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.

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.

Recent work has considered the problem of extending to the case of iterated belief change the so-called `Harper Identity' (HI), which defines single-shot contraction in terms of single-shot revision. The present paper considers the prospects of providing a similar extension of the Levi Identity (LI), in which the direction of definition runs the other way. We restrict our attention here to the three classic iterated revision operators--natural, restrained and lexicographic, for which we provide here the first collective characterisation in the literature, under the appellation of `elementary' operators. We consider two prima facie plausible ways of extending (LI). The first proposal involves the use of the rational closure operator to offer a `reductive' account of iterated revision in terms of iterated contraction. The second, which doesn't commit to reductionism, was put forward some years ago by Nayak et al. We establish that, for elementary revision operators and under mild assumptions regarding contraction, Nayak's proposal is equivalent to a new set of postulates formalising the claim that contraction by $\neg A$ should be considered to be a kind of `mild' revision by $A$. We then show that these, in turn, under slightly weaker assumptions, jointly amount to the conjunction of a pair of constraints on the extension of (HI) that were recently proposed in the literature. Finally, we consider the consequences of endorsing both suggestions and show that this would yield an identification of rational revision with natural revision. We close the paper by discussing the general prospects for defining iterated revision in terms of iterated contraction.

Public debate forums provide a common platform for exchanging opinions on a topic of interest. While recent studies in natural language processing (NLP) have provided empirical evidence that the language of the debaters and their patterns of interaction play a key role in changing the mind of a reader, research in psychology has shown that prior beliefs can affect our interpretation of an argument and could therefore constitute a competing alternative explanation for resistance to changing one's stance. To study the actual effect of language use vs. prior beliefs on persuasion, we provide a new dataset and propose a controlled setting that takes into consideration two reader level factors: political and religious ideology. We find that prior beliefs affected by these reader level factors play a more important role than language use effects and argue that it is important to account for them in NLP studies of persuasion.

When agents interact with a complex environment, they must form and maintain beliefs about the relevant aspects of that environment. We propose a way to efficiently train expressive generative models in complex environments. We show that a predictive algorithm with an expressive generative model can form stable belief-states in visually rich and dynamic 3D environments. More precisely, we show that the learned representation captures the layout of the environment as well as the position and orientation of the agent. Our experiments show that the model substantially improves data-efficiency on a number of reinforcement learning (RL) tasks compared with strong model-free baseline agents. We find that predicting multiple steps into the future (overshooting), in combination with an expressive generative model, is critical for stable representations to emerge. In practice, using expressive generative models in RL is computationally expensive and we propose a scheme to reduce this computational burden, allowing us to build agents that are competitive with model-free baselines.

Probabilistic epistemic argumentation allows for reasoning about argumentation problems in a way that is well founded by probability theory. Epistemic states are represented by probability functions over possible worlds and can be adjusted to new beliefs using update operators. While the use of probability functions puts this approach on a solid foundational basis, it also causes computational challenges as the amount of data to process depends exponentially on the number of arguments. This leads to bottlenecks in applications such as modelling opponent's beliefs for persuasion dialogues. We show how update operators over probability functions can be related to update operators over much more compact representations that allow polynomial-time updates. We discuss the cognitive and probabilistic-logical plausibility of this approach and demonstrate its applicability in computational persuasion.

The analysis of Belief Propagation and other algorithms for the {\em reconstruction problem} plays a key role in the analysis of community detection in inference on graphs, phylogenetic reconstruction in bioinformatics, and the cavity method in statistical physics. We prove a conjecture of Evans, Kenyon, Peres, and Schulman (2000) which states that any bounded memory message passing algorithm is statistically much weaker than Belief Propagation for the reconstruction problem. More formally, any recursive algorithm with bounded memory for the reconstruction problem on the trees with the binary symmetric channel has a phase transition strictly below the Belief Propagation threshold, also known as the Kesten-Stigum bound. The proof combines in novel fashion tools from recursive reconstruction, information theory, and optimal transport, and also establishes an asymptotic normality result for BP and other message-passing algorithms near the critical threshold.

Belief propagation is a fundamental message-passing algorithm for probabilistic reasoning and inference in graphical models. While it is known to be exact on trees, in most applications belief propagation is run on graphs with cycles. Understanding the behavior of "loopy" belief propagation has been a major challenge for researchers in machine learning, and positive convergence results for BP are known under strong assumptions which imply the underlying graphical model exhibits decay of correlations. We show that under a natural initialization, BP converges quickly to the global optimum of the Bethe free energy for Ising models on arbitrary graphs, as long as the Ising model is \emph{ferromagnetic} (i.e. neighbors prefer to be aligned). This holds even though such models can exhibit long range correlations and may have multiple suboptimal BP fixed points. We also show an analogous result for iterating the (naive) mean-field equations; perhaps surprisingly, both results are dimension-free in the sense that a constant number of iterations already provides a good estimate to the Bethe/mean-field free energy.

While research on iterated revision is predominant in the field of iterated belief change, the class of iterated contraction operators received more attention in recent years. In this article, we examine a non-prioritized generalisation of iterated contraction. In particular, the class of weak decrement operators is introduced, which are operators that by multiple steps achieve the same as a contraction. Inspired by Darwiche and Pearl's work on iterated revision the subclass of decrement operators is defined. For both, decrement and weak decrement operators, postulates are presented and for each of them a representation theorem in the framework of total preorders is given. Furthermore, we present two types of decrement operators which have a unique representative.