The primary objective of this paper is to investigate distributed ordinary differential equation (ODE) and distributed temporal difference (TD) learning algorithms for networked multi-agent Markov decision problems (MAMDPs). In our study, we adopt a distributed multi-agent framework where individual agents have access only to their own rewards, lacking insights into the rewards of other agents. Additionally, each agent has the ability to share its parameters with neighboring agents through a communication network, represented by a graph. Our contributions can be summarized in two key points: 1) We introduce novel distributed ODEs, inspired by the averaging consensus method in the continuous-time domain. The convergence of the ODEs is assessed through control theory perspectives. 2) Building upon the aforementioned ODEs, we devise new distributed TD-learning algorithms. A standout feature of one of our proposed distributed ODEs is its incorporation of two independent dynamic systems, each with a distinct role. This characteristic sets the stage for a novel distributed TD-learning strategy, the convergence of which can potentially be established using Borkar-Meyn theorem.

Discrete latent space models have recently achieved performance on par with their continuous counterparts in deep variational inference. While they still face various implementation challenges, these models offer the opportunity for a better interpretation of latent spaces, as well as a more direct representation of naturally discrete phenomena. Most recent approaches propose to train separately very high-dimensional prior models on the discrete latent data which is a challenging task on its own. In this paper, we introduce a latent data model where the discrete state is a Markov chain, which allows fast end-to-end training. The performance of our generative model is assessed on a building management dataset and on the publicly available Electricity Transformer Dataset.

We study provable multi-agent reinforcement learning (MARL) in the general framework of partially observable stochastic games (POSGs). To circumvent the known hardness results and the use of computationally intractable oracles, we advocate leveraging the potential \emph{information-sharing} among agents, a common practice in empirical MARL, and a standard model for multi-agent control systems with communications. We first establish several computation complexity results to justify the necessity of information-sharing, as well as the observability assumption that has enabled quasi-efficient single-agent RL with partial observations, for computational efficiency in solving POSGs. We then propose to further \emph{approximate} the shared common information to construct an {approximate model} of the POSG, in which planning an approximate equilibrium (in terms of solving the original POSG) can be quasi-efficient, i.e., of quasi-polynomial-time, under the aforementioned assumptions. Furthermore, we develop a partially observable MARL algorithm that is both statistically and computationally quasi-efficient. We hope our study may open up the possibilities of leveraging and even designing different \emph{information structures}, for developing both sample- and computation-efficient partially observable MARL.

Living organisms need to acquire both cognitive maps for learning the structure of the world and planning mechanisms able to deal with the challenges of navigating ambiguous environments. Although significant progress has been made in each of these areas independently, the best way to integrate them is an open research question. In this paper, we propose the integration of a statistical model of cognitive map formation within an active inference agent that supports planning under uncertainty. Specifically, we examine the clone-structured cognitive graph (CSCG) model of cognitive map formation and compare a naive clone graph agent with an active inference-driven clone graph agent, in three spatial navigation scenarios. Our findings demonstrate that while both agents are effective in simple scenarios, the active inference agent is more effective when planning in challenging scenarios, in which sensory observations provide ambiguous information about location.

The generation of comprehensible explanations is an essential feature of modern artificial intelligence systems. In this work, we consider probabilistic logic programming, an extension of logic programming which can be useful to model domains with relational structure and uncertainty. Essentially, a program specifies a probability distribution over possible worlds (i.e., sets of facts). The notion of explanation is typically associated with that of a world, so that one often looks for the most probable world as well as for the worlds where the query is true. Unfortunately, such explanations exhibit no causal structure. In particular, the chain of inferences required for a specific prediction (represented by a query) is not shown. In this paper, we propose a novel approach where explanations are represented as programs that are generated from a given query by a number of unfolding-like transformations. Here, the chain of inferences that proves a given query is made explicit. Furthermore, the generated explanations are minimal (i.e., contain no irrelevant information) and can be parameterized w.r.t. a specification of visible predicates, so that the user may hide uninteresting details from explanations.

Neural compression is the application of neural networks and other machine learning methods to data compression. Recent advances in statistical machine learning have opened up new possibilities for data compression, allowing compression algorithms to be learned end-to-end from data using powerful generative models such as normalizing flows, variational autoencoders, diffusion probabilistic models, and generative adversarial networks. The present article aims to introduce this field of research to a broader machine learning audience by reviewing the necessary background in information theory (e.g., entropy coding, rate-distortion theory) and computer vision (e.g., image quality assessment, perceptual metrics), and providing a curated guide through the essential ideas and methods in the literature thus far.

In this work we consider the unbiased estimation of expectations w.r.t.~probability measures that have non-negative Lebesgue density, and which are known point-wise up-to a normalizing constant. We focus upon developing an unbiased method via the underdamped Langevin dynamics, which has proven to be popular of late due to applications in statistics and machine learning. Specifically in continuous-time, the dynamics can be constructed {so that as the time goes to infinity they} admit the probability of interest as a stationary measure. {In many cases, time-discretized versions of the underdamped Langevin dynamics are used in practice which are run only with a fixed number of iterations.} We develop a novel scheme based upon doubly randomized estimation as in \cite{ub_grad,disc_model}, which requires access only to time-discretized versions of the dynamics. {The proposed scheme aims to remove the dicretization bias and the bias resulting from running the dynamics for a finite number of iterations}. We prove, under standard assumptions, that our estimator is of finite variance and either has finite expected cost, or has finite cost with a high probability. To illustrate our theoretical findings we provide numerical experiments which verify our theory, which include challenging examples from Bayesian statistics and statistical physics.

Active Inference is a recent framework for modeling planning under uncertainty. Empirical and theoretical work have now begun to evaluate the strengths and weaknesses of this approach and how it might be improved. A recent extension - the sophisticated inference (SI) algorithm - improves performance on multi-step planning problems through recursive decision tree search. However, little work to date has been done to compare SI to other established planning algorithms. SI was also developed with a focus on inference as opposed to learning. The present paper has two aims. First, we compare performance of SI to Bayesian reinforcement learning (RL) schemes designed to solve similar problems. Second, we present an extension of SI - sophisticated learning (SL) - that more fully incorporates active learning during planning. SL maintains beliefs about how model parameters would change under the future observations expected under each policy. This allows a form of counterfactual retrospective inference in which the agent considers what could be learned from current or past observations given different future observations. To accomplish these aims, we make use of a novel, biologically inspired environment designed to highlight the problem structure for which SL offers a unique solution. Here, an agent must continually search for available (but changing) resources in the presence of competing affordances for information gain. Our simulations show that SL outperforms all other algorithms in this context - most notably, Bayes-adaptive RL and upper confidence bound algorithms, which aim to solve multi-step planning problems using similar principles (i.e., directed exploration and counterfactual reasoning). These results provide added support for the utility of Active Inference in solving this class of biologically-relevant problems and offer added tools for testing hypotheses about human cognition.

Denoising diffusion probabilistic models and score-matching models have proven to be very powerful for generative tasks. While these approaches have also been applied to the generation of discrete graphs, they have, so far, relied on continuous Gaussian perturbations. Instead, in this work, we suggest using discrete noise for the forward Markov process. This ensures that in every intermediate step the graph remains discrete. Compared to the previous approach, our experimental results on four datasets and multiple architectures show that using a discrete noising process results in higher quality generated samples indicated with an average MMDs reduced by a factor of 1.5. Furthermore, the number of denoising steps is reduced from 1000 to 32 steps, leading to a 30 times faster sampling procedure.

We study how to efficiently combine formal methods, Monte Carlo Tree Search (MCTS), and deep learning in order to produce high-quality receding horizon policies in large Markov Decision processes (MDPs). In particular, we use model-checking techniques to guide the MCTS algorithm in order to generate offline samples of high-quality decisions on a representative set of states of the MDP. Those samples can then be used to train a neural network that imitates the policy used to generate them. This neural network can either be used as a guide on a lower-latency MCTS online search, or alternatively be used as a full-fledged policy when minimal latency is required. We use statistical model checking to detect when additional samples are needed and to focus those additional samples on configurations where the learnt neural network policy differs from the (computationally-expensive) offline policy. We illustrate the use of our method on MDPs that model the Frozen Lake and Pac-Man environments -- two popular benchmarks to evaluate reinforcement-learning algorithms.