--Belief Propagation (BP) is a message-passing algorithm for approximate inference over Probabilistic Graphical Models (PGMs), finding many applications such as computer vision, error-correcting codes, and protein-folding. While general, the convergence and speed of the algorithm has limited its practical use on difficult inference problems. As an algorithm that is highly amenable to parallelization, many-core Graphical Processing Units (GPUs) could significantly improve BP performance. Improving BP through many-core systems is nontrivial: the scheduling of messages in the algorithm strongly affects performance. We present a study of message scheduling for BP on GPUs. We demonstrate that BP exhibits a tradeoff between speed and convergence based on parallelism and show that existing message schedulings are not able to utilize this tradeoff. T o this end, we present a novel randomized message scheduling approach, Randomized BP (RnBP), which outperforms existing methods on the GPU. I NTRODUCTION Probabilistic Graphical Models (PGMs) are powerful, general machine learning models that encode distributions over random variables. PGM Inference, in which we seek to compute some probabilistic beliefs within the system modeled by the PGM, is in general an intractable problem, leading to dependence on approximate algorithms. Belief Propagation (BP) is a widely employed approximate inference algorithms for PGMs [1].

To coordinate with other systems, agents must be able to determine what the systems are currently doing and predict what they will be doing in the future---plan and goal recognition. There are many methods for plan and goal recognition, but they assume a passive observer that continually monitors the target system. Real-world domains, where information gathering has a cost (e.g., moving a camera or a robot, or time taken away from another task), will often require a more active observer. We propose to combine goal recognition with other observer tasks in order to obtain \emph{active goal recognition} (AGR). We discuss this problem and provide a model and preliminary experimental results for one form of this composite problem. As expected, the results show that optimal behavior in AGR problems balance information gathering with other actions (e.g., task completion) such as to achieve all tasks jointly and efficiently. We hope that our formulation opens the door for extensive further research on this interesting and realistic problem.

Memory in an agent system is a process of reasoning: it is the l earning process of strengthening a concept. The interaction between an agent and the environment can pla y an important role in constructing its memory and may affect its future behaviour. In fact, through memory an agent is potentially able to recall and to learn from experiences so that its beliefs and i ts future course of action are grounded in these experiences. In computational logic, [2] introduces DLEK (Dynamic Logic of Explicit beliefs and Knowledge) as a logical formalization of the short-term and long-term memory. The underlying idea is to represent reasoning about the formation of beliefs throu gh perception and inference in non-omniscient resource-bounded agents. DLEK has however no notion of time, while agents' actual perceptions are inherently timed and so are many of the inferences drawn from such perceptions. In this paper we present an extension of LEK/DLEK to T-LEK/T-DLEK ("Timed LE K" and "Timed DLEK") obtained by introducing a special function which associates to each b elief the arrival time and controls timed inferences. Through this function it is easier to keep the ev olution of the surrounding world under control and the representation is more complete. This abstr act is an evolution version of [3], where we have introduced explicit time instants and time intervals i n formulas, and it is extracted from [4].

In the literature there different kind of timed logical fram eworks exist, where time is specified directly using hybrid logics (cf., e.g., [2]), temporal epistemic lo gic (cf., e.g., [4]) or simply by using Linear Temporal Logic. We propose a temporal module which can be ado pted to "temporalize" many logical framework. This module is in practice a particular kind of fu nction that assigns a "timing" to atoms. We have exploited this T function in two different settings. The first one is the formalization of the reasoning on the formation of beliefs and the interaction wi th background knowledge in non-omniscient agents' memory.

Belief propagation (BP) can do exact inference in loop-free graphs, but its performance could be poor in graphs with loops, and the understanding of its solution is limited. This work gives an interpretable belief propagation rule that is actually minimization of a localized $\alpha$-divergence. We term this algorithm as $\alpha$ belief propagation ($\alpha$-BP). The performance of $\alpha$-BP is tested in MAP (maximum a posterior) inference problems, where $\alpha$-BP can outperform (loopy) BP by a significant margin even in fully-connected graphs.

Brandenburger, Friedenberg, and Keisler provide an epistemic characterization of iterated admissibility (IA), also known as iterated deletion of weakly dominated strategies, where uncertainty is represented using LPSs (lexicographic probability sequences). Their characterization holds in a rich structure called a complete structure, where all types are possible. In earlier work, we gave a characterization of iterated admissibility using an "all I know" operator, that captures the intuition that "all the agent knows" is that agents satisfy the appropriate rationality assumptions. That characterization did not need complete structures and used probability structures, not LPSs. However, that characterization did not deal with Samuelson's conceptual concern regarding IA, namely, that at higher levels, players do not consider possible strategies that were used to justify their choice of strategy at lower levels. In this paper, we give a characterization of IA using the all I know operator that does deal with Samuelson's concern. However, it uses LPSs. We then show how to modify the characterization using notions of "approximate belief" and "approximately all I know" so as to deal with Samuelson's concern while still working with probability structures.

We propose a new model for forming beliefs and learning about unknown probabilities (such as the probability of picking a red marble from a bag with an unknown distribution of coloured marbles). The most widespread model for such situations of 'radical uncertainty' is in terms of imprecise probabilities, i.e. representing the agent's knowledge as a set of probability measures. We add to this model a plausibility map, associating to each measure a plausibility number, as a way to go beyond what is known with certainty and represent the agent's beliefs about probability. There are a number of standard examples: Shannon Entropy, Centre of Mass etc. We then consider learning of two types of information: (1) learning by repeated sampling from the unknown distribution (e.g. picking marbles from the bag); and (2) learning higher-order information about the distribution (in the shape of linear inequalities, e.g. we are told there are more red marbles than green marbles). The first changes only the plausibility map (via a 'plausibilistic' version of Bayes' Rule), but leaves the given set of measures unchanged; the second shrinks the set of measures, without changing their plausibility. Beliefs are defined as in Belief Revision Theory, in terms of truth in the most plausible worlds. But our belief change does not comply with standard AGM axioms, since the revision induced by (1) is of a non-AGM type. This is essential, as it allows our agents to learn the true probability: we prove that the beliefs obtained by repeated sampling converge almost surely to the correct belief (in the true probability). We end by sketching the contours of a dynamic doxastic logic for statistical learning.

We introduce a semantics for epistemic logic exploiting a belief base abstraction. Differently from existing Kripke-style semantics for epistemic logic in which the notions of possible world and epistemic alternative are primitive, in the proposed semantics they are non-primitive but are defined from the concept of belief base. We show that this semantics allows us to define the universal epistemic model in a simpler and more compact way than existing inductive constructions of it. We provide (i) a number of semantic equivalence results for both the basic epistemic language with "individual belief" operators and its extension by the notion of "only believing", and (ii) a lower bound complexity result for epistemic logic model checking relative to the universal epistemic model.

Many multiagent applications require an agent to learn quickly how to interact with previously unknown other agents. To address this problem, researchers have studied learning algorithms which compute posterior beliefs over a hypothesised set of policies, based on the observed actions of the other agents. The posterior belief is complemented by the prior belief, which specifies the subjective likelihood of policies before any actions are observed. In this paper, we present the first comprehensive empirical study on the practical impact of prior beliefs over policies in repeated interactions. We show that prior beliefs can have a significant impact on the long-term performance of such methods, and that the magnitude of the impact depends on the depth of the planning horizon. Moreover, our results demonstrate that automatic methods can be used to compute prior beliefs with consistent performance effects. This indicates that prior beliefs could be eliminated as a manual parameter and instead be computed automatically.

Goal recognition design (GRD) facilitates understanding the goals of acting agents through the analysis and redesign of goal recognition models, thus offering a solution for assessing and minimizing the maximal progress of any agent in the model before goal recognition is guaranteed. In a nutshell, given a model of a domain and a set of possible goals, a solution to a GRD problem determines (1) the extent to which actions performed by an agent within the model reveal the agent’s objective; and (2) how best to modify the model so that the objective of an agent can be detected as early as possible. This approach is relevant to any domain in which rapid goal recognition is essential and the model design can be controlled. Applications include intrusion detection, assisted cognition, computer games, and human-robot collaboration. A GRD problem has two components: the analyzed goal recognition setting, and a design model specifying the possible ways the environment in which agents act can be modified so as to facilitate recognition. This work formulates a general framework for GRD in deterministic and partially observable environments, and offers a toolbox of solutions for evaluating and optimizing model quality for various settings. For the purpose of evaluation we suggest the worst case distinctiveness (WCD) measure, which represents the maximal cost of a path an agent may follow before its goal can be inferred by a goal recognition system. We offer novel compilations to classical planning for calculating WCD in settings where agents are bounded-suboptimal. We then suggest methods for minimizing WCD by searching for an optimal redesign strategy within the space of possible modifications, and using pruning to increase efficiency. We support our approach with an empirical evaluation that measures WCD in a variety of GRD settings and tests the efficiency of our compilation-based methods for computing it. We also examine the effectiveness of reducing WCD via redesign and the performance gain brought about by our proposed pruning strategy.