM is sufficiently general as to encompass all potential-based reward shaping functions. This paper expands on previous work introducing the PBIM method, and provides an extension to the more general method of GRM, as well as additional proofs, experimental results, and discussion.

Conditional density estimation (CDE) goes beyond regression by modeling the full conditional distribution, providing a richer understanding of the data than just the conditional mean in regression. This makes CDE particularly useful in critical application domains. However, interpretable CDE methods are understudied. Current methods typically employ kernel-based approaches, using kernel functions directly for kernel density estimation or as basis functions in linear models. In contrast, despite their conceptual simplicity and visualization suitability, tree-based methods -- which are arguably more comprehensible -- have been largely overlooked for CDE tasks. Thus, we propose the Conditional Density Tree (CDTree), a fully non-parametric model consisting of a decision tree in which each leaf is formed by a histogram model. Specifically, we formalize the problem of learning a CDTree using the minimum description length (MDL) principle, which eliminates the need for tuning the hyperparameter for regularization. Next, we propose an iterative algorithm that, although greedily, searches the optimal histogram for every possible node split. Our experiments demonstrate that, in comparison to existing interpretable CDE methods, CDTrees are both more accurate (as measured by the log-loss) and more robust against irrelevant features. Further, our approach leads to smaller tree sizes than existing tree-based models, which benefits interpretability.